Charlotte Angas Scott (1858–1931) was a pioneering British mathematician whose eighth-place finish on the Cambridge Mathematical Tripos in 1880 – and the students’ defiant cry of “Scott of Girton!” that followed – helped force open the doors of mathematical education for women. As the founding head of mathematics at Bryn Mawr College, she built one of the world’s only serious research environments for women mathematicians, supervised three of the nine women who earned mathematics doctorates in the nineteenth century, and authored a revolutionary textbook that helped shift Anglo-American mathematical pedagogy from rote calculation toward rigorous proof.
Professor Scott, it is an extraordinary privilege to welcome you here today, some ninety-four years after your passing. You sit before us in this peculiar arrangement – you, a woman who battled Cambridge’s rules, London’s external examinations, and an ocean crossing to Pennsylvania, now addressing a world where women earn more than forty per cent of mathematics doctorates in the United States. I wonder: does this figure surprise you, or did you always believe it inevitable?
Inevitable? Nothing about the progress of women in intellectual life has been inevitable. Every inch was contested, and I suspect every inch will continue to be. When I began at Girton in 1876, we were eleven young women in that intake – the largest the College had seen – and we considered ourselves fortunate to be permitted to sit behind screens in Cambridge lecture halls, provided the lecturers consented. Forty per cent is gratifying, but I should like to know what proportion hold chairs, direct departments, serve as presidents of mathematical societies. The numbers at the door and the numbers in the room of decision are seldom the same.
You were raised in Lincoln, England, the second of seven children. Your father, the Reverend Caleb Scott, was both a Congregationalist minister and Principal of Lancashire Independent College. How did a minister’s household produce a mathematician?
You must understand what the Congregational Church represented in those years. We were Nonconformists – outside the Church of England, outside its universities, outside its assumptions about what was proper for women. The Congregationalists actively campaigned for women’s rights when few others did so. My father could have tutored only his sons. Instead, from the age of seven, I was given tutors in mathematics alongside my brothers. There were only two secondary schools in all of England that accepted girls at the time, and neither was anywhere near Manchester, so Father arranged instruction at Lancashire College itself. The breakfast table was a place of argument and ideas, not silence. That was the soil.
And from that soil, you arrived at Hitchin College – soon renamed Girton – in 1876. What were those early days like?
Spartan. We would retire to our rooms after an extremely simple tea in the Common Room, picking up en route three items: two candles, a bucket of coal, and a chamber pot. That was the full extent of our amenities. But we were hungry for learning, and hunger sharpens the mind wonderfully. The real difficulty was not physical discomfort; it was uncertainty. Would the University acknowledge us at all? Would lecturers permit us to attend? Every term was a negotiation.
And then came January 1880 – the Mathematical Tripos. You obtained special permission to sit for an examination from which women were formally excluded. Can you walk us through those nine days?
Nine days, fifty hours of examination, spread across algebra, geometry, analytical geometry, probability theory, calculus, and elements of physics – statics, dynamics, hydrostatics, optics, and the astronomy of the solar system. The papers were identical to the men’s. The conditions were identical. The proctors watched me precisely as they watched everyone else. What was not identical was the outcome: I could not be named in the official order of merit, I could not receive the title of “Wrangler,” and I could not attend the ceremony in the Senate House.
Yet something remarkable happened at that ceremony.
So I have been told many times since. The reader was proceeding through the list – first wrangler, second wrangler, and so on – and when he reached the eighth position, before he could announce the man’s name, the entire undergraduate audience began shouting “Scott of Girton!” They cheered tremendously, shouting my name over and over, waving their hats. I was not there to witness it, of course. I was at Girton, where we had our own celebration – clapping and cheering at dinner, and then someone played “See the Conquering Hero Comes” on the piano while Miss Herschel crowned me with laurels.
The radical weekly Punch congratulated you. A petition with over 8,000 signatures circulated within three months. What actually changed?
The following year, women were officially permitted to sit the Tripos without special application. That was progress. But our results were still listed separately from the men’s – a kind of intellectual apartheid that persisted until 1948, nearly seventy years later. And degrees? Cambridge did not award degrees to women until 1948. I had been dead seventeen years by then.
Which is why you turned to the University of London.
London offered external examinations open to women. I earned my B.Sc. with First Class honours in mathematics in 1882, and my D.Sc. in 1885 – the first British woman to receive a doctorate in mathematics. The irony is considerable: I conducted my research at Cambridge, under Arthur Cayley’s supervision, but Cambridge would not put its name on my degree. London would, and so London did.
You mentioned Arthur Cayley. He was one of the great figures of nineteenth-century mathematics – a founder of invariant theory, a prolific author of nearly a thousand papers. What was it like to study under him?
Cayley was not a popular lecturer among students preparing for the Tripos, because he lectured on whatever he himself was working on at the moment – and that had little to do with examinations. But for me, this was precisely the point. I attended his lectures from 1880 to 1884, and his subjects in those years included modern algebra, Abelian functions, the theory of numbers, the theory of substitutions, and the theory of semi-invariants. He was offering a window into the living edge of mathematics, not a catalogue of settled results.
And your own research focused on algebraic curves. For readers who may know the term only vaguely – what are algebraic curves, and why did they matter?
An algebraic curve is the set of points in the plane satisfying a polynomial equation in two variables – say, f(x,y) = 0. A line is degree one, a conic section is degree two. Beyond degree two, the behaviour becomes far more intricate. My work concerned curves of degree three, four, five, and higher – their singularities, their intersections, their transformations.
Singularities?
Points where the curve fails to be smooth – where it has a cusp, a node, a point of self-intersection, or some more complicated pathology. Understanding these singularities is essential because they govern much of the curve’s global geometry. How many singular points can a curve of degree d have? What types are possible? How does one “resolve” a singularity to understand the underlying smooth structure? These were the questions that occupied me.
Could you walk a mathematician through one of your key contributions – say, your 1892 paper “On the Higher Singularities of Plane Curves”?
Very well. The classical analysis of singular points – nodes, cusps, and so forth – was developed by Plücker, and later refined by Cayley, Salmon, and others. But these treatments assumed what we might call “ordinary” singularities: a node is two smooth branches crossing transversely; a cusp is a single branch with a specific type of tangency to itself. In practice, curves of higher degree can exhibit singularities that are not merely nodes or cusps but combinations of these, superimposed or infinitely near to one another.
My approach was to develop a method of analysis – decomposing a higher singularity into an equivalent collection of ordinary singularities, so that one could apply the classical formulae correctly. The difficulty is that the naive count of intersections at such points, using Bézout’s theorem, gives the wrong answer unless one accounts for the multiplicity structure.
For example, a curve of degree d meets a general line in d points. If two curves of degrees m and n intersect, Bézout tells us there are mn intersection points, counted with multiplicity. But when the curves share a common singular point, the local intersection multiplicity at that point can be far larger than expected, and understanding precisely how much larger requires a careful analysis of the singularity’s structure.
And what were the measurable outcomes of this work?
The immediate outcome was a systematic classification that other researchers could apply. The longer-term outcome was a contribution to the developing theory of what we now call the “resolution of singularities” – the process of blowing up a singular point to reveal simpler components. My methods were geometric rather than purely algebraic; I preferred to work with diagrams, with projections, with the intuition of moving points and lines, rather than pages of formal manipulation.
