GoKawiilTwenty five Fields medalists were initial signatories of the letter “A Severe Misalignment of AI in Mathematics” in which they opine that “The goals of the AI companies and the goals of the mathematical community are severely misaligned”. They are right.
As they say, the goals of AI companies do not seem to be aligned with “the primary goal of conceptual understanding and insight”, and indeed, the “solutions [by AI companies] are [being] announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others.” This is true (but ironically, the signatories themselves say they released their letter quickly because they “did not have the time to have a more consultative process.”)
It is also true that the goals of the mathematics community do not seem to be aligned with “the primary goal of conceptual understanding and insight”. This is clear, because if that were the goal, then the mathematics community would hold the view that “the most precious resources of [its] profession are students and ideas”, and that they would be “nurture[d] with great care”. But sadly students and ideas in mathematics have not been nurtured with great care.
Since the letter by the twenty five Fields medalists seems to have been precipitated by the OpenAI announcement a solution to the Navier Stokes existence and smoothness problem, let’s take a look at how the mathematics community has nurtured some of the students who worked in that area, and their foundational ideas.
Juliusz Schauder (Leray–Schauder degree): Schauder earned his doctorate in 1923, but antisemitism (by mathematicians) resulted in denial of university positions. Instead he taught high school while producing serious math. A few years later after the Nazis rose to power, Schauder asked for help from mathematicians around the world, and yet numerous mathematicians declined to help. He tried to get an invitation from Princeton and was denied. This wasn’t just a matter of getting a salary. His life was in danger. Eventually he did not even have access to paper to write down his work and he was murdered by the Germans. His wife Emilia hid with their daughter, for a while living in sewers to survive. Emilia was eventually captured and then murdered in a concentration camp. Was this “nurture with great care”?
Oh, you say, but this was a long time ago!
(Leray–Schauder degree): Schauder earned his doctorate in 1923, but antisemitism (by mathematicians) resulted in denial of university positions. Instead he taught high school while producing serious math. A few years later after the Nazis rose to power, Schauder asked for help from mathematicians around the world, and yet numerous mathematicians declined to help. He tried to get an invitation from Princeton and was denied. This wasn’t just a matter of getting a salary. His life was in danger. Eventually he did not even have access to paper to write down his work and he was murdered by the Germans. His wife Emilia hid with their daughter, for a while living in sewers to survive. Emilia was eventually captured and then murdered in a concentration camp. Was this “nurture with great care”? Oh, you say, but this was a long time ago! Olga Ladyzhenskaya (Ladyzhenskaya inequality): By the late 1950s Ladyzhenskaya was a leading mathematician in PDEs and fluid mechanics. In 1958 she proved global existence and uniqueness for the two-dimensional Navier–Stokes equations using what is now known as the Ladyzhenskaya inequality. This work became foundational to Navier–Stokes theory. That same year, at age 36, she was shortlisted for the Fields Medal but was passed over for Klaus Roth and René Thom.
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