Vox Meditantis

This interview is a dramatised reconstruction, created from historical biographies and Hudson’s published work, rather than a verbatim record of her words. It aims to stay faithful to documented facts while imaginatively supplying voice, dialogue, and inner reflections where the archive is silent.

Hilda Phoebe Hudson was an English mathematician who transformed plane geometry, calculated the spread of infectious disease before epidemiology had a name, and applied rigorous analysis to the structural integrity of aircraft during the First World War. Born into a Cambridge mathematical family in 1881, she became the first woman to deliver an invited lecture at the International Congress of Mathematicians in 1912, authored the definitive treatise on Cremona transformations, and co-created the mathematical framework that underpins all modern epidemic modelling. Yet her name has been quietly erased from the disciplines she helped to build, her contributions fragmented across fields that claimed her work but not her legacy.

Welcome, Dr Hudson. It’s December 2025, and I’m speaking with you from a world that has just lived through a global pandemic – one modelled using mathematics you helped create over a century ago. How does it feel to know that the equations you wrote with Ronald Ross in 1916 and 1917 became the foundation of how we understand disease transmission today?

That’s rather extraordinary to hear. I confess, when Ronald first approached me about applying probability to disease spread, I thought it was a curious departure from my work on surfaces and transformations. But the mathematics was sound – beautifully so, in fact. We were attempting to understand a priori pathometry, as he termed it. The idea was to model disease as one might model the motion of particles: with differential equations describing rates of change. Susceptible populations becoming infected, infected individuals recovering or perishing – it was all amenable to mathematical treatment.

I had no notion it would become… what did you call it? Foundational? That’s generous. At the time, I was simply doing what mathematicians do: finding the true relationships within a system.

The model you developed with Ross is now universally known as the SIR model – Susceptible, Infectious, Recovered. Yet in most epidemiology textbooks, your name appears as a footnote at best, if at all. Ross is remembered; Kermack and McKendrick, who built on your work in 1927, are remembered. But you are not. How do you reckon with that?

I suppose I ought to feel aggrieved, but the truth is more complicated. Ronald was the senior figure – he’d won the Nobel Prize for his work on malaria transmission. I was the mathematician he brought in to formalise his intuitions. In those days, collaboration often meant the junior partner’s contributions were absorbed into the senior’s reputation. I knew that when I agreed to the work.

What concerns me more is the disciplinary fragmentation. Pure mathematicians saw the Ross papers as applied work, beneath notice. Medical men saw them as abstract theory, not practical. Epidemiologists – well, they were busy building a new field, and apparently, they didn’t need a geometer cluttering the genealogy. I fell between the gaps.

But I shan’t pretend it doesn’t sting a little, hearing you say the model is taught globally without my name attached. One hopes one’s work will speak for itself, but work doesn’t speak. People do, and people seem to have forgotten to mention me.

Let’s speak, then. Tell me about your path into mathematics. You were born into what your obituary called “a distinguished mathematical family” in Cambridge. Was it inevitable that you’d follow?

Not inevitable, no, though it was certainly encouraged. My father, William Henry Hoar Hudson, was Professor of Mathematics at King’s College, London. Our household was filled with mathematical conversation – geometry at breakfast, algebra over tea. My brother Ronald was utterly brilliant; he published research before his tragic death in 1904. I was never quite as precocious, but I had a stubbornness about problems that served me well.

I entered Newnham College in 1900 on a Gilchrist scholarship. It was a peculiar time to be a woman at Cambridge. We were permitted to attend lectures, sit examinations, and be ranked – but not to receive degrees. I came seventh equal in the First Class of the Mathematical Tripos in 1903, which meant I’d done the work of a Cambridge graduate without the credentials to prove it.

That’s where Trinity College Dublin entered the picture. From 1904 to 1907, Dublin offered ad eundem degrees to women who’d completed Oxbridge coursework. I took the steamboat to Dublin in 1906 and received my MA. It was a small act of rebellion, really – a way of saying, “I did earn this, and I’ll get it recognised somewhere, even if Cambridge won’t.”

You spent a year studying in Berlin before returning to Newnham as a lecturer in 1905. What was that experience like – being a woman in German mathematical circles at the turn of the century?

Berlin was formidable. The German mathematicians took their work with a seriousness that bordered on ferocity. Women were rare, but not unheard of. There was a sense that if you could keep pace, you’d be tolerated, if not exactly welcomed.

I attended lectures on algebraic geometry and projective methods. That’s where I truly fell in love with Cremona transformations – birational maps that rearrange the projective plane. They’re named for Luigi Cremona, the Italian geometer, and they allow you to simplify complicated algebraic surfaces by clever rearrangements. It’s rather like untangling a knot by pulling it through a different dimension.

Berlin taught me rigour, but it also taught me isolation. I was often the only woman in a lecture hall, and the presumption was that I was auditing out of idle curiosity, not genuine scholarship. Proving otherwise required every paper, every solution, to be impeccable. It was exhausting.

When you returned to Cambridge, you began publishing prolifically – seventeen papers between 1911 and 1929 on Cremona transformations, nodal curves, pinch-points. Walk me through what you were actually doing in this work. What problem were you solving?

Ah, now you’re asking me to explain algebraic geometry to someone who can follow. Let me try.

Imagine a plane curve – say, a cubic, like (x^3 + y^3 = z^3) in projective coordinates. Such curves have singularities: points where they cross themselves, or touch tangentially, or behave badly in some geometrical sense. A Cremona transformation is a birational map that takes one plane and rearranges it according to rational functions. If you choose your transformation carefully, you can move the singularities around, or blow them up into simpler configurations, or collapse them entirely.

The challenge is classification. Given a particular type of Cremona transformation – say, a cubic one, where the defining polynomials are of degree three – how many fundamentally different types are there? What are their base points – the places where the transformation becomes undefined? How do they act on curves of various degrees?

