Vox Meditantis

Maryam Mirzakhani (1977-2017) was a revolutionary Iranian mathematician whose work bridged the vast spaces between pure mathematics and theoretical physics, geometry and dynamics, abstraction and profound insight. She became the first woman and the first Iranian to win the prestigious Fields Medal in 2014, recognised for her groundbreaking contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces. Her approach to mathematics was as distinctive as her discoveries – she would map out vast theoretical landscapes on enormous sheets of paper, creating what her young daughter called “paintings” of mathematical universes that curved and twisted beyond human imagination.

Today we welcome Maryam to reflect upon a body of work that has transformed how we understand complex surfaces in higher dimensions, from the quantum mechanics governing subatomic particles to the computer graphics rendering virtual worlds. Her research on curved spaces revealed deep connections between seemingly disparate fields, whilst her journey from a Tehran mathematics classroom to Stanford’s halls illuminates both the barriers faced by women in science and the profound beauty that emerges when brilliant minds are given space to flourish.

Maryam, it’s wonderful to have you with us. I’d like to begin with your childhood in Tehran during the Iran-Iraq War. Mathematics wasn’t your first love – you wanted to be a writer. What shifted your path toward numbers and surfaces?

You know, I always tell people that my older brother was the one who really opened that door for me. I was eight years old, making up stories about a girl who could travel the world and achieve great things. Then one day my brother came home from school and told me about this German mathematician called Carl Friedrich Gauss. He explained how, when Gauss was young, his teacher asked the class to add all the numbers from one to one hundred, expecting it would keep them busy for ages. But Gauss found an elegant solution in seconds – he realised you could pair the numbers: one plus one hundred equals one hundred and one, two plus ninety-nine equals one hundred and one, and so on. Fifty such pairs, each summing to one hundred and one. The answer: 5,050.

That was the first time I experienced the joy of a beautiful solution. It wasn’t just about getting the right answer – it was about finding this hidden pattern, this unexpected elegance. Mathematics suddenly felt like storytelling in a different language.

That sense of storytelling through mathematics became central to your approach. At Farzanegan School, you met your lifelong friend Roya Beheshti, and together you became the first Iranian girls to compete in the Mathematical Olympiad. How did that early recognition shape your understanding of what was possible?

Roya and I, we were just two girls who loved solving problems together. We would spend hours in bookshops, buying mathematics books, working through challenging problems late into the night. I remember for the 1995 Olympiad, there was this particularly difficult problem that everyone gave up on after a few hours. But I stayed awake all night, turning it over in my mind, drawing diagrams, trying different approaches. When I finally solved it at dawn, I felt this tremendous satisfaction – not because I’d won anything, but because I’d pushed through to understanding.

The Olympiad medals were wonderful, but what mattered more was learning that persistence could unlock doors that seemed permanently closed. In Iran at that time, there were many who believed girls couldn’t excel in advanced mathematics. Our success wasn’t just personal – it was proof that talent and determination matter far more than gender or background.

You’ve spoken about the 1998 bus accident that killed seven of your fellow Sharif University students, whilst you and Roya survived. How did that tragedy influence your perspective on mathematics and life?

That was… it changed everything, really. Seven bright young mathematicians, my friends, gone in an instant. Roya and I were among the few survivors, and for a long time I couldn’t understand why. It made me realise how precious and fragile our time truly is.

It taught me not to waste energy on small worries or external recognition. When I later received attention for the Fields Medal, I felt uncomfortable with all the fanfare – I kept thinking about those friends who never had the chance to see their mathematical dreams unfold. Their loss taught me to focus on the work itself, on pushing the boundaries of understanding, rather than on achievement for its own sake.

Moving to Harvard for your PhD under Curtis McMullen’s supervision marked another major transition. Can you walk us through your thesis work on hyperbolic surfaces and moduli spaces – perhaps explaining it first for mathematicians, then for a broader audience?

Certainly. For mathematicians, I was studying the Weil-Petersson volumes of moduli spaces of Riemann surfaces of genus g with n geodesic boundary components. The central breakthrough was establishing a recursive formula that expressed these volumes as polynomials in the boundary lengths.

