William Wright
Will Wright is a soon to be "professional" mathematician who currently has a BSc in Mathematics from Bristol and MSc from Oxford. His primary area of interest is in geometric group theory which as it's name suggests is the study of the intersection between geometry and group theory, whether that be studying groups as geometric objects or studying the group theoretic properties of different geometries.
S: Do you think mathematics is a very collectivist thing?
Will: Yes, definitely. To make any kind of progress in mathematics, there are always these geniuses who come in and make huge breakthroughs, but they're still standing on the shoulders of so many other mathematicians. A lot of mathematics, especially today, is built on an enormous amount of collaborative research. There are articles about articles about articles. You slowly build toward the thing you're trying to understand and eventually prove it. Some of the biggest theorems take hundreds of years and dozens of people to solve—or even to meaningfully approach. So yes, mathematics is definitely collaborative. Almost everyone uploads their papers to arXiv for free, so anyone can read them and build on them. Of course, there are still journals and publishing systems, but overall there's a strong culture of sharing knowledge.
S: Do you think a lot of people enter mathematics because they want to be remembered? Or... do you want to be remembered?
Will: I think my view has changed over the years. When I was a child, I was quite scared of death—the idea that everything just ends after a certain amount of time. Because of that, I wanted to win a Nobel Prize or something like that. I wanted to be immortalised by making some great positive contribution. But as I've got older, that has mattered less. I don't think I'm in mathematics anymore because I want to make some monumental contribution or be remembered forever. I'm perfectly happy if that never happens. I think it's healthier to accept that. Not everyone is going to change the world. Of course, you can try to make it a better place—that's something I'd like to do—but I think there's maybe some ego in believing you're going to fundamentally change everything through mathematics.
S: Mathematics also has a lot of power. It shapes economics, politics, technology. How does morality come into play? Can the thrill of solving problems outweigh thinking about the moral consequences?
Will: I think that's definitely an issue. Mathematics is used in finance, defence, machine learning—lots of applied areas. To some extent, that's also why pure mathematics receives funding. People don't pour money into pure mathematics just so someone can spend years thinking about abstract algebraic structures that only five people in the world care about. They're hoping that somewhere down the line it leads to something economically valuable. I don't know how much mathematicians think about that. A lot of mathematicians end up going into finance, which is... sad. Although I don't know if that's because that's where the most interesting mathematics is. Some people genuinely go into quantitative finance because the hardest mathematical problems which they are interested in happen to be there.
S: I used to be fascinated by mathematics and physics, and I really admire that kind of logical thinking. I also love how collaborative mathematics is. At the same time, though, I feel like mathematics is loaded with this Western symbolism of truth. From the Greeks until now, it's become deeply connected with the idea of civilisation itself. Politically, every country is almost expected to participate in this way of understanding the world. As an artist, I don't quite know how I feel about that.
Will: That's actually a really interesting point. There was a group of French mathematicians in the early twentieth century called Bourbaki. They collectively wrote these enormous books that tried to formally organise all the mathematics known at the time. They completely changed the way mathematics was written. Before that, mathematics was much less standardised. If we're still thinking of mathematics as a language, then different countries almost had different accents. Some traditions were extremely formal and logical, showing every step of an argument. Others were much more intuitive. They focused on the overall picture and expected readers to understand how the details followed. Over time—and especially with the internet—mathematics has become much more homogeneous. Everyone now tends to write in a similar style so that anyone, anywhere, can understand it. I think that's a little sad. You lose something.
Will: Exactly. You lose something cultural. You lose a sense of history. But regarding what you said about mathematics representing a Western idea of truth—I think that's true to some extent. In school we're taught about the Greeks, the Romans, and European mathematicians. But historically, that's not the full story. Persian and Chinese mathematicians both made enormous contributions. Indian mathematics was hugely influential. From a Western perspective we've often...I suppose we've taken credit.
We've told the history in a way that centres ourselves. For example, what we call Pythagoras' Theorem was already known in India something like a thousand years before Pythagoras. So there definitely is a Western narrative that presents Europe as the driver of human civilisation and intellectual progress. That absolutely affects how the history of mathematics is taught. But I don't think mathematics itself is inherently Western. Every culture has done mathematics. Every culture has developed ways of understanding patterns, numbers, geometry, and logic. So I don't think mathematics itself belongs to the West.
Will: Definitely. Especially politically. I think mathematicians are probably more likely to look at statistics and think, The numbers are obvious. You look at a graph and think, Why are people voting this way? The data seems so clear. But people's emotions are much more complicated than that. You can show someone a graph saying their standard of living has increased by ten percent, but if that doesn't match their lived experience, they're not going to believe the graph. I think mathematics probably makes people more analytical in that sense.
S: I also wonder about AI. If AI can solve these problems in mathematics, then what even becomes the motivation for doing mathematics? Is it a subjective human attempt to solve equations? Or is it really about this collective pursuit of knowledge and power?
Will: I think that's the big question AI raises for mathematics. Right now, AI can produce mathematical arguments and proofs that look extremely convincing. Large language models can generate proofs for certain things, but they're very difficult to verify. It takes a long time, and ultimately a human still must check whether they're actually correct. At least, that's how it used to be. Now there's a lot of work happening around mathematical formalisation using systems like Lean. It's similar to a programming language. It has fixed logical rules and a formal mathematical foundation. You essentially write mathematics as a program. If the program runs, then the proof is valid. If it doesn't, then it isn't.