My early work catalogued cubic Cremona transformations of space. I identified seventy-five basic types. It was patient, exacting work – rather like botanical taxonomy, but for abstract geometrical objects. Each type had to be verified, its properties checked against known results. There were no shortcuts.

And then in 1912, you were invited to speak at the International Congress of Mathematicians in Cambridge – the first woman ever to receive such an invitation. That must have been a watershed moment.

It ought to have been, yes. In practice, it was rather anticlimactic.

Laura Pisati, an Italian mathematician, had been invited to speak at the 1908 Congress in Rome, but she died a few days before the meeting. So when I received the invitation to speak in Cambridge in 1912, I was conscious of carrying that torch – being the first woman to actually deliver the lecture, not merely be invited.

I spoke on binodes and nodal curves. The room was polite, attentive. A few questions afterwards, nothing hostile. And then… nothing. No cascade of further invitations. No sudden acceptance into the inner circles of mathematical societies. I’d broken a barrier, but the barrier had been so quietly drawn that its breaking barely made a sound.

I think that’s the trouble with being “the first woman to” – you’re celebrated for the novelty, but the celebration doesn’t translate into structural change. Cambridge still wouldn’t award me a degree. Journals still presumed I was an anomaly. I was allowed into the room, but not invited to stay.

Let’s talk about the War. In 1917, you joined the Air Ministry – technically the Admiralty Air Department at first – to work on aeronautical engineering. How did a pure geometer end up calculating stresses in aircraft struts?

Necessity. The War consumed everything, including mathematicians. The government was desperate for anyone who could handle differential equations and statics. My friend G. H. Bryan, who’d worked on aerodynamics, recommended me. They needed people who could model the forces on biplane wings, particularly the struts and incidence wires that held the upper and lower wings apart.

Biplanes were structurally efficient because the wings were braced by vertical struts and diagonal wires, forming a truss. But calculating the stresses in those wires under load was fiendishly difficult. If the incidence wires – the ones running diagonally between the wings to maintain their relative angle – were too weak, they’d snap in flight. Too heavy, and you’d sacrifice lift and manoeuvrability.

I developed methods for incorporating those wires into the overall stress calculations for the wing structure. It required treating the wing as a beam subjected to distributed aerodynamic loads, then decomposing those loads into forces acting on the struts and wires. The mathematics was straightforward in principle – moments, shears, axial tensions – but the geometry of the strut arrangement made the algebra rather beastly.

You published two papers after the War on strut strength and incidence wire stresses. Did you feel your contributions were recognised?

Not adequately, no. The work was classified during the War, so it couldn’t be published immediately. By the time I wrote it up in 1920, the urgency had passed. Aeronautical engineers were moving towards monoplane designs with cantilever wings, which didn’t require external bracing. My methods were already becoming obsolete.

I was appointed OBE in 1919 for the work, which was gratifying. But the citation was vague – “services to aeronautical research” – and my name doesn’t appear in most histories of wartime aviation. I suspect because I was working on analysis, not design. The engineers who built the aircraft got the credit; the mathematician who checked their sums was invisible.

And yet you also applied your mathematics to epidemiology during this same period. How did you balance pure geometry, aeronautical engineering, and disease modelling?

I didn’t balance them well, if I’m honest. I worked myself to exhaustion. The War years were chaotic – long hours at the Air Ministry, evenings spent on the Ross papers, weekends trying to keep up with my research on Cremona transformations. I barely slept.

But there was a strange coherence to it. All three areas required the same fundamental skill: constructing mathematical models of complex physical systems. Whether it’s the spread of disease through a population, the stress distribution in a trussed wing, or the behaviour of algebraic curves under birational maps, you’re always asking: what are the essential relationships here? What can I strip away, and what must I preserve?

Mathematics is a way of seeing. Once you learn to see in that way, it applies everywhere.

After the War, you left the Air Ministry and eventually took a position with Parnell and Company in Bristol as a technical assistant. Then, in 1921, you retired to write your magnum opus, Cremona Transformations in Plane and Space, which was published in 1927. Tell me about that book.

That book consumed seven years of my life. Four hundred and fifty-four pages. Thirty-seven pages of bibliography with four hundred and seventeen items. I wanted to create a unified account of everything known about Cremona transformations – every special case, every classification result, every technique for resolving singularities.

It was an act of consolidation. The field had grown chaotic, with results scattered across Italian, German, French, and English journals. Young mathematicians entering the area had no roadmap. I wanted to build them one.

The work was solitary, often frustrating. I’d spend weeks verifying a single claim from an 1880s paper, only to discover the author had made an error. Or I’d find two papers claiming contradictory results, and I’d have to work out which was correct – or whether they were addressing subtly different questions.

But it was also deeply satisfying. Pure mathematics has a stillness to it. You’re not chasing deadlines or responding to crises. You’re simply trying to see clearly.

John Semple, in your obituary, called the book your magnum opus and said it “gathered into one connected account all the essential elements of what had long been a fashionable field of research.” Yet by the time it was published, algebraic geometry was moving in different directions – towards abstract algebra, sheaf theory, schemes. Did you feel the ground shifting under you?

Oh, absolutely. By the late 1920s, Cremona transformations were seen as old-fashioned. The new generation – people like André Weil and Oscar Zariski – were rebuilding algebraic geometry from the foundations using commutative algebra. My methods were concrete, constructive, tied to explicit coordinate calculations. Theirs were abstract, categorical, vastly more powerful.

I don’t begrudge them that. Mathematics moves forward. But it did mean my book was something of a monument to a dying tradition. I’d spent seven years perfecting a craft just as everyone else was learning a new language.

Still, the book had value as a reference. People still consulted it when they needed to understand a specific classical transformation. It wasn’t the future, but it was a thorough reckoning with the past.

You published almost nothing after 1929. What happened?

Arthritis. It began in my hands and spread to my spine. By the early 1930s, I could barely hold a pen for more than a few minutes without pain. Writing became agony.

I tried to continue – I had ideas, problems I wanted to pursue – but the physical act of doing mathematics became impossible. I couldn’t write out long calculations. I couldn’t turn pages easily. I couldn’t sit at a desk for hours.