Specifically, if you have a surface and you perform a “hyperbolic cutting” along a simple closed geodesic of length L, you get two simpler surfaces. The volume formula respects this decomposition, allowing the coefficients to be computed recursively. This connected the geometric problem of counting simple closed geodesics on a single surface to the algebraic problem of computing intersection numbers on moduli space.

And for those without a mathematics background?

Imagine you’re trying to understand all possible shapes that a piece of clay can take when you stretch and bend it – but you can’t tear it or glue pieces together. Topologically, surfaces are classified by their genus: a sphere has genus zero, a doughnut has genus one, a pretzel has genus three.

But within each topological type, there are infinitely many different geometric shapes. The collection of all these possible geometric structures forms what we call a “moduli space” – essentially a universe where each point represents a different way of shaping your clay.

My thesis developed a method for measuring the “volume” of these universes. It’s like asking: if you randomly selected a shape from all possible doughnut configurations, what’s the likelihood it would have certain properties? This seemingly abstract question turned out to have profound connections to counting problems in geometry and even to theoretical physics.

One of your most celebrated results was providing a new proof of the Witten conjecture, which connects mathematics to quantum gravity. How did your geometric approach illuminate this physics problem?

Edward Witten had conjectured a formula relating intersection numbers of certain cohomology classes on moduli spaces to gravitational physics. The traditional approaches were quite technical, involving integrable systems and matrix models.

My geometric proof emerged naturally from the volume calculations. When you cut a Riemann surface along a geodesic, you’re performing a geometric operation that has an algebraic shadow in moduli space. By carefully analysing how these cutting operations behave under the recursive volume formula, I could establish relationships between different types of intersection numbers.

The beautiful thing was that the physics problem – about gravitational interactions in quantum field theory – turned out to be asking the same mathematical questions as my geometric counting problems. It’s a perfect example of the unreasonable effectiveness of mathematics: pure geometric intuition about curved surfaces provides insights into the fundamental structure of spacetime.

Your later work with Alex Eskin and Amir Mohammadi on orbit closures in moduli spaces has been described as groundbreaking. Can you explain what you discovered about the regularity of complex geodesics?

This was really about understanding chaos versus order in dynamical systems. When you have a flow on a space – imagine water flowing over a landscape – the question is: what do the flow lines look like over long periods of time?

For real geodesics in moduli space, the behaviour is typically chaotic. Flow lines can form fractal cobwebs, never settling into predictable patterns. But we proved that complex geodesics – which are holomorphic immersions from the hyperbolic plane – behave completely differently.

We showed that the closure of any orbit in the space of holomorphic quadratic differentials is an affine subvariety. This is analogous to Ratner’s theorem for unipotent flows on homogeneous spaces, but the moduli space setting is far more inhomogeneous.

The proof combined tools from Teichmüller theory, algebraic geometry, and ergodic theory. We used the notion of “cylinder deformations” and showed that any accumulation point of an orbit must preserve the periods of holomorphic differentials up to the action of the appropriate linear group.

This relates to your work on earthquake flow as well. William Thurston had introduced this flow as a way of understanding deformations of hyperbolic surfaces, but its ergodic properties were mysterious. What did you prove?

Thurston’s earthquake flow is a beautiful geometric construction. Imagine taking a hyperbolic surface and performing “earthquakes” along a measured lamination – essentially, sliding parts of the surface along fractures. This creates a flow on the space of measured laminations.

I proved that this flow is ergodic and mixing, which means that over long time periods, earthquake paths become uniformly distributed. The key insight was establishing a measurable isomorphism between the earthquake flow and the Teichmüller horocycle flow, whose ergodic properties were already understood.

The technical challenge was that earthquake flow lives naturally in the “hyperbolic world” whilst horocycle flow belongs to the “flat world” of translation surfaces. Bridging these required delicate coordinatisation using Thurston’s shear coordinates and understanding how they interact with the Weil-Petersson symplectic structure.

