Math and AI
OpenAI recently announced that they solved the Navier-Stokes equations, a long-running open problem for mathematicians, and on the list of Millennium Prize Problems.
Two caveats that were immediately brought up by the mathematical community bear mentioning:
Mathematicians Tristan Buckmaster and Levent Alpöge allege that their work on these equations, sitting in Codex transcripts, was used by OpenAI. Buckmaster said OpenAI learned of the direction of his collaboration with Alpöge, and handled credit discussions improperly. OpenAI admits there is a possibility that data derived from usage of their products helped improve models.
These results are subject to human expert review and independent acceptance from the scholarly community.
But what I want to talk about is the broader role of AI in science, and the concerns about AI ‘arriving’ at scientific results. This week, the mathematical community published a declaration titled ‘A Severe Misalignment of AI in Mathematics’. Signed by 25 Field Medalists and endorsed by more than 7,000 academics worldwide, it reads:
“The goals of AI companies and the goals of the mathematical community are severely misaligned. We see these as part of broader alignment issues impacting other scientific and creative professions, as well as the whole of society.”
It is a short and incisive declaration that I urge you to read in full.
Its core message is that looking at science solely as an output-focused and efficiency-driven discipline puts the process of producing science and human scholars at risk. The questions raised in the declaration apply to all other intellectual and artistic pursuits where AI is currently being projected as indispensable.
Expanding on the declaration, a few thoughts on this:
It is the process of science that is at risk.
Mathematics is not simply a sequence of steps, proofs, or true/false statements. It is a rich body of human-transmitted knowledge that becomes part of the discipline after a careful and arduous process. Researchers study, examine, simplify, connect, explain and transmit their science. The process and work of arriving at scientific results is rich, nuanced, and frequently meandering. Humans learn from past work and cite it, they discuss hypotheses with colleagues and scholarly communities, they develop new methods to investigate, refine and test their work.
We stand to lose this richness when these fundamental processes are circumvented entirely — as in the case of Open AI using 10,000 agents over 105 hours and 130 billion output tokens, and declaring a problem ‘solved’.
Human scholars—with their judgment, skills, ideas, imagination and intuition—are a non-replicable asset, that is worth protecting.
Scholars, scientists and researchers develop judgment through decades of training. Via immersion with other human scholars and past scholarship, they learn to cultivate intuition, to ask the right questions, to try different approaches to the same problem, to follow new directions within a canvas of vast possibilities, to know when to give up and when to keep pushing, and to devise creative solutions that at first appear unlikely. They develop depth and imagination by being part of this arc of human progress and failure, often in the context of a single scientific concept or question that dominates their professional careers.
If the mass production of solutions — with AI models that skip straight to ‘answers’ — becomes the benchmark for science, this production of human scholarship is at risk. If outputs, speed and efficiency are incentivized above all else, they could well begin to substitute the slow, germinative work of science. The essence of what it means to train as, and become a scientist — with the creativity and skills that take shape over the course of a human life, from both experience and observation — is non-replicable by today’s AI models.
Science is a living, breathing tool. Solving famous problems with monetary rewards is not its ultimate goal.
The sciences are a sophisticated and fertile body of knowledge that develops over centuries. The manner in which human ideas are integrated into a scientific discipline define its quality of being alive, in motion, changing, transmitting, evolving. Scientific communities and research groups, online and offline, form a human chain that studies, preserves and builds upon the work of those that came long before. This is what makes science a living tool.
The work that creates science is often boring and a slog. Very rarely is it shiny outputs and press releases. Solving famous problems can provide clarity, and serve to guide future work, but it is not the end-all be-all of science. Science is not a scoreboard. It is a human endeavor, not a collection of numbers and facts.
We must stay connected to the purpose of science—and other human pursuits.
The AI gold rush in Silicon Valley in the last three years has already proved highly detrimental to the work of building thoughtful, viable, scalable and safe technology products. We must resist the temptation of a similar approach for the sciences. The risk is that we learn to optimize for speed and outputs, and lose sight of why we do this work. This is a moment to ask ourselves: why do we do science? Why do we make art? What does it mean to create? Why do we pass through tribulations, rejections, confusions and drudgery to follow these human pursuits? Why do some of us dedicate our lives to this work? What makes it worthy and valuable? What are the deeper motivations that underpin this work? In this moment, we need to think about these questions and stay connected to the answers.
The human curiosity, imagination and depth that enables these pursuits cannot be mechanized. In this context, the singer/songwriter Nick Cave rightly called AI-generated songwriting: ‘a grotesque mockery of what it means to be human’.
AI can still be of immense help to the scientific community, as the mathematical community has also clearly stated this week. But as with all else, we must look to scientists themselves, in order to learn how best to build and deploy AI for scientific purposes, while maintaining the essence, purpose and integrity of science.