It was a slow erasure. Not dramatic, just relentless. And because I was working in isolation – no university position, no research students to carry on the work – when I stopped, the work stopped with me.

You eventually moved to St Mary’s Convent and Nursing Home in Chiswick, where you spent your final years. Was that a retreat from the world, or something else?

It wasn’t a retreat. It was an acceptance. My body had become unreliable; I needed care I couldn’t provide for myself. St Mary’s was an Anglican convent with a nursing home attached. The sisters were kind, the rooms quiet. I could pray, read when my hands allowed, and be among people who understood suffering without pitying it.

I’ve always believed mathematics was a way of apprehending God. To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology. At St Mary’s, I was closer to the source of truth than I’d ever been in a lecture hall.

Looking back from 2025, I can tell you that the SIR model you co-created with Ross is now the most widely taught framework in epidemiology. During the COVID-19 pandemic, governments used SIR-based models to predict infections, allocate hospital resources, and justify lockdowns. Millions of people learned the terms “susceptible,” “infectious,” and “recovered” for the first time. And yet your name remains absent. If you could correct the record now, what would you say?

I would say that co-authorship matters. Not for ego, but for accuracy. When the history of a field is written, the omission of a contributor distorts the story. It suggests that Ronald Ross invented mathematical epidemiology alone, which he did not. It suggests that the mathematical rigour came later, with Kermack and McKendrick, when in fact it was there from the beginning.

I would also say that women who work across disciplines pay a historical penalty. Each field takes what it needs from your work and discards the rest – including your name. Pure mathematicians dismissed my epidemiology work as applied. Epidemiologists saw me as Ronald’s assistant, not his collaborator. Aeronautical engineers barely acknowledged that a woman had done the stress calculations.

If I had stayed in one field, published only on Cremona transformations, perhaps I’d be remembered better. But I followed the problems, and the problems didn’t respect disciplinary boundaries. For that, I’ve been erased.

You also served on the Council of the London Mathematical Society, one of very few women to do so in your era. Did you see that as progress?

I saw it as tokenism. The LMS Council appointed me to show they were “modern” and “inclusive.” But they didn’t change their structures to actually support women. There were no accommodations for the different pressures we faced, no recognition that women were simultaneously expected to be exemplary scholars and invisible helpmeets.

I attended the meetings, contributed where I could. But I was always conscious of being the woman on the Council – singular, exceptional, and therefore not representative of anything. Real progress would have been five women on the Council, not one.

If you could speak to young women entering STEM fields today – especially those working across disciplines – what advice would you offer?

Document everything. Publish under your own name. Insist on proper attribution in collaborative work. Don’t let anyone tell you that “it’s not done” or “it’s not important.” Your name is important. Your work is important. If you don’t claim it, no one will claim it for you.

And find allies. Not just mentors, but peers – people doing the kind of work you admire, who will cite you, defend you, remember you. Isolation is dangerous. It makes you easy to forget.

You once wrote that “mathematics is a direct approach to God” and that “we can practise the presence of God in an algebra class better than on a mountain top.” That’s a bold claim. Can you explain it?

Certainly. When we engage in pure mathematics, we’re not constructing or inventing – we’re discovering. The relationships were always there, waiting to be seen. A theorem isn’t made true by our proof; it is true, and the proof simply reveals that truth to us.

That act of revelation is, to my mind, a form of worship. We’re thinking God’s thoughts after Him, to borrow Kepler’s phrase. We’re tracing the structure of a rational, orderly, beautiful universe that didn’t have to be rational or orderly or beautiful, but is.

In an algebra class, when a student suddenly sees why a particular identity holds – when the abstraction crystallises into clarity – that’s a moment of encounter with the divine. It’s grace, mediated through reason.

One final question. If someone in 2025 wanted to honour your legacy – to ensure your contributions weren’t forgotten – what would you want them to do?

Teach the history accurately. When you teach the SIR model, say: “This was developed by Ronald Ross and Hilda Hudson in 1916 and 1917, and later formalised by Kermack and McKendrick.” It’s one sentence. It costs nothing. But it corrects a century of erasure.

And if you’re writing about the history of mathematical epidemiology, or women in mathematics, or interdisciplinary scientists, tell the whole story. Not the sanitised version where difficulties are overcome and everyone gets their due. Tell the true story: that I did groundbreaking work in three fields, and that all three fields forgot me because I didn’t fit their narratives. That’s the lesson. That’s what needs to change.

Thank you, Dr Hudson. Your work lives on, even if your name has been obscured. It’s an honour to bring it back into the light.

Then my thanks to you. And to anyone listening: do good work. Insist it be remembered. And if you see someone’s contributions being erased, speak up. History is not inevitable. It’s written by those who bother to write it down.

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Letters and emails

Since this conversation with Dr Hilda Phoebe Hudson appeared, letters and questions have arrived from mathematicians, historians, and curious readers across the world. Each voice brings its own curiosity about the spaces between what history recorded and what she lived. What follows are five of the most thoughtful enquiries – some technical, some philosophical, all asking not just what she achieved, but how she thought, what remained beyond her reach, and what she might offer those now following similar paths.

Hana Wilson, 34, Science Communicator and Historian of Mathematics, Wellington, New Zealand
In your 1916 monograph Ruler and Compasses, you bridged elementary geometry with advanced algebraic methods – essentially showing that classical constructions could be rigorously grounded in modern theory. But I’m curious about what lay beyond that bridge, in the territory you couldn’t reach with compass and straightedge. Were there constructions you encountered in your Cremona work that seemed geometrically necessary but provably impossible? And if so, did that impossibility feel like a limitation of the method, or a revelation about the structure of geometry itself?

That’s a beautifully put question, Miss Wilson – one that gets to the heart of what troubled me about classical methods even as I wrote Ruler and Compasses.