You mentioned translation surfaces and billiard dynamics. Your work has applications to understanding billiard trajectories on polygonal tables – can you explain this connection?

This is one of my favourite examples of how abstract mathematics connects to concrete problems. When a billiard ball bounces around a polygonal table, tracking its trajectory becomes complicated because of all the reflections off walls.

But there’s an elegant trick: instead of following the ball as it bounces, you can “unfold” the reflections by placing mirror copies of the table edge-to-edge. On this unfolded surface, the ball’s path becomes a straight line! The geometry of this unfolded surface – which is called a translation surface – determines whether trajectories are periodic, dense, or have other special properties.

My work with Alex Eskin on the moduli space of translation surfaces led to results about which points on a billiard table can “illuminate” other points. We proved that on any rational polygonal table, almost every point can illuminate almost every other point – there can only be finitely many “dark spots” that remain forever hidden.

I’d like to turn to your experience as a woman in mathematics. You were often the first – first Iranian girl at the Mathematical Olympiad, first woman to win the Fields Medal. How did you navigate the attention while trying to focus on your research?

You know, I always found the attention quite overwhelming. When I won the Fields Medal, suddenly everyone wanted to interview me, to make me a symbol. But I never saw myself as representing anything beyond my own curiosity about mathematical problems.

The difficulty wasn’t overt discrimination – by the time I reached graduate school, most of my colleagues judged me purely on my mathematical abilities. The harder challenge was subtler: the assumption that my work must be somehow different because I’m a woman, or Iranian, or because I approach problems visually rather than through pure symbol manipulation.

I remember colleagues being surprised that I worked by drawing on large sheets of paper, sketching surfaces and flows rather than starting with formal definitions. My daughter Anahita would watch me work and call it “painting.” I had to learn to trust that my geometric intuition was as valid as anyone’s algebraic approach.

Speaking of visual thinking, your unconventional work style – drawing mathematical landscapes on enormous sheets of paper – became almost as famous as your theorems. How did this develop?

I am a very slow thinker. I need time to understand problems from multiple angles before I can make progress. Writing down formal mathematics immediately felt constraining – like trying to compose poetry while someone demands you follow strict grammatical rules.

But when I draw, I can explore relationships between geometric objects, try different configurations, see how surfaces might fit together or flow apart. The drawing helps me stay connected to the intuitive heart of a problem, even as I work through technical details.

Other mathematicians would sometimes visit my office and find these huge papers covered with sketches of surfaces, flow lines, coordinate systems. It looked chaotic, but for me, it was a way of thinking with my hands as well as my mind.

Your diagnosis of breast cancer came in 2013, just a year before you won the Fields Medal. How did facing mortality influence your approach to mathematics?

It clarified priorities remarkably. Suddenly, time felt both more precious and more fleeting. I stopped worrying about whether my work would be immediately appreciated or understood – I focused on pursuing the problems that genuinely fascinated me.

During treatment, I couldn’t work for long stretches, but when I could focus, my thinking felt sharper somehow. The cancer forced me to be more selective about which problems deserved my limited energy. I think it made me a better mathematician, even as it shortened the time I had.

Looking at how your work is being applied today – in quantum physics, computer graphics, materials science – what surprises you about the trajectory your research has taken?

The quantum applications particularly fascinate me. My work on moduli spaces turns out to be relevant to understanding topological phases of matter, where the quantum state space has the kind of curved geometry I was studying abstractly.

In computer graphics, the surfaces and flows I analysed help with realistic animation – making digital water flow naturally, or ensuring that animated characters move smoothly through complex environments. It’s remarkable that mathematical structures I encountered through pure curiosity turn out to describe phenomena we encounter daily.

What advice would you give to young mathematicians, particularly women or those from underrepresented backgrounds, who might face obstacles similar to what you experienced?

Find the problems that make you lose track of time. Mathematics is too difficult to pursue unless you genuinely love the puzzles it presents. Don’t worry about whether your approach looks like everyone else’s – some of the most important discoveries come from seeing familiar problems from unexpected angles.