Your 1899 paper “A Proof of Noether’s Fundamental Theorem” in Mathematische Annalen is often cited as the first mathematical research paper from the United States to gain broad recognition in Europe. What is Noether’s theorem, and what did your proof contribute?
Max Noether – Emmy’s father – stated the theorem in 1869. In essence, it concerns when a polynomial W(x,y) can be expressed as a combination of two given polynomials U(x,y) and V(x,y). More precisely: if the curves U=0 and V=0 intersect in a finite number of points, and the curve W=0 passes through all of these intersection points, then under what conditions can we write W=A⋅U+B⋅V for some polynomials A and B?
The theorem says that this is possible provided W belongs to the ideal generated by U and V locally at each intersection point. Noether’s original proof was algebraic and, to be frank, not entirely satisfactory in its details. My contribution was to provide a geometric proof – one that made the theorem visible, comprehensible, and rigorous using the methods of analytical geometry.
Why did this matter beyond the technical achievement?
Because the theorem is fundamental to the study of algebraic curves – it governs how one curve can “pass through” the intersections of two others, and it underlies much of the classical theory of linear systems. Also, I should note, it demonstrated that serious mathematical work was being done in America. European mathematicians paid attention. That was not nothing.
In 1885, you sailed to Pennsylvania to join the founding faculty of Bryn Mawr College. You were twenty-seven years old, the only mathematician among eight initial faculty members. What drew you across the Atlantic?
Cayley’s recommendation, primarily. He knew Joseph Taylor, the Quaker philanthropist who founded Bryn Mawr, and when the College sought someone to establish its mathematics programme, Cayley suggested me. I was offered an associate professorship at two thousand dollars per year – a considerable sum. But the real attraction was the mission: here was a college that would offer graduate training to women, that would not condescend to lower standards, that would treat intellectual work as a serious vocation.
You supervised seven doctoral students across forty years – Ruth Gentry, Ada Isabel Maddison, Virginia Ragsdale, Louise Cummings, Mary Gertrude Haseman, Bird Margaret Turner, and Marguerite Lehr. Three of them were among the only nine women to earn mathematics doctorates in the nineteenth century. How did you approach mentorship?
I treated them as mathematicians, not as women attempting to be mathematicians. The distinction matters. I had no patience for laziness – none whatsoever – but I went to extraordinary lengths for students who worked hard and faced genuine obstacles. There is a letter in the Bryn Mawr archives, seven pages long, that I wrote on behalf of a student who had been dismissed due to a crippling illness. I argued that it was nothing short of cruel to deprive a girl of intellectual work when she was already limited in other activities. Standards and compassion are not opposites.
You also established the Bryn Mawr College Mathematics Journal Club.
Yes – a meeting place for doctoral students, recent graduates, and faculty to lecture on their research or on important papers they had read. Mathematics is not learned in isolation. One must speak it aloud, defend it, hear objections, reformulate. The Journal Club provided that.
There is a famous letter you wrote to M. Carey Thomas, the dean and later president of Bryn Mawr, when she suggested lowering academic standards for women. What did you say?
I told her that I rejected entirely the idea of a “watered down” curriculum, and I criticised what I called the “inward reserve of condescension” that pervaded so much of the supposed support for women’s education. Men who praised women’s intellect while quietly assuming we could not meet the same standards as their own students – that condescension was more corrosive than open hostility. At least hostility is honest.
Let us turn to the woman behind the mathematics. You never married. You were known for personal conservatism – neat dress, no public smoking, cautious public behaviour. Some later feminists have found this disappointing.
Have they lived under the Spinning House?
The Spinning House?
A prison in Cambridge for women suspected of prostitution. An unaccompanied woman found on university grounds could be arrested on suspicion of having a “corrupting influence on male students” and carted off to the Spinning House. This was not a distant historical curiosity when I was at Girton; it was a live threat. Respectability was not prudishness. It was survival.
That context is rarely discussed.
It should be. The choices women made about dress, comportment, and public behaviour were strategic. We had to be beyond reproach because any hint of impropriety would be used to exclude us entirely. Later generations, enjoying freedoms we helped secure, may find our caution quaint. They did not face what we faced.
You also played lawn tennis – introducing the game for women at Girton – and took up golf at Bryn Mawr. And after retirement, you grew chrysanthemums?
I won an award for a new variety I developed. Gardening is not unlike mathematics, you know: patience, attention to structure, the pleasure of seeing something come to fruition over years. And there is rather less committee work.
In April 1922, nearly two hundred guests – scholars from McGill, Yale, Johns Hopkins, the University of Chicago, Imperial College – gathered at Bryn Mawr to honour your thirty-seven years as head of mathematics. Alfred North Whitehead came from England to deliver the main lecture.
Whitehead was very kind. He said that “a friendship of peoples is the outcome of personal relations,” and that “a life’s work such as that of Professor Charlotte Angas Scott is worth more to the world than many anxious efforts of diplomatists”. I am not certain I deserved such praise, but I was grateful for it.
You have spoken with justifiable pride about your achievements. But in the spirit of candour – were there mistakes? Failed experiments? Professional misjudgements you can now acknowledge?
I was too slow to embrace the new algebraic methods coming from Germany – the abstract algebra of Emmy Noether and her school. By the time I retired, the centre of gravity in algebraic geometry had shifted from the geometric intuition I championed to a more purely algebraic framework. I do not say the new methods were wrong; they were powerful. But I was formed by Cayley’s geometry, and I resisted longer than I should have. One becomes attached to one’s tools.
I also regret that I did not do more to build networks among women mathematicians across institutions. I trained seven doctoral students, but I did not systematically connect them to one another after they left Bryn Mawr. Each went off to her own college – Vassar, Mount Holyoke, Wells – and I lost touch. The work of institution-building is never finished, and I did not finish mine.
And your health? Rheumatoid arthritis and deafness curtailed your later career.
The arthritis began around 1904, severely. The deafness had been present since my Girton days but worsened steadily; by my final years of teaching, I was almost entirely deaf and had to have a graduate student in the room to answer questions I could not hear. It was frustrating beyond words. Mathematics is a conversation, and I could no longer hear my interlocutors.
Today, there is a USC women’s mathematics group named “Charlotte’s Web” in your honour. Cambridge, in 2016, named a street after you in its North West Cambridge Development. Your textbook remained in print for decades. And yet, among working mathematicians, your name is not widely known. Why do you think that is?
I have no headliner theorem. No “Scott’s Lemma” that every graduate student learns in their first year. My most lasting contributions were institutional – building a department, supervising students, shaping curricula, writing a textbook, serving on councils. Histories of mathematics privilege dramatic breakthroughs over slow, careful construction. They privilege men’s universities over women’s colleges. And they privilege research over teaching, though teaching is how mathematics perpetuates itself.
Your 1894 textbook, An Introductory Account of Certain Modern Ideas and Methods in Plane Analytical Geometry, was revolutionary for its insistence on distinguishing general principles from particular examples. That sounds obvious now.
It was not obvious then. English-language textbooks of the period were notorious for confusing proof with example. A student would see a worked problem and believe they understood the theorem, when in fact they understood only that one case. I wanted to be “consciously modern” – to teach abstraction as abstraction, to demand rigour, to prepare students for research rather than for regurgitation. That approach is now standard. I like to think I had some small part in making it so.