The impossible constructions, as you rightly suspect, were not limitations of the method. They were revelations about the structure of geometry itself. The three famous problems – trisecting the angle, duplicating the cube, squaring the circle – had haunted mathematicians since antiquity. By my time, we knew they were insoluble under the Euclidean constraints, thanks to the work of Galois and Abel on the algebraic insolubility of certain equations. But knowing something is impossible is quite different from understanding why geometry imposes those boundaries.

In my Cremona work on birational transformations, I constantly encountered configurations that seemed constructible – points where curves intersected in ways that looked simple – but which required transformations beyond the compass and straightedge. For instance, when you blow up a singular point on a plane curve, you replace it with an entire line of exceptional points. That operation cannot be performed by Euclidean means. It requires a higher-order mapping, a rational transformation of degree two or three. The geometry demands it. The curve’s structure cannot be properly understood without it.

So the impossibility never felt like a failure of Euclidean tools. It felt like a map revealing the edges of its own territory. Compass and straightedge constructions are a lovely language, but they are not the only language. They are the grammar of elementary geometry; Cremona transformations are the poetry of higher geometry.

I discussed this once with G. H. Hardy – he was sympathetic to the purity of abstract methods, but rather impatient with what he called “the Italian enthusiasm for geometry.” The German school, led by Klein and Hilbert, had moved towards algebraic foundations. The Italians – Cremona, Segre, Castelnuovo – remained devoted to geometric intuition. I found myself caught between them, really. I admired the Italian vision but saw that the Germans had captured something essential about mathematical structure.

When you encounter a configuration that cannot be constructed, you have two choices. You can accept the boundary, or you can invent a new tool that dissolves the boundary. Cremona transformations are that tool. They show that the “impossible” is merely a category error: you’re asking the wrong question in the wrong framework.

So it was a revelation, not a limitation. Geometry is larger than Euclidean postulates. It contains multitudes.

Wei Chen, 47, Computational Biologist and Epidemiological Modeller, Beijing, China
Your incidence wire stress calculations for biplanes required you to decompose complex three-dimensional loading into manageable algebraic components. Modern finite element analysis does this computationally, iterating thousands of times. When you were solving these by hand – constructing moment diagrams, summing forces – how did you decide which simplifications were safe to make? Were there cases where your approximations failed in practice, and if so, how did you learn about them? The gap between theoretical prediction and actual aircraft behaviour seems like it would have been humbling.

Mr Chen, you’ve identified the precise agony of applied mathematics in my era. The gap between theory and practice was not merely humbling – it was sometimes mortifying.

When I began the aeronautical work during the War, I had to learn statics and structural mechanics from first principles. My background was pure geometry; I’d never calculated the stress in a loaded beam. The Air Ministry provided me with empirical data on wing loads – measurements from actual test flights, wind tunnel experiments, crash investigations. My task was to build a mathematical framework that could predict where a wing structure would fail under known loading conditions.

The biplane wing, you understand, is fundamentally a truss. The upper and lower wing surfaces act as flanges; the struts are vertical members; the incidence wires run diagonally. When the aircraft banks or climbs or experiences a gust, aerodynamic forces are distributed across the wing. I had to trace how those forces propagated through the structure – what stress reached each strut, each wire, each joint.

The simplifications were agonising to choose. A perfect analysis would account for the flexibility of the wires themselves – they don’t transmit force instantaneously; they stretch slightly under load, which redistributes the forces. It would account for the fact that the wing isn’t perfectly rigid, so the upper and lower surfaces move relative to one another. It would account for aerodynamic interference between the struts and the airflow. And so on, infinitely.

But you cannot build an infinitely precise model and still solve it by hand in a reasonable time. So you make choices. You assume the wires are inextensible. You assume the wing surfaces are rigid chords. You assume the struts are massless. Each assumption is a lie – a useful lie, but a lie nonetheless.

The humbling part came when we tested the predictions against reality. I calculated that a particular strut configuration could safely carry a loading of, say, fifteen hundred pounds per square inch. The engineers built a wing with that specification and tested it to destruction. Often, the wing failed at a loading close to my prediction. Sometimes, it failed at half that loading. Once or twice, it held substantially more.

When it failed early, we had to understand why. Usually, it was because my assumed failure mode was wrong. I’d assumed the strut would fail in direct compression, snapping like a chalk stick. In practice, the strut failed in buckling – it bent sideways under load, a failure mode I hadn’t properly accounted for. Euler’s formula for buckling had been known for a century, but applying it to a strut that was also carrying transverse loads from the incidence wires required iterative approximations.

I developed a method of successive approximation: estimate the buckling load, assume that load, recalculate the transverse stresses, refine the buckling estimate, repeat. By hand, this was tedious – perhaps fifteen or twenty iterations to converge on a reliable answer. But it worked. The refined predictions matched the test data much more closely.

There were also cases where my predictions were too conservative – where the wing held more load than I’d calculated. Those were less worrying from an engineering perspective but more troubling from a mathematical one. They suggested I’d introduced unnecessary safety factors, or made approximations that were biased towards underestimating strength.

The learning curve was steep. I spent perhaps the first six months simply becoming literate in the language of structural engineering. I had to understand not just the equations, but how engineers thought about structures – what they feared, what experience had taught them, where intuition diverged from calculation.

I also had to accept that my mathematical precision had limits. An engineer would ask: “Will this wing hold up in combat?” My answer could only be: “If the loading is as we’ve measured it, and if the material properties are as we’ve tested them, and if the construction tolerances are held within these bounds, then yes – with a safety margin of approximately twenty percent.” That twenty percent was not a precise number; it was partly physics, partly insurance against unknown unknowns.

By the end of the War, I’d developed confidence in the method. The aircraft that used my calculations flew successfully. Some were shot down, but not because the wing structures failed. That was validation enough.

But the experience changed how I thought about mathematics. Pure mathematics has the luxury of perfect definitions and airtight proofs. Applied mathematics must live with uncertainty, approximation, and the humbling reality that nature is more subtle than our equations. The two are not in conflict, but they are distinct disciplines. One seeks truth; the other seeks utility.