And be patient with yourself. I was a slow learner who needed time to develop intuition before I could prove theorems. In a field that sometimes values quick answers, remember that deep understanding often requires years of patient exploration.

Finally, as we look toward the challenges facing mathematics and science today – climate modelling, artificial intelligence, quantum computing – what role do you see your type of geometric thinking playing?

Climate systems are incredibly complex dynamical systems, and understanding their long-term behaviour requires exactly the kind of tools I developed for studying flows on moduli spaces. The mathematical structures underlying machine learning – optimization landscapes, neural network geometries – often have the curved, high-dimensional character of the spaces I studied.

Most importantly, the diversity of approaches in mathematics needs to expand dramatically. The problems facing humanity are too complex for any single mathematical tradition to solve alone. We need geometers working alongside algebraists, physicists collaborating with pure mathematicians, visual thinkers partnering with symbolic manipulators.

The surfaces I studied may seem abstract, but they’re part of the mathematical language we’ll need to describe our complex, interconnected world. Understanding how spaces curve and flow, how different regions connect and separate – these geometric insights will be essential as we navigate the challenges ahead.

Thank you, Maryam. Your work continues to inspire mathematicians worldwide, and your approach to problem-solving offers a model for tackling the profound challenges we face.

Thank you. I hope young mathematicians will remember that the most beautiful discoveries often emerge not from trying to solve famous problems, but from following your curiosity wherever it leads, even into territories that seem impossibly abstract. The universe has a mathematical structure we’re only beginning to understand, and every genuine insight – no matter how small – brings us closer to that deeper comprehension.

Letters and emails

Since our interview with Professor Mirzakhani, we’ve received an extraordinary response from readers around the world who were moved by her insights into mathematical beauty, resilience, and the power of visual thinking. We’ve selected five letters and emails from our growing community who want to ask her more about her life, her work, and what she might say to those walking in her footsteps.

Khadija Mbaye, 34, Mathematical Physics Researcher, Dakar, Senegal
Professor Mirzakhani, your recursive volume formulas have found unexpected applications in string theory and quantum gravity. When you were developing these techniques in the early 2000s, computational tools were far more limited than today’s machine learning approaches to mathematical discovery. How do you think your hand-drawn, intuitive methods might complement or even outperform modern algorithmic approaches to exploring moduli spaces?

You know, Khadija, this is such a fascinating question because it touches on something I’ve been thinking about quite a lot. When I was working on those volume calculations at Harvard and later at Princeton, we had Mathematica and some basic computer algebra systems, but nothing like what exists now. I remember spending weeks just computing examples by hand – calculating the first few cases of the recursion to see if patterns emerged.

That slowness was actually crucial. When you’re forced to work through calculations step by step, you develop an intimate relationship with the mathematical objects. You start to notice small irregularities, unexpected symmetries, places where the formulas seem to “want” to factor in particular ways. These observations often led to the key insights – like realising that certain combinations of intersection numbers were behaving like derivatives of a generating function.

I think there’s something fundamentally different between human pattern recognition and algorithmic pattern detection. When I was sketching moduli spaces, my drawings weren’t just illustrations – they were thinking tools. The way surfaces curved on paper helped me understand how geodesics might flow, how different regions of moduli space connected to each other. That kind of geometric intuition emerges from years of working with your hands, making mistakes, redrawing the same surface dozens of times until you really understand its shape.

Machine learning algorithms can certainly discover correlations that would take humans years to find. But I worry they might miss the “why” behind the patterns. In my experience, the most important mathematical insights come from understanding not just that something is true, but why it has to be true – what geometric or algebraic structure makes it inevitable.

The recursive nature of my volume formulas, for instance, emerged from thinking about how you physically cut a surface apart and glue new boundaries. An algorithm might find the same recursion numerically, but would it understand that this reflects something deep about how hyperbolic geometry interacts with topological operations?

I think the future lies in combining both approaches. Use computational power to explore vast parameter spaces and identify interesting phenomena, but then step back and ask: what is the geometry trying to tell us? Draw pictures. Work through small examples by hand. Let your intuition guide you toward the underlying reasons.

