If you scroll around broader topics this week, you might notice AI and math showing up together a lot. You don’t need to love math or be especially good at it, just a little curious. Although the connection between LLMs and math may seem natural, we decided to explore what has been happening.

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So, what exactly is the case?

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A tough math problem finally receives a solution. Actually not one, but two. Proofs that have all of a sudden sparked greater public interest in the solver's authenticity and how they got there, rather than the actual research breakthrough.

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N.Y.U. Mathematician Tristan Buckmaster went public with an announcement that he managed to resolve an equation that could lead to the solution of the Navier-Stokes, a math problem known as one of the Millennium Prize Problems. Buckmaster worked together with a colleague, Levent Alpöge, a fellow mathematician and Anthropic researcher. As stated by Buckmaster, the two researchers worked together on this privately, as a personal collaboration and a side project, free of any type of institutional agreements and employer involvement.

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It was stated that in their research, the mathematicians used various AI tools, including OpenAI’s Codex.

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Within hours of the announcement, OpenAI had a big reveal that they managed to solve one of the Millennium Prize Problems… and it happened to be the Navier-Stokes equation.

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According to Buckmaster’s statement, the mathematician duo worked for over a year on the problem. Buckmaster believes that their research helped train OpenAI’s model, which then led the AI tool to the equation’s solution, which the company apparently managed to find within days.

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The mathematician believes that OpenAI used the same strategy that the math duo used in the course of the year to get to the result. Sam Altman has said that they only approached the math problem because they heard that someone from Anthropic was working on it.

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Looking precisely, both solutions are based on formulas and strategies that have existed before. Buckmaster credits two Spanish mathematicians who initially came up with a new strategy on how to attack problems related to the Navier-Stokes equation.

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Now, many sides of the story, and communities are hurt and confused. There is a race of who gets to be first in the tech world, who gets credit for what, and who is able to afford to work on problems this big, without the risk of inauthenticity looming behind someone's back.

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What are Millennium Prize Problems?

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Throughout history, mathematicians have been grappling with different equations that did not always have definite solutions. At the beginning of the 2000’s the Clay Mathematics Institute established seven Prize Problems, reflecting light on some of the most difficult and unresolvable problems at the turn of the new millennium.

This was done with a simple goal. Keep the general public informed about math as a field of study and its openness to new discoveries. Moreover, to highlight the importance of unresolved math problems acknowledge the work of mathematicians and the importance of their achievements.

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The founding Scientific Advisory Board of the Clay Mathematics Institute (CMI), in consultation with reading experts worldwide, has chosen the seven Millennium Prize Problems. The focus was to highlight important classic mathematical questions that did not have definite solutions for many years.

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A $7 million prize fund was designated for the solutions to these problems. A $1 million allocated to the solution of each problem.

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Since then, only one problem has been resolved in 2001. The Navier-Stokes Equation is one of the remaining six, referred to as “currently active”.

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What exactly is the Navier-Stokes equation?

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The Navier-Stokes equation explores the mechanics of fluids; it mathematically explains how fluids move.

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Written in the 19th century as an equation, both mathematicians and physicists have failed to resolve the mathematical side, which would explain the physics in mathematical terms.

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Navier-Stokes explains everything that flows. It basically explains that fluids push themselves around. If you create a swirl in the water, with every spin the swirl gets tighter, which makes it spin faster, moving more water in the process. The goal of the equation is to explain how and why everything depends on everything at once.

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In everyday life, you can notice these movements when you are on a boat in the water. Meteorologists use them in weather forecasts, it’s used in aviation and in medicine to create a simulation of how blood moves through an artery.

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The aftermath

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Following all the extraordinary news, naturally people (especially mathematicians) started to take sides.

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“A Severe Misalignment of AI in Mathematics” a declaration signed by 25 Field Medalists, was sent out to the public.

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Following that, OpenAI withdrew its sponsorship of a math event at CalTech. This move comes after researchers from the university criticized the company and its approach to Buckmaster and his work.

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Mathematicians’ open letter, of which the first signees include people like Terrence Tao, Maxim Kontsevich, Pierre Deligne, and Maryna Viazovska, among others, highlights the concern that mathematicians would probably have to completely rethink mathematical research.

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AI can do math. There is no doubt about that. What is striking is that AI can do math so fast, which means that human mathematicians have to reconsider what mathematical progress actually means in times of AI.

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Models are trained on existing data, but creative work lives on citing relevant work of others, isolation of new ideas and methods, and human transmission of ideas between mathematicians.

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The professionals raise the question of plagiarism and the threat to the culture of open research.

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The AI impact on a (math) community

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Everything taken into consideration, the discussion here can take on multiple routes. In the context of current events and many opinions and sides, the questions raised contribute to the bigger picture of what it means to be a human researcher in a technologically advanced society.

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The first and the most obvious one is whether AI has a place within math or not. The answer to this one might come as a direct response to current events and resemble a sharp criticism. Dismay is an understandable reaction, but we cannot deny the benefits of modern technologies, including LLM’s and their integration into work and everyday life.

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Equations, resolving problems, unanswered questions, interconnected processes - these are all things that math as a field of study and technology have in common.

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This is something that is happening to the math community for the first time. Scientists take everything with a grain of salt. They want to get behind the “why” even when it means spending days, months, years. The current events have led to reactions, which could serve as an excellent base for taking action. New policymakers, rules of work, recommendations for institutes, mathematicians, researchers. Collective human effort for navigating the new spheres.

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What does it mean for the future? The future of math? Research? Science? Human curiosity?

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An opportunity to evolve. No matter your beliefs, and which side you want to be on. We can evolve in our curiosity, our doubt, our support, our contribution. This goes for technology and real life.

Interested in learning more about what's happening in the AI world? Don’t miss our previous blogs!

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