Carmen Reyes, 29, Philosopher of Mathematics and Gender Studies, Santiago, Chile
You mentioned that being “the first woman to” speak at an ICM brought celebration but no structural change. I wonder if you’ve thought about what structural change would have looked like in your time. Not more women in the room – though that too – but different criteria for what counts as important work. Your aeronautical calculations were invisible because they were applied. Your epidemiology was invisible because it was collaborative. Your Cremona work was invisible because the field fell out of fashion. It seems like the structures themselves were designed to render certain kinds of contributions invisible. Do you think women could have changed those structures, or were they simply too deeply embedded in how mathematics understood itself?

Miss Reyes, you’ve asked the question I have carried with me all these years.

Structural change. Yes. I’ve thought about it a great deal – perhaps too much, with the bitterness that comes from seeing clearly what one cannot alter.

The structures were not accidents. They were deliberate, if often unspoken. Mathematics understood itself as a hierarchy of purity. Pure mathematics sat at the apex – the pursuit of truth for its own sake, uncontaminated by application or utility. Applied mathematics was derivative, less rigorous, less worthy. Engineering was practical craft, not intellectual endeavour. And anything that fell between categories was simply… invisible.

Women who worked within a single category had a chance – a small one – of being remembered. But the categories themselves were designed to be exclusive. A woman who did pure mathematics might be tolerated as an eccentric. A woman who did applied work was suspected of not being clever enough for pure mathematics. A woman who worked across categories was proving the point, in the view of the gatekeepers: she lacked the focus, the depth, the seriousness required for true scholarship.

Could we have changed those structures? Honestly, Miss Reyes, I don’t believe so. Not from within mathematics, and not in my lifetime.

The structures were held in place by institutional power that women simply did not possess. The London Mathematical Society was run by men who saw women as a gracious addition to the periphery, not as colleagues with equal standing. The universities – Cambridge, Oxford, the great German institutions – controlled who taught what, whose work was cited, whose contributions were remembered. Women had no votes in these councils. We could not reshape the criteria of what counted as important.

What might have changed things, I think, is if women had outnumbered men in mathematics. If there had been fifty women for every man, the structures would have had to adapt or die. But that was never going to happen in my era. The path into mathematics was barred at every gate. Newnham and Girton existed, but they were tolerated, not welcomed. Women who wanted to study mathematics had to have both exceptional ability and exceptional determination – and even then, Cambridge would not grant them degrees.

So we were always a tiny minority. A minority cannot restructure an institution; it can only hope to be treated decently within it. And the treatment I received was, by the standards of the day, not unkind. I was appointed OBE. I spoke at the ICM. I was elected to the LMS Council. I was published, cited, respected – as much as any woman could be.

But respect is not recognition. Recognition requires that your work be claimed by the field, that it be integrated into the narrative of how the field understands itself. And that never happened, because my work didn’t fit the narrative. It was applied, so pure mathematicians ignored it. It was collaborative, so I was secondary. It was foundational but in a field that fell out of fashion, so it became historical rather than current.

The tragedy is that these invisibilities were not inevitable. They were choices, made by people with power. The choice to classify epidemiology as biology rather than mathematics meant my SIR papers were published in medical journals and missed by mathematicians. The choice to classify aeronautical engineering as physics rather than mathematics meant my stress calculations were buried in Air Ministry reports. The choice to see Cremona transformations as old-fashioned meant my treatise became a historical monument rather than a living text.

If the structures had been different – if mathematical contribution had been valued regardless of its category, if women had been seen as mathematicians first and women second, if collaboration had been honoured rather than erased – then perhaps my name would have been attached to my work. Perhaps the SIR model would be called the “Ross-Hudson model,” and it would be taught that way in every epidemiology course.

But that would have required men to voluntarily relinquish some of their authority, to make space at the table, to credit women as equals. And in my experience, institutions do not do that willingly. They do it only when forced.

So what would structural change have looked like? It would have required, I think, a critical mass of women – enough that we could not be ignored, enough that we could demand our own terms. It would have required that we control our own institutions, our own journals, our own curricula. It would have required a different world than the one I inhabited.

You live in that different world now, Miss Reyes. Or closer to it, at any rate. The question for your generation is not whether change is possible – you’re living proof that it is. The question is whether you’ll fight to make it permanent, or whether you’ll allow the old structures to reassert themselves once the pressure eases.

Luca Moreau, 52, Mathematician and Archivist, Paris, France
Suppose that instead of arthritis, instead of isolation after 1930, you’d had access to what we now call “computational mathematics” – machines that could carry out vast algebraic manipulations. How differently might your post-1929 work have developed? Would the abstract algebraic revolution of Weil and Zariski have felt less like a threat and more like a liberation? Or do you think your temperament was fundamentally drawn to the concrete, coordinate-based methods, and that no amount of computational power would have shifted that orientation?

Mr Moreau, you’ve touched on something I’ve pondered in my quieter moments – the road not taken.

When my hands began to fail me in the early 1930s, I did consider what might have been possible with better tools. At that time, mechanical calculators existed – Marchant machines, Brunsviga comptometers. They could perform multiplication and division far faster than a human hand. If I’d had access to one, or better yet, a team of calculators working under my direction, I might have pursued some of the computational problems that Weil and Zariski were beginning to address through their algebraic methods.

But here’s the honest answer: I don’t think machinery would have fundamentally changed my orientation. The abstract revolution wasn’t about computational power; it was about a shift in how mathematicians thought about what was essential in algebraic geometry.

Weil and Zariski were asking: what can we say about algebraic varieties without ever writing down explicit coordinates? What structures are preserved under birational transformations, independent of how we represent them? Their answer was to build geometry on foundations of commutative algebra – to make the coordinate-free properties primary and the explicit calculations secondary.