Mathematics isn’t just about finding patterns – it’s about understanding the invisible structures that make those patterns inevitable.

Stefan Petrovic, 41, Science Policy Analyst, Belgrade, Serbia
You mentioned that the 1998 bus accident taught you not to waste energy on external recognition. Yet your Fields Medal brought enormous visibility to both women in mathematics and Iranian scientific achievement during a period of strained international relations. Looking back, do you think there’s an ethical responsibility for groundbreaking scientists to engage with the political dimensions of their recognition, even when they’d prefer to focus purely on research?

Stefan, this is something I’ve thought deeply about, and I’m not sure I have a clean answer. When I won the Fields Medal in 2014, the attention was overwhelming. Suddenly, everyone wanted me to speak about being Iranian, about being a woman, about making statements about politics or educational policy. All I wanted was to continue working on earthquake flows and moduli spaces.

But then I would receive emails from young girls in Iran, or from mathematics students who felt isolated in their programs, saying that seeing me receive this recognition gave them hope. How do you weigh your desire for privacy against that kind of impact?

I think the key distinction is between using your platform responsibly and becoming primarily a political figure rather than a mathematician. I always tried to focus my public comments on mathematics education, on the importance of supporting young researchers regardless of their background, on the beauty of mathematical discovery. These aren’t partisan positions – they’re fundamental human values.

When the Iranian government tried to claim credit for my success while simultaneously restricting educational opportunities for women, I felt I had to speak out. Not as a political activist, but as someone who knows that mathematical talent exists everywhere and deserves to be nurtured. That felt like an extension of my work, not a departure from it.

The hardest part was realizing that my visibility could be both empowering and limiting. Young women would see me and think, “I can become a mathematician too,” which is wonderful. But sometimes the narrative became so focused on my being “the first woman” that the actual mathematics got lost. People would attend my lectures hoping to understand what made me different as a female mathematician, rather than engaging with the geometric ideas themselves.

I’ve come to believe that scientists do have responsibilities beyond their research, but those responsibilities should flow naturally from who we are as people and what we’ve learned through our work. Mathematics taught me that beautiful, universal truths exist regardless of borders or politics. Sharing that perspective – not through grand political statements, but through patient explanation of why mathematical understanding matters – feels like the most honest way to use whatever influence I might have.

The goal isn’t to become a spokesperson, but to remain authentically yourself whilst acknowledging that your work exists in a broader human context.

Alexis Turner, 37, Science Education Coordinator, Toronto, Canada
You spoke beautifully about mathematics as storytelling, but many students – especially girls – still see maths as cold and disconnected from creativity. If you could redesign how we introduce topology and geometric thinking to teenagers today, what would you change? How might we help young people experience that same joy you felt when your brother told you about Gauss’s elegant solution?

Alexis, this breaks my heart because I see it all the time – bright students who think mathematics is just memorising formulas and following procedures. We’re teaching them to see mathematics as a collection of rules rather than as a language for describing the hidden patterns in our world.

I would start by throwing out most traditional geometry curricula. Instead of beginning with formal definitions and proofs, let students play with soap bubbles. Have them blow bubbles between wire frames of different shapes and watch how the soap film naturally finds the minimal surface. They’re seeing calculus of variations in action, watching nature solve optimisation problems right before their eyes. Only after they’ve developed intuition about how surfaces behave would I introduce the mathematical machinery to describe what they’ve observed.

The same with topology – don’t start with abstract definitions of continuity and homeomorphisms. Give students clay and ask them to explore which shapes can be transformed into others without tearing or gluing. Let them discover that a coffee mug and a doughnut are topologically identical by actually moulding one into the other. Mathematics should feel tactile, visual, experimental.

Most importantly, we need to show students that making mistakes is not just acceptable – it’s essential. Some of my best insights came from calculations that went wrong, drawings that didn’t turn out as expected, conjectures that failed in interesting ways. But our educational system punishes errors instead of treating them as stepping stones to understanding.

