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Category: mathematics

Why does AI being good at math matter?

This is the second time in recent months that the AI world has got all excited about math. The rumor mill went into overdrive last November, when there were reports that the boardroom drama at OpenAI, which saw CEO Sam Altman temporarily ousted, was caused by a new powerful AI breakthrough. It was reported that the AI system in question was called Q* and could solve complex math calculations. (The company has not commented on Q*, and we still don’t know if there was any link to the Altman ouster or not.) I unpacked the drama and hype in this story.

You don’t need to be really into math to see why this stuff is potentially very exciting. Math is really, really hard for AI models. Complex math, such as geometry, requires sophisticated reasoning skills, and many AI researchers believe that the ability to crack it could herald more powerful and intelligent systems. Innovations like AlphaGeometry show that we are edging closer to machines with more human-like reasoning skills. This could allow us to build more powerful AI tools that could be used to help mathematicians solve equations and perhaps come up with better tutoring tools.

John Forbes Nash Jr

(June 13, 1928 – May 23, 2015), known and published as John Nash, was an American mathematician who made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations. [ 1 ] [ 2 ] Nash and fellow game theorists John Harsanyi and Reinhard Selten were awarded the 1994 Nobel Prize in Economics. [ 3 ] In 2015, Louis Nirenberg and he were awarded the Abel Prize for their contributions to the field of partial differential equations.

As a graduate student in the Princeton University Department of Mathematics, Nash introduced a number of concepts (including the Nash equilibrium and the Nash bargaining solution), which are now considered central to game theory and its applications in various sciences. In the 1950s, Nash discovered and proved the Nash embedding theorems by solving a system of nonlinear partial differential equations arising in Riemannian geometry. This work, also introducing a preliminary form of the Nash–Moser theorem, was later recognized by the American Mathematical Society with the Leroy P. Steele Prize for Seminal Contribution to Research. Ennio De Giorgi and Nash found, with separate methods, a body of results paving the way for a systematic understanding of elliptic and parabolic partial differential equations.

Wormholes may not exist—we’ve found they reveal something deeper about time and the universe

Wormholes are often imagined as tunnels through space or time—shortcuts across the universe. But this image rests on a misunderstanding of work by physicists Albert Einstein and Nathan Rosen.

In 1935, while studying the behavior of particles in regions of extreme gravity, Einstein and Rosen introduced what they called a “bridge”: a mathematical link between two perfectly symmetrical copies of spacetime. It was not intended as a passage for travel, but as a way to maintain consistency between gravity and quantum physics. Only later did Einstein–Rosen bridges become associated with wormholes, despite having little to do with the original idea.

But in new research published in Classical and Quantum Gravity, my colleagues and I show that the original Einstein–Rosen bridge points to something far stranger—and more fundamental—than a wormhole.

Boys and girls tend to use different strategies to solve math problems, new research shows

New studies show girls prefer step-by-step math algorithms, while boys favor creative shortcuts. This difference in approach, rather than raw ability, may explain why men continue to outnumber women in advanced STEM fields.

The Math Behind Evo Devo (TMEB #3)

The math behind Evo-devo~

Uri Alon’s Book:

Jim Collins paper:
https://www.researchgate.net/publication/12654725_Constructi…ichia_coli.
https://www.nature.com/articles/s41467-017-01498-0

The math behind fly development:
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.

Music:
City Life – Artificial. Music (No Copyright Music)
Link: https://www.youtube.com/watch?v=caT3j… ure Water by Meydän Link: • Meydän — Pure Water [Creative Commons — CC… Forever Sunrise — by Jonny Easton Link: • Forever Sunrise — Soft Inspirational Piano… Softwares used: Manim CE Keynote.
Pure Water by Meydän.
Link: https://youtu.be/BU85yzb0nMU
Forever Sunrise — by Jonny Easton.
Link: https://youtu.be/9Xndx7nhGAs.

Softwares used:

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Physics of foam strangely resembles AI training

Foams are everywhere: soap suds, shaving cream, whipped toppings and food emulsions like mayonnaise. For decades, scientists believed that foams behave like glass, their microscopic components trapped in static, disordered configurations.

Now, engineers at the University of Pennsylvania have found that foams actually flow ceaselessly inside while holding their external shape. More strangely, from a mathematical perspective, this internal motion resembles the process of deep learning, the method typically used to train modern AI systems.

The discovery could hint that learning, in a broad mathematical sense, may be a common organizing principle across physical, biological and computational systems, and provide a conceptual foundation for future efforts to design adaptive materials. The insight could also shed new light on biological structures that continuously rearrange themselves, like the scaffolding in living cells.

These Brain-Inspired Computers Are Shockingly Good at Math

New research shows that advances in technology could help make future supercomputers far more energy efficient. Neuromorphic computers are modeled after the structure of the human brain, and researchers are finding that they can tackle difficult mathematical problems at the heart of many scientif

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