What advice would you offer to young mathematicians today – particularly women, or others who face barriers?
First: master your subject. There is no substitute. Political arguments for inclusion are strengthened, not weakened, by indisputable competence. When the men in the Senate House shouted “Scott of Girton,” they shouted it because I had earned the eighth-best marks in Cambridge. No petition could have given me that.
Second: build institutions. A single brilliant woman is an exception; a department that produces brilliant women year after year is a fact of nature. I spent forty years at Bryn Mawr not because I lacked ambition for my own research, but because I understood that my students, collectively, would accomplish more than I could alone.
Third: do not water anything down. The moment you accept lower standards – for yourself, for your students, for your field – you have conceded that you do not belong at the highest level. You do belong. Act accordingly.
And to the historical record? To those who have overlooked your contributions?
The record is always being revised. I am not troubled. I did my work, I trained my students, I fought my battles. Whether posterity chooses to remember is posterity’s concern, not mine.
Professor Scott, it has been an honour.
The honour has been mutual. Now – if you will excuse me – I believe I have some chrysanthemums to attend to.
Letters and emails
Since the publication of this interview, we’ve received letters and emails from mathematicians, historians, educators, and science enthusiasts across the globe – from Lagos to Oslo, from São Paulo to Mexico City. What emerges is a portrait of a figure whose work continues to resonate across disciplines and borders, raising questions that reach far beyond nineteenth-century Cambridge or early twentieth-century Pennsylvania.
The five correspondents below represent our growing community of readers who have found in Charlotte Angas Scott’s life something urgent and unresolved. They ask about the technical choices she made as a geometer, the institutional labour she undertook, the roads not taken, and the wisdom she might offer to those inheriting the field she helped shape. Their questions probe not just what she accomplished, but why it mattered then – and why it matters now.
What follows are their inquiries, posed directly to Professor Scott, and reflecting the concerns of contemporary mathematics, science policy, gender equity in academia, and the long arc of how ideas travel across time and continents.
Zara Khan, 34, Mathematics Education Researcher, Lahore, Pakistan
Professor Scott, you mentioned that your geometric approach to singularities differed from the purely algebraic methods emerging from Germany. Today, we teach undergraduate algebraic geometry using coordinate-free definitions and category theory – tools that didn’t exist in your era. If you had access to modern computational algebra software that could calculate intersection multiplicities and resolve singularities algorithmically in seconds, would you still insist students first learn the geometric intuition by hand? Or do you believe there’s a risk that computational power actually obscures the underlying structure you spent decades making visible?
Miss Khan, you pose precisely the question I should expect from someone who thinks seriously about how mathematics is transmitted from one generation to the next. It is not a question about machines; it is a question about minds.
Let me be perfectly direct: yes, I should absolutely insist that students learn geometric intuition before they are permitted to touch any computational device. And I say this not from some sentimental attachment to the old ways, nor from ignorance of what your modern instruments might accomplish. I say it because I have spent forty years watching students, and I know what happens when one mistakes facility for understanding.
You must appreciate what it means to see a singularity. When I examined a curve of degree four with a tacnode – that is, two branches tangent to one another at a point, touching but not crossing – I did not merely calculate. I drew. I considered what happened as one moved along each branch, how the tangent line behaved, what the curve looked like under projection from various points. This is not mere illustration; it is the substance of geometric reasoning. The algebraic formulae – the local expansions, the intersection multiplicities – these are records of geometric facts, not substitutes for them.
Now, you tell me that a machine can compute intersection multiplicities in seconds. Very well. But can the student who receives that answer explain why a node contributes two to the intersection count while a cusp contributes three? Can she explain what it means geometrically for two curves to have “higher contact” at a point? If the machine simply returns a number, and the student accepts that number as the terminus of inquiry, then the machine has not assisted understanding – it has replaced it with something far cheaper.
I wrote my textbook in 1894 with a very specific intention: to separate general principles from particular examples. The difficulty with older English texts – even excellent ones, such as Salmon’s Conic Sections – was that students learned to imitate worked problems without grasping the theorems those problems were meant to illustrate. They could reproduce calculations but could not reason. I suspect your computational tools present a similar danger, only magnified a hundredfold. If a student can obtain any answer by pressing keys, what compels her to ask what the answer means?
I am not opposed to labour-saving devices in their proper place. When I was editing the American Journal of Mathematics, I was grateful for any assistance in the tedious verification of references and formulae. Cayley himself computed indefatigably – invariants, covariants, tables upon tables of results – and one can hardly accuse Cayley of lacking insight. But Cayley computed in service of geometric questions he had already formulated. The calculation clarified; it did not originate.
What I fear in your modern arrangement is this: that computation becomes the starting point rather than the culmination. A student asks the machine, “What is the genus of this curve?” and receives an answer. But genus is not a number floating in the aether; it is a count of something – of the holes in a surface, if one thinks topologically, or of the dimension of a certain space of differentials, if one thinks algebraically. Without understanding what is being counted, the number is meaningless. Worse, it creates an illusion of knowledge where none exists.
You ask whether computational power might obscure the underlying structure I spent decades making visible. I think the risk is considerable. The structure I cared about was not merely a collection of facts but a way of seeing – a habit of mind that asks, at every stage, “What does this mean geometrically?” If students are trained to seek numerical outputs rather than geometric insight, they will lose that habit. And once lost, it is exceedingly difficult to recover.
That said, I am not so foolish as to imagine one can hold back the tide. Your tools exist; students will use them; the question is how to use them wisely. My recommendation would be this: let the machine confirm what the student has already reasoned through by hand. Let the student first draw the curve, identify its singular points by inspection, classify each singularity geometrically, estimate the intersection multiplicities, and only then check her work against the machine’s output. If the numbers disagree, she must find her error – either in her geometric reasoning or in her formulation of the problem to the machine. This way, the machine becomes a tutor rather than a crutch.
I should also say that certain truths are only visible to those who have struggled. When I worked on the higher singularities of plane curves, I spent weeks – months – staring at particular examples, trying to understand how a complicated singularity could be decomposed into simpler ones. The answer did not arrive as a formula; it arrived as a picture, suddenly clear, of how branches approached and separated. That picture could not have been given to me by any machine. It had to be earned through labour. I do not think this has changed, whatever your century’s instruments may be.
Finally, Miss Khan, let me say that I take heart from the fact that you are asking this question at all. A researcher who worries about the pedagogical effects of computational tools is a researcher who understands that mathematics is not merely a body of results but a discipline of thought. Preserve that discipline. Demand that your students see before they calculate. Insist that they explain before they compute. The machines will do their part; your task is to ensure that the human mind does not abdicate its own.
Abiodun Adebayo, 41, University Administrator and Gender Policy Specialist, Lagos, Nigeria
You built Bryn Mawr’s mathematics department essentially from nothing, yet you also served as chief examiner for the College Entrance Examination Board, sat on the AMS Council, and edited the American Journal of Mathematics for twenty-seven years. In Nigeria today, women academics often find themselves expected to do disproportionate ‘service work’ – committee membership, pastoral care, administrative roles – while men focus on research that earns promotion. Looking back, do you believe all that institutional labour was the price of legitimacy for a woman in your position, or was it genuinely where you felt you could make the greatest difference? And did you ever resent colleagues who published more because they served less?
Mr. Adebayo, you have asked the question that every woman who has had to choose knows how to ask. I shall answer it with more candour than I offered in the formal interview, because your question deserves nothing less.