I think we also need to connect mathematical ideas to stories that students already care about. When I explain billiard ball dynamics, I don’t start with differential equations – I ask students to imagine they’re designing a miniature golf course. How would you create a hole where the ball follows an interesting path? How might you use mirrors to create unexpected trajectories? Once they’re engaged with the puzzle, the mathematics becomes a tool for exploring their own curiosity.

The key is patience. Let students spend time with problems, make conjectures, test ideas. Don’t rush to give them the “right” answer. The joy of mathematics comes from that moment when you suddenly see why something has to be true – when the pattern clicks into place in your mind. You can’t manufacture that moment, but you can create conditions where it’s more likely to happen.

Mathematics is the most creative subject there is. We just need to teach it that way.

Bruno Álvarez, 45, Theoretical Physics Professor, São Paulo, Brazil
Imagine you had been born fifty years earlier, during an era when women were almost entirely excluded from advanced mathematics. Your visual, intuitive approach might have been dismissed as ‘unrigorous’ even if you’d managed to access mathematical training. Do you think the revolutionary insights about moduli spaces and earthquake flows could have emerged from someone working within the more formal, symbolic traditions that dominated mid-20th century mathematics?

Bruno, this is such a haunting question because it forces me to confront how much my mathematical development depended on being in the right place at the right time. If I’d been born in the 1920s, would I have even made it past secondary school mathematics? The barriers were so absolute then.

But let’s imagine, hypothetically, that I had somehow managed to access mathematical training in that era. You’re absolutely right that my approach would have been seen as suspect. The mid-20th century was dominated by the Bourbaki school’s emphasis on pure abstraction and formal rigor. Drawing pictures was considered almost childish – real mathematicians worked with symbols and logical structures.

I think about Emmy Noether, who faced exactly these kinds of dismissals. Her work was groundbreaking, but she had to fight constantly for recognition, and even then, she was often seen as an exception rather than as someone whose methods might be widely valuable. The mathematical community was so much smaller, more insular, more resistant to approaches that didn’t fit established patterns.

Here’s what’s interesting, though: the insights I found about moduli spaces came precisely from thinking geometrically about what these abstract objects actually look like. If I’d been forced to work purely symbolically, I might never have developed the intuition about how surfaces fit together, how geodesic flows behave over long time periods, how cutting and pasting operations relate to algebraic structures.

But perhaps – and this is speculative – those insights would have emerged eventually from someone else working in that more formal tradition. The mathematics itself has an internal logic that pushes toward certain discoveries. Maybe a purely algebraic approach would have found different pathways to similar results.

What troubles me most about your question is realizing how many brilliant minds we probably lost to those institutional barriers. How many women had the geometric intuition that could have transformed our understanding of complex spaces, but never got the chance to develop it? How many different approaches to mathematical thinking were suppressed because they didn’t match the dominant style?

I was fortunate to work during a period when the mathematical community was becoming more open to diverse approaches, when computer visualization was making geometric thinking more respectable again. My work built on foundations laid by people like Thurston, who had already begun rehabilitating geometric methods in the 1970s and 1980s.

Perhaps the real tragedy isn’t just individual careers that were thwarted, but entire ways of understanding mathematics that we may have lost forever.

Mai Nguyen, 28, Computer Graphics Developer, Ho Chi Minh City, Vietnam
Your work on translation surfaces and billiard dynamics now helps render realistic water simulations in video games and animated films. But I’m curious about the reverse direction – could interactive visualisation tools that didn’t exist during your career have accelerated your own mathematical insights? When you were sketching surfaces on paper, did you ever imagine what it would be like to manipulate these geometric objects in virtual reality?

Mai, you’ve touched on something I think about often, especially watching how my daughter’s generation interacts with technology. When I was working on my thesis in the early 2000s, we had basic computer graphics – I remember being amazed by some of the early visualisations that David Hoffman and others were creating for minimal surfaces. But the idea of actually reaching into a virtual space and manipulating a Riemann surface with your hands? That seemed like pure science fiction.