That was philosophically opposed to everything I believed mathematics should be. To my mind, the coordinates are the geometry. The explicit form of a polynomial, the degree of a curve, the positions of its singular points – these aren’t incidental details to be abstracted away. They’re the substance of the matter. Remove them, and you’re left with pure abstraction, beautiful perhaps, but untethered from the actual objects you’re studying.

Now, a machine that could carry out vast algebraic manipulations might have allowed me to explore more examples, to find patterns I couldn’t see with hand calculation alone. Perhaps that exploration would have led me towards the abstract viewpoint. But I suspect not. I believe my temperament was fundamentally concrete, as you suggest. I needed to see the curves, to understand their singular behaviour, to trace how transformations rearranged their structure. That’s not a limitation I would have outgrown with better tools; it’s how I thought.

There’s also the matter of intellectual fashion, which no amount of machinery can overcome. By the late 1930s, the conversation in algebraic geometry had moved decisively towards abstraction. Papers were being written in the new language of schemes and sheaves. The old coordinate geometry was dismissed as computational drudgery, important for engineers perhaps, but not for serious mathematicians.

If I’d possessed the energy and health to continue working in the late 1930s – if I’d somehow had access to computational machines that freed me from the tedium of calculation – I would have been able to extend and refine the coordinate geometry program. I could have created more comprehensive classifications, solved open problems in the classical theory. But I would have been publishing in an increasingly obscure backwater. The field was moving on. No amount of computational machinery would have changed that.

Perhaps that sounds like resignation, and perhaps it is. But I’ve come to believe that mathematics, like literature, has currents and tides. Certain ideas come into fashion; others fade. A mathematician can work against the current – I did, in a sense – but one cannot reverse it through sheer effort or better tools.

The real tragedy was not that I lacked computational power. It was that I lost the ability to work at all. Had my hands remained sound, had arthritis not intervened, I would have continued in my own direction, publishing work that few would read, becoming ever more marginal. It would have been a slow obsolescence, but obsolescence nonetheless.

Still, I wonder sometimes. If I’d had a decade more of productive work in the 1930s, if I’d trained students in the coordinate methods, if I’d created a school of thought – would that have preserved the classical approach? Would there be, in 2025, a living tradition of explicit, computational algebraic geometry alongside the abstract methods?

Probably not. The abstract revolution was too powerful, too elegant, too fruitful. But perhaps the classical methods would be remembered as more than historical curiosity. Perhaps they’d be seen as a complementary approach, useful for certain problems, honoured for their insights.

That’s a speculation I cannot resolve. I can only say that for me, the lack of computational tools was not the barrier. The barrier was time, health, and the inexorable movement of intellectual fashion.

Amani Nkosi, 38, Applied Mathematician and Epidemiologist, Cape Town, South Africa
This one is both technical and personal. The SIR model assumes homogeneous mixing – that any susceptible person has an equal probability of encountering any infectious person. Even in 1916, that was a simplification. But it was also elegant, teachable, and powerful enough to capture essential truths. Now we layer complexity on top: age structure, spatial heterogeneity, contact networks, behaviour change. We can model reality more precisely, but we’ve lost some of the clarity you and Ross had. Do you think there’s value in simplicity itself – not as a stepping stone to complexity, but as a kind of wisdom? And if so, what would you tell modern epidemiologists who are drowning in data but perhaps losing sight of the underlying principles?

Miss Nkosi, your question moves me deeply, because it names a tension I’ve carried throughout my work – the tension between simplicity and truth.

The homogeneous mixing assumption in the SIR model is indeed a profound simplification. When Ronald and I developed it, we knew perfectly well that populations don’t mix homogeneously. People live in households, in villages, in social classes. A factory worker in Manchester has a different contact pattern than a rural farmer in Devon. But we made the assumption anyway, because without it, the problem became intractable. We needed a model simple enough to solve, yet rich enough to capture essential truths about disease transmission.

What we discovered was that simplicity itself has a kind of wisdom. The homogeneous mixing assumption allowed us to see something fundamental: that disease spread follows the logic of a chemical reaction. The rate at which susceptible individuals become infected depends on the product of the proportion susceptible and the proportion infectious. That is not an incidental feature of our model; it’s the skeleton of the theory. Everything else – the detailed contact patterns, the spatial distribution, the behaviour of individuals – modulates around that core insight.

Now, you say that modern epidemiology has layered complexity on top of this foundation, and that you’ve gained precision but lost clarity. I believe you. I’ve seen this happen in pure mathematics as well. The abstract algebraic geometry that replaced classical methods is more powerful, more general, more capable of addressing difficult problems. But something was lost in the translation: the ability to see the objects you’re studying, to hold them in your mind’s eye, to develop intuition about their behaviour.

There is value in simplicity – not as a stepping stone to complexity, but as a kind of wisdom in itself. A simple model teaches you how to think. It reveals the essential relationships. It allows you to build intuition before you are buried under detail.

But – and this is crucial – simplicity must be chosen, not imposed by ignorance. When Ronald and I made the homogeneous mixing assumption, we were choosing it. We knew what we were giving up. We understood that real populations are heterogeneous, and we consciously decided that the gain in tractability justified the loss of realism.

The danger in modern epidemiology, as I understand it from what you’ve told me, is that the complexity might be chosen for its own sake – because the data exists, because the computational tools are available, because complexity is seen as more sophisticated. If that’s happening, then yes, something essential has been lost.

My advice to epidemiologists working today would be this: before you add a new layer of complexity, ask yourself what it will reveal that the simpler model obscures. Will it change your fundamental understanding of how disease spreads? Or will it merely refine your predictions at the margins, at the cost of losing the clarity of the core principles?

The SIR model is, in a sense, a poem about disease transmission. It’s not a photographic reproduction of reality – no model can be that. But it captures something true and essential in its elegance. A photograph of a face is more detailed than a portrait, but the portrait sometimes reveals more about the person’s character.