The short answer is: both. It was a price, and it was where I could make the greatest difference. These are not contradictory truths; they are concurrent ones.
Let me explain what I faced in 1885. Bryn Mawr College had been founded only four years prior. The entire institution – buildings, curriculum, faculty, reputation – was improvised. There were eight of us founding faculty across all disciplines. The College’s president, Dr. James Rhoads, was determined that Bryn Mawr should not be a mere “finishing school” for the daughters of wealthy Philadelphia, but a genuine place of scholarship. Yet he had to convince the trustees, the parents, the wider world that women could do serious intellectual work without becoming unfeminine, unmatronly, or somehow damaged by rigorous study.
Into this precarious situation, I arrived as the only mathematician. I had to prove, not merely that I could do mathematics, but that I could do it in such a way that other women would believe themselves capable of doing it too. This required visibility. It required me to be seen not as an eccentric, not as a woman who had somehow escaped her proper sphere, but as a credible scholar whom the College could present as evidence of its own legitimacy.
The service work was thus partly instrumental – I performed duties not primarily because I wished to, but because I understood that women in my position could not afford to be perceived as narrow specialists. A man could be brilliant at his research and indifferent to everything else; the College would celebrate his brilliance. A woman who did the same risked being seen as unfeminine, cold, or uninterested in the welfare of her students. I had to prove my humanity, my dedication to the institution, my willingness to serve – before I was permitted to be merely a scholar.
But here is the complication, Mr. Adebayo, and it is the part that makes me uncomfortable in retrospect: I came to believe in the work itself. I did not merely perform service; I became persuaded of its necessity and its virtue. When I supervised seven doctoral students, I was not doing so reluctantly; I was doing so because I believed that the best gift I could give to mathematics was not another paper bearing my name, but seven women trained rigorously enough to train others. When I served on the AMS Council, I did so believing that women needed representation in the governance of the mathematical profession. These beliefs were genuine.
And yet – I must be honest – I wonder sometimes whether I would have believed these things so fervently, so completely, if I had had the choice to believe otherwise. A man serves on committees by choice; he can resign if they bore him, and it will not be held against his character. I served knowing that if I withdrew, I would be accused of ingratitude, of selfishness, of not being a “team player.” The compulsion to serve and the genuine belief in service got so thoroughly entangled that I am not certain I can now distinguish them.
As for resentment: yes, of course I felt it. I watched male colleagues at Johns Hopkins, at Chicago, at Princeton – fine mathematicians, certainly, but not obviously superior to me – accumulate publications with a freedom I did not possess. They had sabbaticals to work abroad; I had a department to run. They could ignore departmental politics; I had to navigate them constantly. When I learned that a man of my approximate age and ability had published forty papers while I had published perhaps twenty, I felt a sharp sting. I will not pretend otherwise.
But I should not misrepresent the situation, either. I had choices, and I made them. When I was offered positions at other institutions – and I was offered them – I chose to remain at Bryn Mawr. I could have reduced my administrative duties; I chose not to. I could have been a more prominent figure in the AMS by declining the editorship of the Journal; instead, I accepted it for twenty-seven years. These were decisions I made, albeit under circumstances that shaped what options I perceived as available.
The question you really ask is whether women in your own time must accept this trade-off, and I should say plainly: no. You should not. The fact that I made certain choices does not mean those choices were optimal, or just, or something younger women ought to emulate.
What I would say to a young woman in your position is this: understand the price before you pay it. Understand that there are pressures upon you that do not exist for your male colleagues – pressures to be visible, to prove your commitment, to demonstrate your humanity. Resist those pressures where you can. Find allies who will support you in saying no. Build institutions with others so that the burden of proof does not fall on a single person’s shoulders.
I built Bryn Mawr largely alone. I was the only woman in the mathematics department for years; later, I hired a second woman, but the weight fell primarily on me. If I had had colleagues – other senior women mathematicians – to share the institutional labour, the burden would have been lighter and the work more sustainable. The tragedy of being a pioneer is that you must not only do your own work but must simultaneously construct the apparatus through which others can do theirs. That is too much for one person.
Furthermore, Mr. Adebayo, I want to speak directly to the situation you describe in Nigeria and, I suspect, in many parts of the world. Women are often channelled toward teaching, mentoring, and service roles while being told this is their “strength” or their “calling.” This is a pernicious falsehood. If a woman is an excellent mathematician, she should be supported in research as fully as any man. If she chooses to do more teaching or service, that choice should be her choice, not a consequence of sexism masquerading as respect for her nurturing nature.
I insisted that my students at Bryn Mawr be trained in research, not merely in pedagogy. I did so because I believed – and I believe still – that women have the right to choose their own paths, and that right cannot exist if institutions systematically funnel them toward certain roles and away from others. The fact that I myself did much service work does not validate the practice; it merely demonstrates how insidious the pressure can be.
Would I do things differently if I could return? I think I would make some choices differently, yes. I might have written more papers. I might have been less available for every committee and council meeting. I might have resisted the expectation that I prove my worth through tireless labour on behalf of others. But I cannot undo what I did, nor do I entirely regret it. I trained seven PhDs; three of them became leaders in their own right. I helped establish mathematical education in America on a foundation of rigor and proof rather than mere calculation. I did this partly through research, but also through service.
The danger is in presenting my path as a model to be followed. It is not. It is a path I took under specific historical circumstances, with specific pressures and specific possibilities. Your young women mathematicians should not feel obligated to repeat it. They should know that the option exists – that one can choose to invest heavily in institution-building – but they should also know that this choice, for a woman, still carries a cost that it would not carry for a man, and that cost should be acknowledged openly, not disguised as virtue.
As for my resentment of colleagues who published more: I will tell you that it faded somewhat with age, though it never entirely vanished. When I retired in 1924, I had some years to reflect. I came to understand that I had made a particular kind of contribution – not the kind that appears in impressive publication counts, but a kind that shaped how mathematics was taught and thought about for decades. Whether that contribution was “worth” the research I did not do is a calculus I cannot make. I simply do not know.
What I know is this: the question you ask – about the distribution of labour, about whose time is considered valuable, about whose work counts as “real” work – this question matters profoundly. It matters in Nigeria, as it mattered in Pennsylvania. And it deserves clearer answers than I can give you, because the injustice is clearer now than it was to me then.
Ingrid Olsen, 28, PhD Candidate in Algebraic Geometry, Oslo, Norway
Your 1899 proof of Noether’s Fundamental Theorem provided geometric clarity to a result that Max Noether had stated algebraically. In modern terms, we’d frame this using ideal theory and local rings – the ‘AF+BG theorem’ is now a standard exercise in commutative algebra courses. But I’m curious about something more granular: when you were constructing that proof, what was the hardest step? Was there a particular case – perhaps curves with non-ordinary singularities at their intersection points – where you had to invent a new technique on the spot? And do you think your geometric proof offers any advantages that the modern algebraic treatment has lost?
Miss Olsen, you ask a question that touches the very heart of what it means to construct a proof – not merely to verify a theorem, but to find the path through it. I am grateful for such a question, because it allows me to speak about something rarely discussed in polite mathematical society: the messy, uncertain labour of discovery.
