Life is nonlinear. So handle it using Math.
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In 1985, Carl Sagan warned the US Senate that increasing greenhouse gases could transform Earth's climate.
He used Venus, with its surface temperature near 470°C, to explain the physics.
Postcard from Albert Einstein to David Hilbert, Berlin, 18 November 1915
Dear Colleague,
The system of equations you have presented agrees, as far as I can see, exactly with what I have found in recent weeks and submitted to the Academy.
The difficulty was not in finding generally covariant equations for the g₍μν₎, since this can easily be accomplished using the Riemann tensor.
Rather, the difficulty was in recognizing that these equations represent a generalization, indeed a simple and natural generalization, of Newton's law.
I succeeded in recognizing this only in the last few weeks (I sent you my first communication), although three years ago, together with my friend Grossmann, I had already considered the only possible generally covariant equations, which have now proved to be the correct ones.
We abandoned them only with great reluctance, because my physical analysis had apparently indicated that they were incompatible with Newton's law.
The important thing is that these difficulties have now been overcome.
Today I am presenting to the Academy a paper in which, using general relativity and without any auxiliary hypothesis, I quantitatively derive the perihelion motion of Mercury discovered by Le Verrier.
No theory of gravitation has succeeded in doing this until now.
With best regards,
Yours, Einstein
“Mathematics Is a Subject for the Young”
In a new essay published on Terence Tao's blog, NYU mathematician Tristan Buckmaster offers a notably optimistic perspective on the future of mathematics after recent breakthroughs in AI-generated proofs.
His central argument is that the next generation of mathematicians, particularly graduate students and postdoctoral researchers, will shape the future of AI-assisted mathematics.
Buckmaster compares this moment with IBM's Deep Blue defeating Garry Kasparov in 1997. Chess did not disappear when computers became stronger than humans. Instead, powerful engines transformed how people studied and played it.
He believes something similar could happen in mathematics, although mathematical understanding presents a different challenge.
He also raises concerns about the concentration of advanced AI capabilities inside a handful of corporations and argues for wider access, better attribution, and stronger protection of researchers' work.
An interesting observation from the essay:
"Mathematics has never been a list of true statements. Certifying a result settles the question, not the search for understanding."
On July 17, 2014, a 67-year-old retired mathematician was brushing his teeth when an idea suddenly struck him.
Thomas Royen had found a proof of the Gaussian correlation inequality, a problem that had resisted mathematicians for decades.
He wrote the proof in Microsoft Word and published it.
Almost nobody noticed.
It took years for the mathematical community to fully recognize what he had accomplished.
In July 1986, Terence Tao represented Australia at the International Mathematical Olympiad in Warsaw.
He was just 10 years old. He earned 19 out of 42 points and received a bronze medal, becoming the youngest IMO medalist.
He earned full marks on Problems 1 and 2, although he received only one point on the final problem.
Tao returned in 1987 to win silver with 40 points, and in 1988 he won gold at age 13, becoming the youngest gold medalist in IMO history.
A prime number that survives being erased from either end.
739397 → 39397 → 9397 → 397 → 97 → 7
739397 → 73939 → 7393 → 739 → 73 → 7
Every number shown is prime.
Even more remarkable: 739397 is the largest prime with this property. Only 15 such primes exist.
A number that attracts almost every four-digit number.
Start with 3524. Arrange its digits in descending and ascending order, then subtract.
5432 − 2345 = 3087
8730 − 0378 = 8352
8532 − 2358 = 6174
Now something remarkable:
7641 − 1467 = 6174
Every four-digit number containing at least two distinct digits eventually reaches 6174 by repeating this procedure, always within seven steps.
A numerical curiosity discovered by Indian mathematician D. R. Kaprekar.
Twelve Harvard mathematicians have offered sharply different views on the future of mathematics in the age of AI.
In new interviews published by The Harvard Crimson, Melanie Matchett Wood argues that AI should strengthen human mathematical understanding rather than replace it.
Other researchers emphasize the correctness of results, regardless of whether humans or machines discover them.
Meanwhile, several introductory mathematics courses at Harvard have introduced technology-free classroom policies.
The contrast is striking. At the research frontier, mathematicians are exploring increasingly powerful AI tools. In the classroom, they are also trying to protect the independent reasoning that makes mathematical discovery possible.
They are consecutive integers, and both are perfect powers.
No other two integers greater than 1, each expressible as a square or higher power, are consecutive.
Not even among infinitely many integers.
This was conjectured in 1844 and finally proved in 2002.
A new NPR investigation has found a troubling problem in AI-generated mathematics.
Cambridge mathematician Anders Hansen identified a discrepancy between an AI-generated proof and its Lean formalization.
A constant had changed from 4 to 5, making the formally verified statement weaker than the original claim.
The Lean verification itself was not necessarily incorrect. The concern is that it may have verified something different from what the original mathematical argument asserted.
The report also features Daniel Litt, who identified an error invalidating a separate AI-generated paper, and Dana Moshkovitz, who discusses a proposed solution to the Unique Games Conjecture.
The investigation highlights a distinction that is becoming increasingly important: verifying a formal proof is not enough unless the formal statement faithfully represents the intended theorem.
Source: NPR, 21 October 2026 (US), 22 October 2026 (IST).
A Fields Medalist has joined the growing discussion about the future of mathematics in the age of AI.
In a new episode of The Economist's Babbage, released on 21 October, James Maynard of Oxford and Yang-Hui He of the London Institute for Mathematical Sciences discuss how AI is transforming mathematical research.
The conversation follows the recent release of hundreds of AI-generated mathematical manuscripts, which has raised questions about the future of mathematical discovery.
Can AI open entirely new directions in mathematics, or will the growing volume of machine-generated results make mathematical understanding increasingly difficult?
The episode examines both possibilities.
Source: The Economist, AI Eats Science 1: The Mathpocalypse, 21 October 2026.