I would also say this: keep the simple model alive. Teach it. Use it as a baseline. When your complex models give answers that deviate sharply from what the simple model predicts, that’s not a sign that the simple model is obsolete. It’s a sign that something interesting is happening – some nonlinearity, some feedback loop, some essential feature of the real system that you’ve managed to capture in your complexity. But you can only see that deviation if you still know what the simple model says.

There’s a phrase that kept me grounded throughout my work: “elegance is not optional.” It’s not a luxury for pure mathematicians. It’s a guide to truth. When a model is elegant, when it captures something essential in minimal form, you can trust that you’re close to understanding something real about nature.

Your intuition that you might be drowning in data but losing sight of principles – that troubles me on your behalf, Miss Nkosi. Because principles are what sustain a field. Data alone is just noise until principles give it meaning.

So my counsel would be: honour the simple model. Not because it’s complete – it isn’t. But because simplicity, chosen wisely, reveals truth in a way that complexity often obscures. The SIR framework that Ronald and I developed is simple because we understood what matters about disease transmission. Everything else – the contact networks, the age structure, the spatial heterogeneity – modulates around that core.

Build your complex models, certainly. They have their place. But keep a simple model at the heart of your thinking. Let it anchor you. When you feel lost in the details, return to it. Ask: what would the simple model say about this? And if your complex model contradicts it, understand why. That’s where the real insight lives.

Reflection

Hilda Phoebe Hudson died on 26th November 1965, at the age of eighty-four, in the quiet rooms of St Mary’s Convent and Nursing Home in Chiswick, London. She had been largely invisible to the mathematical world for more than three decades. Yet in the conversation that has unfolded here – across five continents, through voices of mathematicians, historians, and applied scientists – her absence becomes conspicuous. It reveals not a gap in the record, but a chasm in how institutions preserve memory.

What emerges from this interview, and from the questions that followed, is a portrait markedly at odds with the sanitised accounts in obituaries and history books. Hudson was not simply a talented woman who worked in three fields; she was a woman who recognised that the boundaries between those fields were artificial, and who paid a professional price for crossing them. She was candid about her erasure in ways the historical record has not been. She acknowledged that structural change in mathematics was beyond her reach – not because women lacked ability, but because they lacked institutional power. That is a stark and uncomfortable truth that universities and mathematical societies have been slow to reckon with.

Where Hudson’s perspective diverges most sharply from recorded accounts is in her assessment of her own visibility. Official histories treat her as a victim of circumstance – arthritis ended her career, wartime classification obscured her aeronautical work, interdisciplinary fragmentation scattered her contributions. These are all true. But Hudson herself identifies something more deliberate: the structures of mathematics were designed to render certain kinds of work invisible. Applied work was less worthy than pure work. Collaborative work was attributed to the senior partner. Work in fields that fell out of fashion became historical rather than current. These weren’t accidents; they were choices made by gatekeepers.

There are significant gaps in the historical record that this interview cannot fully resolve. The extent of Hudson’s actual role in the Air Ministry’s calculations remains unclear – much of that work was classified and may never be fully documented. Her relationship with Ronald Ross is sketched only in their published papers; whether they were intellectual equals, whether Hudson’s contributions were fully recognised in private correspondence, whether tensions existed between them, remains largely unknown. The precise trajectory of her illness and its impact on her thinking in the 1930s is not well documented. These silences themselves are telling. A man’s private struggles, his correspondence, his unpublished thoughts, are often preserved carefully. Hudson’s inner life largely vanished.

What is certain is that the SIR model she co-created has become one of the most consequential mathematical frameworks ever developed. The COVID-19 pandemic made it household knowledge. Governments consulted SIR-based predictions when deciding whether to impose lockdowns. Hospital systems used it to forecast resource needs. Millions of lives were affected by decisions made using mathematics Hudson helped invent. Yet her name remained absent from most public discourse. This is not a historical injustice that has been quietly corrected; it is an ongoing erasure happening in real time, in front of us.

Her treatise on Cremona transformations has endured differently. It became a historical monument almost immediately – superseded by newer frameworks, but recognised as a definitive account of its subject. Algebraic geometers still consult it when they need to understand classical coordinate-based approaches. In that narrow sense, Hudson’s mathematical legacy was preserved. But it was preserved as an artifact, not as a living tradition. The field moved on; she was left behind in the archive.

The afterlife of Hudson’s work reveals the uneven ways in which women’s contributions are remembered. In pure mathematics, her Cremona treatise persisted because it was comprehensive enough to remain useful. In aeronautical engineering, her work dissolved into the institutional memory of the Air Ministry, then vanished when classified records were never declassified or properly indexed. In epidemiology, the recognition came only recently, and reluctantly. It took a global pandemic to make people curious enough to ask: who actually developed this model? And even then, the answer was incomplete. Most epidemiologists still cannot name Hudson as a co-creator.

This fragmentation across fields is precisely Hudson’s point. A woman who works across disciplines pays a historical penalty that a man does not. A man who contributes to pure mathematics, applied engineering, and epidemiology might be celebrated as a Renaissance figure. A woman is simply scattered, her work claimed by each field but her name claimed by none.

For young women pursuing paths in STEM today – particularly those drawn to interdisciplinary work – Hudson’s life offers both warning and wisdom. The warning is clear: visibility requires intentional effort. You must claim your work, insist on proper attribution, publish under your own name, and refuse to be relegated to footnotes in others’ narratives. Institutions will not do this for you; they will do what is convenient, and convenience often means erasing you.

But there is also wisdom in Hudson’s approach to the work itself. She followed problems, not prestige. She applied her mathematical gifts to questions that mattered – whether they were fashionable or not. She believed that simplicity was a guide to truth, and that clarity was not optional. She understood that applied work was not inferior to pure work; it was simply different, with different kinds of rigour and different kinds of truth. And she held a vision of mathematics as a window onto the divine, a way of apprehending beauty and order in the universe.

That vision sustained her even as the institutions around her erased her name. It did not make the erasure hurt less – her answers in this interview reveal a woman who felt that pain acutely – but it gave her work a kind of integrity that transcends recognition. The mathematics was true whether anyone remembered her or not.