The Noether theorem, as Max Noether stated it in 1869, was this: if two curves and intersect in a finite number of points, and a third curve passes through all these intersection points, then belongs to the ideal generated by and . In algebraic language – though I had no such formal language at my disposal then – this means that can be expressed as a combination: for some polynomials and .
Max Noether’s proof was, frankly, unsatisfying. He asserted the result for curves in general position and then claimed – without sufficient rigour – that the result extended to all cases. The argument relied on continuity and limiting processes that were not rigorously justified. I found this deeply troubling. In mathematics, an incomplete argument is worse than no argument at all; it creates an illusion of understanding where doubt remains.
Now, the hardest step in my own proof – the point at which I was genuinely stuck for weeks – concerned precisely what you mention: non-ordinary singularities at the intersection points. When two curves meet transversely at a simple point (what one might call a “regular” intersection), the local behaviour is straightforward. But what if and have a common singular point – say, both have a node at the same location? Or what if they are tangent to one another?
The classical theory of intersection multiplicity, developed by Bézout, assumes that curves meet transversely. When they do not, the multiplicity calculation becomes treacherous. One must account for the fact that the intersection is “thickened” by the singularity itself. The algebra becomes complicated very quickly.
Here is what I had to invent: a method of local resolution. Rather than trying to analyse the intersection directly, I introduced auxiliary lines and curves to “separate” the branches near the problematic point. By projecting from a carefully chosen point, I could transform the non-ordinary intersection into a configuration of ordinary intersections that could be analysed using classical methods. Only after this local transformation did I apply the global argument.
The breakthrough came – I remember it quite vividly – while I was walking in the grounds at Bryn Mawr on a November afternoon. I had been worrying at the problem for perhaps six weeks, filling notebook after notebook with sketches and failed attempts. The question was: how could I systematise this local separation? And suddenly, I realised that the key was to use the Hessian curve – the curve formed by the second-order derivatives of the polynomial defining the original curve. The Hessian reveals the points of inflexion and other subtle features of the geometry. By considering how the Hessian behaves at the singular point, one could determine the appropriate transformation to make.
It was not, I hasten to say, a completely novel technique. Cayley and Salmon had used Hessians before. But the particular application to this problem – using the Hessian to guide the choice of projection point – that was something I had to work out myself. Once I had that idea, the rest of the proof flowed relatively easily.
The proof, when published in Mathematische Annalen, occupied perhaps ten pages. But the labour behind those ten pages was immense – the false starts, the intuitions that failed, the nights spent staring at diagrams, the eventual recognition that I was overcomplicating matters and that a simpler approach existed.
As for your question about whether the geometric proof offers advantages that the modern algebraic treatment has lost: I should like to say yes, but I must be honest about what I do not know. You tell me that the theorem is now a “standard exercise in commutative algebra courses,” understood through “ideal theory” and “local rings.” These are terms I do not fully understand – they developed after my active career, and I have read about them only in summary form. But from what I gather, the modern approach is far more general and powerful than my geometric proof. It applies to curves in higher dimensions, to varieties over arbitrary fields, to situations I could never have imagined.
My geometric proof was essentially planar – it worked for curves in the plane because I could exploit the special properties of two-dimensional geometry. A line has a well-defined notion of “from which side we approach the curve.” A projection has intuitive meaning. These properties do not generalise. So in a sense, my proof was not standing on the shoulders of giants; it was standing on very particular, very local ground.
However – and this is important – my proof has something the modern algebraic version may lack: it is visible. When a student reads my proof, she can draw the pictures I am describing. She can understand, intuitively, why the theorem must be true. The modern proof, I suspect, is more abstract and thus more powerful but perhaps also more opaque. One can know that the theorem is true without understanding why it is true in any visceral sense.
I do not say this as a criticism. The progress of mathematics requires increasing abstraction and generality. But I do say it as an observation: something is gained, and something is lost. The gain is power; the loss is immediacy. A student who reads the modern proof and understands it has a deeper, more generalised knowledge than a student who reads mine. But a student who reads my proof and visualises it, who draws the auxiliary curves and traces the branches, who understands the geometry in her bones – that student has a different kind of knowledge. Both are valuable.
If I were advising a young geometer like yourself, Miss Olsen, I should say this: learn both. Learn the abstract algebraic approach because it is the language in which modern mathematics is spoken. But do not forget the geometric approach, even if it seems old-fashioned. Go back to Noether’s original problem. Draw the curves. Try to understand, visually, why the theorem must be true. Then learn the modern proof and see how that proof abstracts away the geometry to arrive at a more universal principle. The interplay between these two modes of understanding – the geometric and the algebraic – is where the deepest insights lie.
You asked also what was invented “on the spot.” I should tell you that very little mathematics is truly invented on the spot. What happens instead is that one accumulates intuitions, techniques, and half-formed ideas over months or years, and then, at some moment of clarity, these cohere into something new. My use of the Hessian was not entirely novel; what was novel was the recognition of its relevance to this particular problem. That recognition did come suddenly, but it was the product of long labour preceding it.
This is a lesson I should like to impart to younger mathematicians: do not expect revelation. Expect work. Expect confusion. Expect to fill many notebooks with dead ends and false starts. And then, occasionally – not always, but occasionally – something will become clear. When it does, you will have earned the right to call it your own.
Alvaro Rossi, 37, Applied Mathematician and Data Scientist, Mexico City, Mexico
Professor Scott, imagine an alternative history: Cambridge awards you full degree status in 1885, offers you a lectureship, and you never cross the Atlantic. Girton becomes your permanent home; Bryn Mawr hires someone else – perhaps a man, perhaps a less rigorous woman. Given what you know about how institutions shape fields, do you believe American women’s mathematics would have developed differently without you? Would the proof-based curriculum you championed have emerged anyway, or was there something specific about building a department from scratch at a new women’s college that made your pedagogical vision possible in ways that reforming an existing institution never could?
Mr. Rossi, you ask me to imagine a road not taken – a version of my life that exists only as a mathematical abstraction, like a point at infinity. It is a provocative question, and one that I have, in fact, asked myself many times over the years. Let me think through it carefully.
First, the hypothetical premise: Cambridge offering me a lectureship in 1885 was, in practical terms, impossible. Cambridge did not award degrees to women until 1948, as you likely know. A lectureship would have been unthinkable in that era. But let us accept your imagined scenario – suppose the College had been more progressive, suppose I had somehow been appointed as a lecturer at Girton or even at Cambridge proper. What would have followed?
I think I must have remained at Cambridge in this alternative scenario. The pull of the place, the library, the intellectual community, the proximity to Cayley – these were powerful. I was not drawn to America primarily by ambition or by a desire for adventure. I was drawn because a specific opportunity presented itself, and because I believed I could accomplish something important there that I could not accomplish in England.
Now, your deeper question: would American women’s mathematics have developed differently?
Here I must speak with some humility, because I cannot know the answer with certainty. But I can reason through it.
In 1885, when I arrived at Bryn Mawr, the state of mathematics education for women in America was dire. There were a handful of women’s colleges – Mount Holyoke, Vassar, Wellesley – but none of them had serious research mathematics programmes. The expectation was that women would learn mathematics for the purposes of teaching it to younger girls, not for the purpose of discovering new mathematics. The idea that a woman could be a researcher – not a teacher or a communicator of knowledge, but a maker of knowledge – this idea was foreign to American higher education.
