Twenty five medalists sign

Twenty five Fields medalists put their names to a letter called "A Severe Misalignment of AI in Mathematics," arguing the goals of AI companies and the mathematical community have come apart.

“The goals of the AI companies and the goals of the mathematical community are severely misaligned”

They are right

AI companies do not seem to be chasing conceptual understanding and insight. Solutions get announced in a rush, with no proper writeup, no isolation of new ideas, and no citation of prior work.

“solutions [by AI companies] are [being] announced in a rush, leaving no time for a proper writeup”

An irony in the timing

The letter itself was pushed out fast. The signatories admit they skipped a more consultative process because they did not have time, which is the exact habit they criticize.

“did not have the time to have a more consultative process”

Now turn it around

If conceptual understanding were really the profession's goal, mathematics would treat students and ideas as its most precious resources. The record says otherwise.

“the most precious resources of [its] profession are students and ideas”

Start where the letter started

OpenAI's claimed solution to Navier Stokes existence and smoothness set this off. So look at how the field treated the people who built that theory.

Schauder had no paper

Juliusz Schauder finished his doctorate in 1923 and was denied university posts by antisemitic mathematicians. He taught high school and did serious work anyway.

The world said no

When the Nazis came to power Schauder asked mathematicians worldwide for help. Many declined. Princeton refused him an invitation. He ended up without paper to write on, and was murdered by the Germans.

“This wasn't just a matter of getting a salary. His life was in danger.”

His family too

Schauder's wife Emilia hid with their daughter, living in sewers for a time. Emilia was captured and murdered in a concentration camp.

Ladyzhenskaya, passed over

In 1958 Olga Ladyzhenskaya proved global existence and uniqueness for 2D Navier Stokes using the inequality now carrying her name. At 36 she was shortlisted for the Fields Medal and lost out to Klaus Roth and Rene Thom.

The committee was not merit

Records from the 1958 committee show Hirzebruch was cut because he was doing fine and needed no encouragement, and Grothendieck was judged next most talented but could win later.

Fifty six more years

Maryam Mirzakhani became the first woman to win a Fields Medal in 2014. Of the 25 primary signatories on the letter, one is a woman.

Uhlenbeck was told no

Karen Uhlenbeck won the Abel Prize in 2019. After her 1968 PhD she was told plainly that people did not hire women, and that women should go home and have babies.

“people did not hire women”

The nepotism excuse

MIT, Stanford and Princeton wanted her husband, not her, citing nepotism rules. Years later Uhlenbeck went looking for those rules and could not find them.

“I hated Champaign-Urbana, I felt out of place mathematically and socially”

Mathematics is very difficult

Cathleen Morawetz led the Courant Institute, presided over the AMS, and won the National Medal of Science. When she raised how few women were in the field, Saunders Mac Lane's answer was a shrug.

“Well, mathematics is a very difficult subject.”

Berkeley, both directions

Berkeley barred Julia Robinson from teaching for 35 years, again on nepotism grounds, appointing her only after the National Academy elected her in 1976. She had to log for the personnel office exactly what she worked on each day.

And who it did hire

Yuval Peres was a Berkeley math professor from roughly 2001 to 2011. Mathematicians later described at least seven cases involving junior women, some of whom skipped conferences and lectures to avoid his advances.

Told they are stupid

Three years after Pachter arrived, the department lost an NSF grant over poor mentorship. A grad student came to his office in tears saying she had just been called stupid. She is now a successful professor.

“I'm doing nothing. He's stupid.”

Rejection of the person

Plenty of mathematicians have had not just their ideas rejected but themselves. Yitang Zhang was told by his advisor that no Chinese student is good.

“no Chinese student is good”

Why sign as medalist

The signatories used "Fields medalist" instead of an affiliation. The medal reflects extraordinary ability, but it also reflects a tiny group's taste in problems and styles. Erdos thought Szemeredi was robbed because the deciders did not care for combinatorics.

“prizes encode judgments about which mathematics, and therefore which mathematicians, matter”

Align to something else

Ability is not responsibility, and the profession's incentives and hierarchies are no model to copy. Align AI and mathematics both to understanding, attribution, generosity, and the nurturing of students and ideas.

“not merely the production or recognition of results”