I have to admit, there were so many times when I wished I could step inside my drawings. Picture this: I’m working on understanding how geodesics flow on a hyperbolic surface, and I’ve got these enormous sheets of paper covered with sketches showing different time slices of the flow. But I can only see two-dimensional projections of what’s happening. I found myself constantly rotating these mental objects, trying to understand how the three-dimensional structure was evolving.

Interactive visualization could have been revolutionary for my work on earthquake flow. Thurston’s earthquakes involve sliding parts of a surface along fractures – imagine being able to grab part of a virtual surface and actually perform that sliding motion, watching in real time how the geometry changes, how geodesics get bent and twisted. With paper and pencil, I had to track these deformations algebraically, keeping careful records of how coordinates transformed.

But here’s what’s interesting – I’m not sure it would have purely accelerated my insights. Some of my best understanding came from the struggle of working through calculations by hand, from making mistakes and having to backtrack. When you can manipulate objects too easily, you might miss the deeper structural reasons why certain transformations are natural while others feel forced.

There’s something about the resistance of pencil on paper, the physical effort of redrawing a complicated surface when you realize you’ve made an error – that difficulty forces you to think more carefully about what you’re doing. Virtual reality might make exploration easier, but would it make understanding deeper?

I think the ideal would be combining both approaches. Use virtual reality to build intuition quickly, to explore parameter spaces that would take weeks to map by hand. But then step back, work through key examples with pencil and paper, make sure you understand why the patterns you’ve discovered have to be true.

The most important mathematical insights often come not from seeing something new, but from understanding why you’re seeing it.

Reflection

Maryam Mirzakhani passed away on 14th July 2017, at just forty years old, leaving behind mathematical landscapes that continue to reveal new territories to explorers who follow her hand-drawn maps. Her death from breast cancer robbed the world not only of future discoveries, but of a voice that might have guided mathematics toward greater inclusivity and geometric intuition.

Throughout our conversation, several themes emerged that challenge conventional narratives about mathematical genius. Mirzakhani’s emphasis on slowness and visual thinking contradicts stereotypes of mathematicians as rapid-fire symbol manipulators. Her insistence that mistakes and patient exploration matter more than quick answers offers a different model for mathematical education. Most strikingly, her reluctance to embrace the role of spokesperson – whilst acknowledging the responsibility that comes with visibility – reveals the complex burden placed on pioneering women in STEM fields.

The historical record often portrays Mirzakhani’s work in technical terms that obscure its revolutionary nature. Our conversation attempted to capture not just what she accomplished, but how she thought – the geometric intuition that allowed her to see abstract spaces as tangible landscapes. Whether her actual perspectives aligned with those presented here remains, necessarily, uncertain. The gaps in our understanding of her private thoughts and informal methods remind us how much mathematical insight remains unrecorded.

Today, as artificial intelligence transforms mathematical discovery and virtual reality enables new forms of geometric exploration, Mirzakhani’s emphasis on hand-drawn understanding feels both antiquated and prophetic. Her recursive formulas now inform quantum computing research, whilst her ergodic theory insights guide climate modelling efforts. Recent work by researchers like Alex Wright and Anton Zorich continues expanding the frameworks she established, proving that her geometric vision was not just beautiful but foundational.

Perhaps most importantly, Mirzakhani demonstrated that mathematical truth emerges not from conforming to established patterns of thinking, but from trusting your own way of seeing – even when that vision requires enormous sheets of paper and looks, to others, like abstract art rather than rigorous mathematics.

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.

Editorial Note: This interview is a dramatised reconstruction inspired by historical records, published accounts, and the documented achievements of Maryam Mirzakhani. While every effort has been made to base her words and perspectives on authentic sources and era-appropriate insights, certain passages have been imagined to evoke her personality and illuminate complex ideas. Readers should understand this is not a verbatim transcript but a creative exploration intended to honour her legacy. By presenting Mirzakhani’s story in this way, we aim to deepen appreciation for her life and work while maintaining respect for the historical record and its limitations.

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