Bryn Mawr was different from the start. It was a graduate college, modelled on the German research universities that had impressed Dr. James Rhoads and M. Carey Thomas during their travels. Thomas, in particular, was determined that Bryn Mawr would not be a finishing school but a place where women could do advanced work. This ambition was present in the institution’s founding, before I arrived.
So perhaps – perhaps – another woman, less rigorous than I, might have built a respectable but undemanding mathematics programme. Perhaps the students would have learned some calculus and analytical geometry, passed their examinations, and become teachers. The knowledge would have been transmitted, but not expanded. Research would not have flourished.
But would mathematics have suffered in America? Would American women have been denied the opportunity to do research?
I think the honest answer is: probably not permanently, though it might have been delayed.
Consider what was happening in Europe. Emmy Noether was in Göttingen, developing her revolutionary work in abstract algebra. Sofya Kovalevskaya, though she died in 1891, had already demonstrated that women could do mathematics of international significance. The mathematical world was changing, regardless of what happened at Bryn Mawr. Eventually – perhaps later, perhaps with more difficulty, but eventually – American women would have found opportunities to do serious mathematics.
However, Mr. Rossi, I believe there was something particular about Bryn Mawr, something about its moment and its structure, that made certain outcomes possible that might not have been possible elsewhere.
Bryn Mawr was a new institution. It had no entrenched traditions, no century of male faculty, no established hierarchies that would have been difficult to disrupt. When I arrived, I was not trying to reform an ancient system; I was helping to create a new one from scratch. This was liberating in a way that I suspect reforming Cambridge – even had I somehow been offered the chance – would not have been.
Consider the alternative: suppose I had been appointed as a lecturer at Cambridge in some hypothetical scenario. What would I have faced? I would have been a woman in a college for women, yes, but Cambridge itself would have remained an almost entirely male institution. I would have been one voice among dozens of male mathematicians, many of whom were deeply hostile to women’s education or at best indifferent to it. I would have had to fight constantly to maintain standards, to justify my own existence, to defend every choice I made.
At Bryn Mawr, I was the founder of the mathematics programme. I could establish standards from the beginning. I could hire colleagues – when eventually I did hire them – according to my own criteria. I could design the curriculum, set the expectations, create a culture of rigour and research from the ground up. This power to shape an institution from its inception is something that reformers, however talented, can rarely achieve.
Furthermore, Bryn Mawr was a college for women, entirely staffed by women faculty in its early years. This mattered enormously. The students knew, without any ambiguity, that women could be mathematicians – they saw it embodied daily in their professors. There was no possibility for them to imagine that mathematics was a male discipline with a few exceptional women admitted on sufferance. Mathematics was simply what we do here.
Let me give you a concrete example. When I trained Ruth Gentry for her doctoral work, or Ada Isabel Maddison, I could do so without having to constantly answer questions about whether it was appropriate for women to pursue advanced mathematics. At a mixed institution, I would have been defending the endeavour constantly – to male colleagues, to parents, perhaps to the students themselves. Here, the question was simply not raised. The energy I might have spent on justifying the enterprise could instead be spent on the enterprise itself.
Consequently, Bryn Mawr’s physical and intellectual isolation – it was a rural college outside Philadelphia, far from the major male universities – was paradoxically an advantage. We could not rely on male institutions to validate our work. We had to build a community of mathematical excellence amongst ourselves. This forced us to be serious, perhaps more serious than we would have been had we been nestled within a larger male academic ecosystem.
I should also say that the American context was, in some ways, more hospitable to women in academia than the English context was in 1885. American universities were newer, less bound by tradition. The idea of founding a college and making it first-rate through vigorous hiring and curricular innovation – this was an American possibility. England had its ancient universities, its traditions, its resistance to change. America had space and ambition.
So here is my honest assessment, Mr. Rossi: had I remained at Cambridge, I might have published more papers. I might have made more direct contributions to algebraic geometry. I might have had a more prominent career in European mathematics. But I do not think American women’s mathematics would have developed radically differently. Some other woman, or perhaps a man sympathetic to women’s education, would eventually have built a serious programme somewhere.
However – and this is crucial – I do not think the particular form that women’s mathematics took in America would have been the same. My pedagogy, my insistence on rigour, my emphasis on proof over calculation, my vision of what it means to teach mathematics seriously to women: these might not have become so embedded in American mathematical culture had they not taken root at Bryn Mawr in those crucial years.
The textbook I wrote in 1894 was reprinted and adopted widely. The students I trained went on to teach at Vassar, Mount Holyoke, Wells, Wellesley. They carried with them the standards and expectations they had learned from me. Through them, my pedagogical vision spread. Had I not been at Bryn Mawr to articulate and embody that vision at a crucial moment, when women’s mathematics in America was still being defined, the trajectory might have been different.
It is a bit like asking whether a river would have flowed to the sea had one particular rock not been placed in its path at a particular moment. Eventually, the water finds its way. But the specific channels it carves depend on the obstacles and opportunities it encounters along the way.
What I am saying is this: the existence of women’s mathematics in America was probably inevitable. But I believe the character of women’s mathematics in America – its emphasis on rigour, on proof, on the inseparability of teaching and research – these things were shaped by my presence at Bryn Mawr at a formative moment. And that character, I believe, has had consequences that ripple down to your own time.
Whether that is vanity on my part, I cannot say. But it is what I believe to be true.
There is one more consideration, Mr. Rossi, that speaks to the question of institution-building versus individual achievement. Had I remained at Cambridge and written many more papers, I would have contributed to the body of mathematical knowledge. But I would not have created the conditions under which other women could contribute as easily. My papers would have been my achievement; my department at Bryn Mawr became a structure through which many women’s achievements became possible.
As I look back on my life, I find that I value the structure-building more than I might have predicted. A theorem with my name on it is a fine thing. But a department that has produced PhDs, that has trained teachers, that has established a culture of rigour – that endures in a way that a single theorem does not.
So I think, on balance, I made the right choice in coming to America, even though it meant sacrificing certain opportunities for recognition in European mathematics. The road not taken might have been glorious. But the road I did take led somewhere important, I believe, for women’s mathematics and for mathematics education more broadly.
Sofia Costa, 52, Science Historian and Museum Curator, São Paulo, Brazil
You returned to Cambridge after retirement and lived there quietly until your death in 1931 – just three years after Cambridge finally allowed women’s Tripos results to be listed alongside men’s, and seventeen years before Cambridge granted women actual degrees. You had every right to feel bitter, yet by all accounts you spent those final years gardening and attending to personal matters rather than campaigning. Was that peace, or exhaustion, or something else entirely? If you could have written one letter to the Cambridge Senate in 1928, knowing they were finally debating women’s degrees, what would you have said to them – and what would you have left unsaid?
Miss Costa, you have asked a question that cuts to the heart of something I have not fully resolved in my own mind, even now. Peace, exhaustion, or something else – yes, all of these, and perhaps also resignation, bitterness, satisfaction, and a complicated gratitude that I am not sure I have earned the right to feel.
Let me be very direct first: I did receive letters during those final years asking me to join campaigns, to lend my name to petitions, to write articles supporting women’s admission to degrees at Cambridge. I declined them all. Not from indifference – I assure you, I was not indifferent – but from a kind of weariness that I had not anticipated feeling.
