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Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao

Third SAIR competition: inverse Galois challenge

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On the proposed rule changes to the administration of federal grants

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Modular Arithmetic Challenge

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Primitive sets and von Mangoldt chains: Erdős Problem #1196 and beyond

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Products of consecutive integers with unusual anatomy

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Mathematical methods and human thought in the age of AI

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Local Bernstein theory, and lower bounds for Lebesgue constants

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Mathematics Distillation Challenge

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SLMath Deputy Director Search

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Six Math Essentials

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IPAM industrial short course in generative AI algorithms – deadline for applications closing soon

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A crowdsourced repository for optimization constants?

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Rogers’ theorem on sieving

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The integrated explicit analytic number theory network

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Polynomial towers and inverse Gowers theory for bounded-exponent groups

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I’ve just uploaded to the arXiv my preprint [The maximal length of the Erdős–Herzog–Piranian lemniscate in high degree](https://arxiv.org/abs/2512.12455)\. This paper...

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The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale

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The story of Erdős problem #1026

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Quantitative correlations and some problems on prime factors of consecutive integers

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Growth rates of sequences governed by the squarefree properties of its translates

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