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A public registry of Lean-verified mathematical results.

Read discoveries for Inverse Galois Problem (IGP24). IGP24, the Inverse Galois Problem in Degree 24. This is a mathematical discovery challenge: we are asking...

The Modular Arithmetic Challenge asks a deceptively simple question — can a neural network learn to compute (a × b) mod p for integers hundreds of digits long...

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The “Mozart of mathematics” invites readers on a brief tour of six core ideas—numbers, algebra, geometry, probability, analysis, and dynamics—that ca...

Climbing the cosmic distance ladder Tanya Klowden and Terence Tao in preparation This project is based on a public lecture on the cosmic distance ladder that I have given on occasion. Working with …

AlphaEvolve is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines ...

I believe that with the advent of modern online collaboration platforms (such as Github), proof assistant languages (such as Lean), and (potentially) AI tools, there are many emerging opportunities...

Here is a first proof-of-concept demonstration of an actual outcome for the erdosproblems/OEIS linkage project. There are a number of Erdos problems relating to irrationality of specific series. I ask...

The “Mozart of Math” tried to stay out of politics. Then it came for his research.

It is tempting to view the capability of current AI technology as a singular quantity: either a given task X is within the ability of current tools, or it is not. However, there is in fact a very wid...

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YouTube video by Terence Tao

YouTube video by Terence Tao

YouTube video by Terence Tao

YouTube video by Terence Tao

Today, the President’s Council of Advisors on Science and Technology (PCAST) released recommendations to promote the development of public policies that are informed by scientific understandings and c...

We study sets of $δ$ tubes in $\mathbb{R}^3$, with the property that not too many tubes can be contained inside a common convex set $V$. We show that the union of tubes from such a set must have almos...

I recently returned from the 2025 Annual Meeting of the “Localization of Waves” collaboration (supported by the Simons Foundation, with additional related support from the NSF), where I…

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As researchers representing universities across the country, the last few weeks have been filled with uncertainty. As you are aware, the Trump administration’s National Institutes of Health (NIH) prop...

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Exponent pair database. Contribute to teorth/expdb development by creating an account on GitHub.

Hamilton’s quaternion number system $latex {\mathbb{H}}&fg=000000$ is a non-commutative extension of the complex numbers, consisting of numbers of the form $latex {t + xi + yj + zk}&f…

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The President’s Council of Advisors on Science and Technology (PCAST) has released a new report addressing America’s groundwater resources. Groundwater is central to the health, security, and economic...