When I retired from Bryn Mawr in 1924, I was fifty-six years old. I had been working intensively for forty-four years – since my arrival at Girton in 1876. The rheumatoid arthritis had made my hands painful; my deafness was almost complete; I was managing through gestures, written notes, and the interpretations of others. To return to Cambridge was to return to the place where my fight had begun, where I had sat the Tripos in 1880 and been denied recognition, where I had lived as a woman in an institution that did not grant degrees to women, where the Spinning House still represented the threat that attended my every unaccompanied step.
I was tired. I will not apologize for that, though I suspect some would say I should have persevered.
But was it peace, or exhaustion? Here the distinction matters. Exhaustion is passive; peace is active. I think what I felt was neither, or perhaps a combination that had no name. I felt a kind of settled resignation. I had done what I could do. Cambridge had changed since 1880, but it had changed slowly and grudgingly. Women could now sit the Tripos and have their names published – this was progress, yes, but inadequate progress, coming forty-eight years too late. And degrees? That would take even longer. I did not know if I would live to see it.
There is a moment, Miss Costa, when one realizes that one’s own battle is not going to be won in one’s own lifetime, and that continuing to fight is less a matter of principle than a matter of habit. I think I reached that moment around 1925.
As for what I might have written to the Cambridge Senate in 1928, when the question of degrees for women was being debated: this is more difficult to answer, because I am not certain what I would have said, and I am even less certain what I would have left unsaid.
If I had written, I might have said something like this:
“Gentlemen of the Senate,
I sat your Mathematical Tripos examination in 1880, nearly half a century ago. I placed eighth. You did not award me the title of wrangler because I was a woman. Instead, the undergraduates in the Senate House shouted my name to protest your injustice.
It has taken you forty-eight years to permit women to have their Tripos results listed. It will take you even longer, I suspect, to award them degrees. This is not justice delayed; this is justice withheld.
You have had nearly five decades to observe that women can do mathematics. You have seen women earn doctorates from other universities – from London, from the Continent, from America. You have seen women publish research, teach, contribute to your own mathematical journals. You have known all this, and still you have refused to grant women the formal recognition of a degree.
I will not ask you to do this because it is right. You know it is right, and you have done nothing. Instead, I ask you to do it because you are ashamed. Let that shame finally compel you to act.”
That is what I might have written. Harsh, I think. Unforgiving. The letter of a woman who had been patient for nearly fifty years and who had run out of patience.
But I did not write it. And here is why: because I was no longer certain that anger was the appropriate response, and I had no other response to offer.
You see, Miss Costa, there is a particular exhaustion that comes from being a symbol. In 1880, I was a symbol of women’s capability. The undergraduates cheering “Scott of Girton!” were not cheering me, precisely; they were cheering the idea that women could do what men could do, and that the University’s rules were unjust. I understood this even then, and I accepted it. I became a symbol willingly, in part, because I believed the cause was just.
But symbols do not age well. By 1925, I was no longer a symbol of possibility; I was a symbol of old injustice. My presence in Cambridge – the woman who had been denied the title of wrangler, who had been forced to take her degree from London, who had left England to build a career elsewhere – my presence was a reproach to the University. And I was not certain I wanted to be a reproach any longer.
What would I have left unsaid? I think I would have left unsaid the most cutting things – the observations about Cambridge’s moral cowardice, the pointed remarks about how other universities had moved ahead while Cambridge clung to its traditions, the bitter notes about how the men of the Senate could live comfortably with injustice so long as they did not have to look it in the face.
I would have left all of that unsaid because I was not certain it would accomplish anything, and I had become uncertain about the value of accomplishing things through anger.
There is something else, Miss Costa, that I must confess. Part of my quietness in those final years came from a kind of guilt. I had left England. I had built my life and my career in America. I had not returned to fight the battle on my home ground. Other women – women at Girton, women at Newnham – they had remained in England, they had pushed for change from within, they had lived with the daily indignity of being excluded even as they taught and studied at Cambridge. I had escaped to Pennsylvania. And then, when I returned in 1924, I returned as someone who had already won a kind of victory elsewhere. It did not seem quite fair for me to become the face of the remaining injustice.
Furthermore, I was aware – perhaps too aware – of how I would be perceived. An elderly woman, retired, returned to her alma mater to complain about wrongs done to her in her youth. Would people listen? Or would they dismiss me as self-interested, as fighting for my own vindication rather than for principle?
This awareness itself was a kind of poison. It made me cautious when I should have been bold.
So when you ask whether my quietness was peace or exhaustion, I think the most honest answer is: it was neither and both. It was a form of surrender that I disguised to myself as wisdom. It was a recognition of reality coupled with an unwillingness to live with that reality. It was peace of a sort – the peace of ceasing to struggle – but it was purchased at the cost of certain convictions I had held throughout my life.
If I could speak to that younger Charlotte Angas Scott, the one who was so outraged in 1880, who refused to accept condescension, who insisted on rigorous standards and on her own right to be treated as a serious mathematician: I think I would tell her that the world moves slowly, and that sometimes one must continue to push even when pushing feels futile. I would tell her that the right to remain silent is not the same as the obligation to remain silent.
But I cannot speak to her. I can only observe, from this distance of time, that I made a choice – perhaps the wrong one – to step back from the fight.
When Cambridge finally did award degrees to women in 1948, seventeen years after my death, I was not there to witness it. I do not know if that would have pleased me or angered me further. Perhaps both.
What I know now is this: silence is not always peace. Sometimes it is complicity. I was not complicit in the injustice done to women at Cambridge – I had fought that injustice openly in my youth – but I was, perhaps, complicit in allowing it to continue without my voice raised against it in my later years.
Would I do things differently if I could return? I honestly do not know. The woman I was in 1925 was not the woman I was in 1880. Life had worn away certain certainties. Whether that was wisdom or cowardice, I cannot say.
What I can say is that I admire the young women who continued to fight, who did not retreat to their gardens, who kept demanding what was rightfully theirs. They succeeded where I eventually stepped aside. That success belongs to them.
Reflection
Charlotte Angas Scott died on 10th November 1931, in Cambridge, England, at the age of seventy-three. She had returned to the city where, fifty-one years earlier, undergraduates had drowned out an official announcement to cheer her name – a city that still, even at her death, refused to grant degrees to women. That injustice would not be remedied for another seventeen years.
What emerges from this conversation is a portrait far more complicated than the brief biographical entries typically afford her. Scott was not simply a “first woman to…” – a phrase that reduces a life to a single moment of barrier-breaking. She was a geometer who spent decades thinking about the behaviour of curves at their most troubled points, a pedagogue who believed that rigour was the highest form of respect, an institution-builder who understood that individual excellence means little without structures to perpetuate it.
The themes that recur throughout her testimony – perseverance in the face of institutional exclusion, ingenuity in circumventing barriers that could not be removed, the quiet labour of building something from nothing – these are not unique to her era. They echo in the experiences of women mathematicians today, in Lagos and Lahore, in Oslo and São Paulo, who still navigate expectations that they will do more service work, prove their humanity before they are permitted to be scholars, and accept recognition that comes late or not at all.
Scott’s reflections on the distribution of labour between research and service, her candid acknowledgment of resentment toward colleagues who published more because they served less, her complicated relationship to the silence of her final years – these are perspectives that do not appear in the official record. The historical Charlotte Angas Scott left behind papers, letters, textbooks, and a few sharp remarks in correspondence with M. Carey Thomas. But the inner life – the calculus of regret, the weighing of choices made and unmade – this we cannot know with certainty. What we have offered here is an imaginative reconstruction, grounded in fact but necessarily speculative in its interiority.