Because of that, we now have a way of objectively verifying an AI's output. If an AI produces a proof and Lean verifies it, then the theorem has genuinely been proved. That raises a really interesting question about why we do mathematics. Imagine an AI proves a famous theorem that people have been trying to solve for centuries. The proof is correct. It's been formally verified. But the proof itself is completely incomprehensible to humans. You can read it, but you don't actually understand why it's true. Then you arrive at this strange situation where you know something is true, but you have no intuition for it. Does that actually have value?
S: So you're saying we don't necessarily understand the logic that AI is using?
Will: Not necessarily. At the moment, all the significant results AI has produced are still understandable by humans. But in the future it's possible that AI could produce valid proofs that we simply can't comprehend. That separates mathematics from understanding. It forces us to ask whether mathematics is about knowing that something is true, or about genuinely understanding why it's true. I think the role of mathematicians could shift. Rather than proving new theorems themselves, they might become interpreters—taking AI-generated proofs and turning them into forms humans can actually understand. Because I think that's where the beauty of mathematics really lies. Not in the final statement of whether something is true or false. The beauty is in the proof itself. It's in the ideas. The intuition.
S: I'm also wondering whether AI can really generate something that humans don't understand. I was watching an interview with Hito Steyerl, and she was arguing that AI feeds on the past. It learns from existing information. Because of that, maybe it can't really generate something genuinely new. So perhaps the idea that it could suddenly leap far beyond us is questionable.
Will: Definitely. But I think we're right on the edge of that question. AI hasn't transformed mathematics yet. But it's definitely possible that it could. What makes mathematics unique is that we have these formal verification systems. Normally an AI can hallucinate and the only way to know it's wrong is for a human to check. With Lean and similar systems, the AI gets immediate feedback. It knows whether a proof works or not.
S: And what is that system based on?
Will: Ultimately, it's based on human mathematics. A lot of AI's early mathematical proofs were really just combinations of existing literature. It has this enormous encyclopaedic knowledge of mathematics. It can connect ideas that humans simply hadn't thought to combine before. Recently, though, AI produced a proof using what appears to be a genuinely novel technique. Not just combining existing results, but introducing a new method. I think that's probably going to continue. Maybe humans will always understand those proofs. But it's certainly possible that one day we won't.
Also in the current system through which mathematical prowess is judged we currently have a very "to the victor goes the spoils" attitude where the final person who proves the theorem gets all of the credit and the academic positions. If AI is now proving things are true and humans are relegated to explaining AI's proofs we will need a new way of measuring what it means to be a good mathematician. The current system is definitely far from perfect, since people who made valuable contributions are often overlooked, however such a radical change would doubtless upend how academic institutions function.
S: There's something deeply human in all of this. Can you really accept that something we built ourselves—a machine—is now telling us what truth is?
Will: I think another question is whether simply knowing something is true has any value by itself. Take the Twin Prime Conjecture. It's a very old problem. It asks whether there are infinitely many prime numbers that differ by two. People think the answer is yes. Mathematicians have been trying to prove it for centuries. Imagine an AI eventually outputs: ‘Yes. It's true.’ And alongside that it produces an unintelligible proof that no human can understand. Does simply knowing that it's true actually have value? That question has already come up before with computers. The first computer-assisted proof—I'm forgetting whether it was the Four Colour Theorem or another early example—reduced the problem to thousands of separate cases and then had a computer check every single one. People argued about whether that should count as a proof. Could you really say something had been proved if no human had actually followed every step themselves? Or were you simply trusting a machine?
S: Someone described capitalism as the first real computational machine—a system always trying to optimise itself. If AI becomes part of that system, then mathematics can't really escape capitalism. And maybe that makes the whole idea of truth even more complicated. For me, mathematics represents the human attempt to solve problems.
Will: For me, that's exactly what's beautiful about it. It's something humans have built. We've figured all of this out ourselves. Handing that over to AI feels... It feels like it goes against the reason we do mathematics in the first place. But I also think it's unavoidable. Because of capitalism. Eventually, the people who use AI will outperform the people who refuse to.
S: Then who comes up with the problems? Can AI decide what is worth solving?
Will: I don't think we know yet. At the moment, most people seem to think humans will still decide what questions are interesting. We'll become the people asking the questions. The AI will prove things for us. That's an interesting future. It's just completely different from the way mathematics has always been done. Having not really done research myself yet, I'm still unsure how I feel about it.
S: It brings me back to my original question about truth. Why are we so determined to reach it? Why do we want to know? Wouldn't AI eventually make curiosity itself boring? Almost as if we're becoming machines ourselves—consuming curiosity by endlessly solving problems.
Will: Yeah. I think it does risk becoming the death of curiosity and creativity. AI thinks for you. That's probably the saddest thing about it. It removes critical thinking. It removes creativity. For me, I've almost accepted that AI might eventually replace what I do. I've spent a long time trying to reconcile myself with that possibility.
S: I suppose artists always know who the audience is. Ultimately we're speaking to other humans. We're all trying to understand one another. But when you're proving a theorem, who is the audience?
Will: Exactly. I think that's where two different motivations collide. On one hand, mathematics receives funding because people hope discoveries will eventually become economically useful. On the other hand, mathematicians themselves are usually driven by curiosity. By the enjoyment of solving problems. Those two motivations have always existed together. I don't think AI allows us to reconcile them anymore. I think we need a new way of thinking about mathematics.