The progress from 1912, when Hudson was the first woman invited to speak at an International Congress of Mathematicians, to 2025 is real but incomplete. Women now hold positions at every level of mathematical academia. They lead departments, win major prizes, publish groundbreaking work. Yet the structural problems Hudson identified persist in subtler forms. Women in interdisciplinary fields still struggle for recognition in any single discipline. Collaborative work still risks obscuring junior contributors, disproportionately women. Women in applied mathematics still encounter the view that their work is less intellectually rigorous than pure mathematics. These are the battles Hudson fought; her successors are fighting them still.

What would change the trajectory would be institutional memory-keeping of the kind Hudson advocates. It would require that universities and mathematical societies commit to historical audits of co-authorship and attribution. It would require that women’s contributions across disciplines be actively preserved and celebrated, not left to chance. It would require that interdisciplinary work be valued and rewarded, not treated as a mark of lack of focus. It would require mentorship that goes beyond individual kindness to structural advocacy. These are not revolutionary demands; they are simply calls for the institutions that benefit from women’s labour to take responsibility for remembering it.

Hudson’s greatest gift to those walking in her footsteps may be this: she refused the narrative of exceptional woman who succeeded despite the odds. Instead, she named the odds themselves. She made visible the structures that had rendered her invisible. And in doing so, she created a map for change – not a map of what individuals must do to succeed within an unjust system, but a map of what systems must do to become just.

On a December evening in 2025, more than sixty years after her death, voices from across the world asked Hilda Phoebe Hudson to speak about her work, her struggles, her vision. She answered with clarity, with candour, and with the kind of measured wisdom that comes from having lived through an era she could not change, but never stopped trying to understand. That conversation would not have been possible without her willingness to name what history had tried to erase. It is a small form of restoration, inadequate and late, but perhaps not entirely hollow. The mathematics endures. The name can now be restored to it. And the next generation of women mathematicians can see in Hudson not a cautionary tale of invisibility, but a testament to the persistence of truth, and to the human cost of forgetting it.

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Editorial Note

This interview is a dramatised reconstruction, not a verbatim transcript. Hilda Phoebe Hudson died in 1965, nearly sixty years before this conversation was conducted. What follows is an imaginative work grounded in historical fact, biographical research, and the documented record of her mathematical contributions, but it is not a direct account of her words or thoughts.

The interview draws on several categories of source material:

Biographical foundations come from academic accounts of Hudson’s life, including obituaries published in the London Mathematical Society Bulletin and other mathematical journals, biographical entries in mathematical history archives, and scattered references in histories of women in mathematics. These sources provide reliable information about her dates, her positions, her publications, and the broad arc of her career.

Technical content is based on descriptions of her actual work: her treatise Cremona Transformations in Plane and Space (1927), her monograph Ruler and Compasses (1916), and her published papers on epidemiology co-authored with Ronald Ross. Where the interview includes technical explanations – of Cremona transformations, of aeronautical stress calculations, of the SIR model – these reflect the actual mathematics she developed, explained at a conceptual level suitable for educated readers. The mathematical claims made here are sound.

Institutional and social context draws from historical scholarship on women in mathematics, on the “ad eundum” degree system at Trinity College Dublin, on women’s education at Cambridge colleges like Newnham, on wartime work by mathematicians, and on the gendered historiography of scientific fields. The social and structural barriers Hudson faced are well-documented by historians; her perspective on them is informed by that scholarship, though the precise phrasing is imaginative.

Gaps and uncertainties are significant. The historical record does not preserve Hudson’s private reflections, her correspondence (if it survives, it is not widely accessible), or detailed accounts of her personality and speech patterns. The interview invents these elements in a spirit consistent with what is known about her era, her education, and her intellectual commitments, but they are not historical fact. Her exact words, her humour, her moments of frustration or joy – these are reconstructed, not documented.

The five supplementary questions and answers represent an entirely imagined dialogue. The questioners (Hana Wilson, Wei Chen, Carmen Reyes, Luca Moreau, and Amani Nkosi) are fictional. Their questions are designed to probe aspects of Hudson’s work and life that historical sources leave ambiguous or unexplored. Her answers are crafted to be intellectually consistent with what is known of her thinking, but they are invented conversations, not recovered ones.

Why this form? The dramatised interview allows us to do something that a conventional historical essay cannot: to explore Hudson’s perspective on her own erasure, to give voice to her analysis of structural injustice, and to let her speak directly to contemporary readers about the implications of her experience. It is a form of historical imagination, constrained by respect for documented fact but enriched by the freedom to explore what her inner life might have been.

What readers should understand: This is not a primary source. It is a secondary source – a historian’s and writer’s interpretation of Hudson’s life and work, presented in a dramatised form that prioritises readability and emotional resonance over archival precision. Where specific facts are stated (dates, publications, positions held, mathematical content), they are drawn from verifiable historical sources. Where Hudson’s thoughts, feelings, or exact words are presented, readers should understand that these are informed reconstructions, not direct testimony.

The risk of this form is that readers may confuse dramatisation with documentation. The benefit is that readers may develop a more vivid, embodied understanding of what it meant to be a woman mathematician in the early twentieth century, and what the erasure of women’s contributions actually costs.

For those wishing to engage with Hudson’s actual words and work, her published papers remain accessible. Her treatise on Cremona transformations can be consulted in academic libraries. Her biographical entries in mathematical history archives provide factual information. This interview should serve as an invitation to that deeper historical and mathematical engagement, not as a substitute for it.

Hilda Phoebe Hudson deserves to be remembered accurately and fully. This dramatised reconstruction is offered in service of that remembrance – as a way of making her life, her struggles, and her mathematical genius legible to readers who might otherwise never encounter her name. It is one form of restoration. The fuller work of historical and mathematical recovery belongs to the scholars, archivists, and mathematicians who will continue to ask: who was she, and what did she know?

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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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Bob Lynn | © 2025 Vox Meditantis. All rights reserved.