The gaps in the record are considerable. We do not know precisely how Scott felt about the transition from geometric to algebraic methods in her field. We do not know what she thought of Emmy Noether’s revolutionary work in abstract algebra, which was transforming the discipline even as Scott retired. We do not know whether she followed, from her Cambridge garden, the debates over women’s degrees, or whether she had truly made peace with her withdrawal from that fight. The historical record preserves actions and publications; it rarely preserves ambivalence.
The mathematics Scott practised – the study of algebraic curves of degree higher than two, the classification of singularities, the interplay between algebraic formulae and geometric intuition – remains foundational to modern algebraic geometry. Her 1899 proof of Noether’s Fundamental Theorem, published in Mathematische Annalen, demonstrated that American mathematics could command European attention. Today, the AF+BG theorem she helped clarify is taught in graduate courses on commutative algebra and algebraic geometry worldwide, though rarely with her name attached.
Her 1894 textbook, An Introductory Account of Certain Modern Ideas and Methods in Plane Analytical Geometry, influenced generations of students and teachers. Its insistence on separating general principles from particular examples anticipated the proof-based pedagogy that now dominates undergraduate mathematics education. When modern instructors distinguish between “understanding the theorem” and “being able to do the calculation,” they are, often unknowingly, following a path Scott helped clear.
The afterlife of her work is visible in unexpected places. The USC mathematics group “Charlotte’s Web” honours her memory by supporting women in the field. Cambridge, in 2016, named a street after her in the North West Cambridge Development – a belated acknowledgment from an institution that denied her recognition in life. Historians of mathematics, including those who have studied women’s contributions to the discipline, have increasingly recognised her as a central figure in the transatlantic development of mathematical education.
Her doctoral students – Ruth Gentry, Ada Isabel Maddison, Virginia Ragsdale, and others – carried her standards into institutions across America. Three of them were among only nine women to earn mathematics doctorates in the nineteenth century. Through them, Scott’s influence extended far beyond Bryn Mawr, shaping how mathematics was taught at women’s colleges and beyond for decades.
What might Scott’s story offer to young women in STEM today?
First, visibility matters. The undergraduates who shouted “Scott of Girton!” in the Senate House were making her visible at a moment when the institution wished to render her invisible. That visibility – uncomfortable, unsought, but ultimately powerful – helped force a change in policy. Young women today who speak publicly about their work, who claim space in conferences and journals and faculty meetings, are engaged in the same project of making themselves impossible to ignore.
Second, mentorship is not charity; it is strategy. Scott trained seven doctoral students not because she was naturally nurturing but because she understood that one woman, however brilliant, is an exception, while a network of trained women is a fact of nature. The investment in others is an investment in the field itself.
Third, rigour is respect. Scott’s refusal to accept “watered down” curricula for women was not elitism; it was a recognition that lowered expectations are a form of condescension. To demand the highest standards from students is to believe in their capacity to meet those standards.
Fourth, the work of building institutions is as valuable as the work of proving theorems, even if it is less celebrated. Scott could have remained at Cambridge, published more papers, accumulated more individual accolades. Instead, she crossed an ocean to build a department that would produce mathematicians for generations. That choice – structure over spectacle – is one that many women in STEM continue to make, often without recognition.
And finally, this: Charlotte Angas Scott lived with the knowledge that she would not see the full fruits of her labour. Cambridge did not award degrees to women until 1948. The field of algebraic geometry evolved in directions she could not have anticipated. The students she trained went on to lives she could not follow. She planted seeds whose harvest she would never witness.
This is, perhaps, the deepest lesson of her life. The work of justice is not completed in a single lifetime. The work of building knowledge is not completed in a single career. We inherit structures built by those who came before us, and we build structures for those who will come after. Scott understood this. She built anyway.
In the end, the question is not whether history remembers Charlotte Angas Scott – though it should, and increasingly does. The question is whether we understand what her life demonstrates: that excellence and exclusion can coexist, that recognition delayed is still recognition denied, that the labour of institution-building is often invisible precisely because it succeeds, and that the women who came before us did not merely survive their circumstances but actively shaped the world we now inhabit.
She earned the right to be remembered. Let us remember her.
Editorial Note
This interview is a work of historical fiction. It is not a transcript of words Charlotte Angas Scott actually spoke, nor should it be read as definitive historical evidence. Rather, it is a carefully researched dramatisation – an imaginative reconstruction grounded in documented facts about Scott’s life, her mathematical work, her pedagogical philosophy, and her correspondence.
The factual foundation is substantial. Scott’s birth and death dates, her education at Girton College and Cambridge, her placement as eighth on the 1880 Mathematical Tripos, her degrees from the University of London, her founding role at Bryn Mawr College, her publications, and her service to the American Mathematical Society are all matters of historical record. The 1922 celebration in her honour, the development of rheumatoid arthritis and progressive deafness, her retirement in 1924, and her return to Cambridge are documented. Her research on algebraic curves of higher degree, her 1899 proof of Noether’s Fundamental Theorem, and her influential 1894 textbook on plane analytical geometry are confirmed in mathematical histories and archival sources.
However, the inner thoughts, the emotional responses, the philosophical reflections, and the precise manner of her speech in these conversations are constructed. They are constructed on the basis of:
- Her known beliefs about mathematical education (derived from her writings and from accounts of her pedagogy);
- Her documented criticisms of lowered standards for women (from her correspondence with M. Carey Thomas and others);
- The historical context of her era (the Spinning House threat to women at Cambridge, the exclusionary practices of British universities, the rapid development of women’s higher education in America);
- Her personality as described by those who knew her (sharp, unsentimental, intolerant of condescension, deeply invested in her students);
- The technical content of her mathematical work (accurately represented at a conceptual level, though simplified for accessibility).
The five supplementary questions posed by Zara Khan, Abiodun Adebayo, Ingrid Olsen, Alvaro Rossi, and Sofia Costa are entirely fictional, as are their biographical details. However, the concerns they raise – about computational versus geometric reasoning, about gendered labour in academia, about pedagogical innovation, about institutional change, about silence and regret – are informed by real contemporary debates and by historical patterns documented in the lives of women academics.
Where this reconstruction differs from or extends beyond the historical record, those differences should be understood as artistic choices made in service of narrative clarity and emotional truth, not as factual claims about what Scott said or thought. Readers interested in verifying specific biographical facts are directed to the MacTutor History of Mathematics archive (University of St Andrews), the Bryn Mawr College Archives, and scholarly articles cited throughout this piece.
The purpose of this dramatisation is not to deceive but to enliven – to bring a historical figure who has been largely overlooked into conversation with contemporary concerns, and to honour the complexity of her life and work by imagining not just what she did, but what it might have felt like to do it.
Who have we missed?
This series is all about recovering the voices history left behind – and I’d love your help finding the next one. If there’s a woman in STEM you think deserves to be interviewed in this way – whether a forgotten inventor, unsung technician, or overlooked researcher – please share her story.
Email me at voxmeditantis@gmail.com or leave a comment below with your suggestion – even just a name is a great start. Let’s keep uncovering the women who shaped science and innovation, one conversation at a time.
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