With over 1600 signatories, mathematicians issue a declaration warning of AI. Really!

I bet, some mathematicians were also complaining when the Abacus was introduced more than 4,000 years ago! 😊 Same old story!

Of course, machine learning and AI is coming to mathematics, the queen of sciences (according to a famous quote from Carl Friedrich Gauss). I am already curious what ML & AI will contribute to mathematics. Apparently, it has already provided some proofs to some very old mathematical problems.

It is probably safe to largely ignore these warnings!

"Few communities have felt that pressure more acutely than mathematicians, who have haplessly watched AI get frighteningly smart, frighteningly fast.

Today, 16 math specialists have turned that unease into a public cry for help—and call to action. Part warning, part manifesto, the 11-page Leiden Declaration on Artificial Intelligence and Mathematics cautions that unchecked automation threatens not only how math is practiced, but what the discipline stands for. It also lays out principles for using AI in ways that support, rather than erode, the field. ..."

Mathematicians issue warning as AI rapidly gains ground | Science | AAAS

Leiden Declaration on Artificial Intelligence and Mathematics "This declaration calls for action to address the challenges posed by the use of artificial intelligence within mathematics research. It is the result of a community initiative and is endorsed by the International Mathematical Union (IMU)."

A short biography of mathematician Georg Cantor

Recommendable!

The Man Who Stole Infinity | Quanta Magazine "In an 1874 paper, Georg Cantor proved that there are different sizes of infinity and changed math forever. A trove of newly unearthed letters shows that it was also an act of plagiarism."

Georg Cantor

Math long resisted a digital disruption. AI is poised to change that

Food for thought! I also had the impression that the queen of science was kind of aloof and resisted machine learning & AI to some extent. However, we may see a revolution in the making!

"Mathematician ... is training computers how to prove one of the most famous problems in math history: Fermat’s last theorem.

Resolving the problem isn’t the point. There’s already an accepted proof that was finalized in 1998. That work is a tortuous maze of mathematics that fills about 130 pages over two papers. It spans mathematical fields and unites abstract ideas that previously seemed to have little to say to one another. ... 

Now, the explosion in artificial intelligence has propelled efforts, spearheaded by technology companies, to combine large language models with theorem provers to develop systems capable of autoformalization. In theory, such systems may ultimately be able to do things that humans can’t. ..."

AI could radically change how math proofs are verified "Modern formalization, supercharged by AI, could radically change the way people do mathematics"

The AI Revolution in Math Has Arrived "AI is being used to prove new results at a rapid pace. Mathematicians think this is just the beginning."

Who was Évariste Galois? The genius rejected by Gauss

Recommendable!

(150) Who was Évariste Galois? The genius rejected by Gauss. - YouTube

Niels Henrik Abel: The Genius Who Died in Poverty

Recommendable!

(237) Niels Henrik Abel: The Genius Who Died in Poverty - YouTube

AI mathematics startup Axiom proves two longstanding mathematical problems of Paul Erdős

Good news! Math may benefit a lot from ML & AI especially when it comes to complex problems etc.! It will be leaner and meaner!

Unfortunately, neither Google nor Bing search produce relevant news articles on this story. Interestingly, there are apparently some Chinese news outlets which reported on this story, but their articles are in Chinese (see e.g. here). Is this not curious! Maybe another sign that the West is falling behind?

"AI mathematics startup Axiom produced formalized proofs for two open conjectures in the mathematical language Lean. Erdös problem #481 has been open since 1980 and problem #124 has been open for about 30 years.

Prolific mathematician Paul Erdős formulated roughly 1,100 problems, but only 266 have ever been proved. The solutions come weeks after OpenAI claimed GPT-5 solved Erdős problems, only for mathematicians to observe the model had retrieved existing solutions rather than having discovered new proofs."

Data Points: Gemini 3 adds compute-intensive Deep Think

24-year-old founder and CEO Carina Hong created Axiom Math in March 2025 and has recruited a team of ten employees, most of whom are from Meta, to build a math-focused AI model. Axiom Math (Source)

Image of the day

If you mention a fancy, new mathematical term like then Lebesgue integral on a park bench and it gets overheard your career in mathematics may just take off. So it happened to Stefan Banach in 1916.

Otto Nikodym and Stefan Banach Memorial Bench in Kraków, Poland

One Step Closer to a 'Grand Unified Theory of Math': Geometric Langlands

Recommendable!

The Man Who Solved the World’s Most Famous Math Problem Fermat's Last Theorem: Andrew Wiles

Very recommendable! Standing on the shoulders of giants is not always easy! What a tenacious pursuit!

The Jagged, Monstrous Weierstrass Function of 1872 That Broke Calculus

Recommendable!

The Jagged, Monstrous Function That Broke Calculus | Quanta Magazine "In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics."'

Source

How a Blind Mathematician Became the World's Greatest Leonhard Euler

Very recommendable!

The Strangest Mathematician in History - Archimedes

Very recommendable!

One of The Greatest Mathematician Who Ever Lived Carl Gauss

Very recommendable! Don't miss his love letters!

A Rosetta Stone for Mathematics or was it a philosopher's stone?

Recommendable! What about a philosopher's stone? 😊

"In 1940, from a jailhouse in Rouen, France, André Weil wrote one of the most consequential letters of 20th-century mathematics. He was serving time for refusing to join the French army, and he filled his days in part by writing letters to his sister, Simone, an accomplished philosopher living in London.

In a previous letter, Simone had asked André to tell her about his work. With war all around, André began his reply cautiously, warning his sister that past a certain point “you will understand nothing of what follows.” Over the next 14 pages, he sketched his idea for a “Rosetta stone” for mathematics. ...

Weil’s Rosetta stone linked three fields of mathematics: number theory, geometry, and, in the middle, the study of finite fields.

Other mathematicians had proposed ideas in this direction, but Weil was the first to spell out an exact vision. His letter presaged the Langlands program, a major initiative in contemporary mathematical research. ..."

A Rosetta Stone for Mathematics | Quanta Magazine In 1940 André Weil wrote a letter to his sister, Simone, outlining his vision for translating between three distinct areas of mathematics. Eighty years later, it still animates many of the most exciting developments in the field.

Credits: Institute for Advanced Study Monthly Enews

André Weil and his sister Simone pictured when he was 16 and she was 13. Both grew up to become influential intellectuals.

2023's Biggest Breakthroughs in Math

Very recommendable! Amazing stuff! Great video! Well done!

Math’s Famous Map Problem: The Four Color Theorem

Very recommendable! It is a very well known story, but well told!

Klara Dan von Neumann, the wife of John von Neumann

John von Neumann and Klara Dan von Neumann, another couple where both together were engaged in scientific and/or technical research reminiscent of the famous Curie couple.

Wikipedia summarizes: "was a [Jewish] Hungarian-American self-taught computer scientist, noted as one of the first computer programmers. ..."

I am afraid, the Wikipedia entry of her is possibly incomplete.

Her collaboration with Nick Metropolis is not mentioned in her entry, but indirectly in the Wikipedia entry for the MANIAC computer: "... In the 1940’s Nick Metropolis, a young physicist, designed new controls for the state-of-the-art computer (ENIAC) with Klari Von Neumann, John’s wife. He (Nicholas Metropolis) was fascinated with Monte Carlo methods and this new computing device. Soon he designed an improved computer, which he named the MANIAC in the hope that computer scientists would stop using acronyms. ..." (Source)

She lived only 52 years, but she had 4 husbands!

Klára Dán von Neumann - Wikipedia

For attribution of this photo see Wikipedia entry