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After Math
[This is a guest post by Silvia De Toffoli and Eamon Duede. This blog post was initially written in a different file format and converted using AI. — T.] Silvia De Toffoli (University School …
Terence Tao
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
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Visit terrytao.wordpress.com → RSS feedOn Hacker News Jan 2010 – Nov 2026
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A Misalignment of AI in Mathematics
I am proud to be among the list of 25 initial signatories — all Fields Medallists — to the declaration below, which grew out of discussions between ourselves over the last week. We have…
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Will it be a golden age or a dark age for mathematics (and science)?
[This is a guest post by Francesco Maggi. This blog post was initially written in a different file format and converted using AI. — T.] Large language models (LLMs) and the research systems b…
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What Are the Odds?
An unusual lottery result made the news recently: on October 1, 2022, the PCSO Grand Lotto in the Philippines, which draws six numbers from $latex {1}&fg=000000$ to $latex {55}&fg=000000$ a…
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Options for giving math talks and lectures online
As part of social distancing efforts to slow down the spread of the novel coronavirus, several universities have now transitioned, or begun transitioning, to online teaching models. (My home unive…
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Decomposing a Factorial into Large Factors
I’ve just uploaded to the arXiv the paper “Decomposing a factorial into large factors”. This paper studies the quantity $latex {t(N)}&fg=000000$, defined as the largest quanti…
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Be sceptical of your own work (2009)
An expert is a man who has made all the mistakes, which can be made, in a very narrow field. (Niels Bohr) If you unexpectedly find a problem solving itself almost effortlessly, and you can’t quite …
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Bill Thurston has died
Bill Thurston, who made fundamental contributions to our understanding of low-dimensional manifolds and related structures, died on Tuesday, aged 65. Perhaps Thurston’s best known achievement…
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The Future of Mathematics
[This is a guest post by Jeremy Avigad. This blog post was initially written in a different file format and converted using AI. — T.] “Mathematics underwent, in the nineteenth century, …
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Quaternions and spherical trigonometry
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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Does one have to be a genius to do maths?
Better beware of notions like genius and inspiration; they are a sort of magic wand and should be used sparingly by anybody who wants to see things clearly. (José Ortega y Gasset, “Notes on t…
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Closing the “green gap”: energy savings from the math of the landscape function
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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Special Relativity and Middle-Earth
This post is an unofficial sequel to one of my first blog posts from 2007, which was entitled “Quantum mechanics and Tomb Raider”. One of the oldest and most famous allegories is Plato&…
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Mathematics Distillation Challenge – Equational Theories
Mathematical research traditionally involves a small number of professional mathematicians working closely on difficult problems. However, I have long believed that there is a complementary way to …
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Terry Tao on how to compute non-converging infinite sums (2010)
The Riemann zeta function $latex {\zeta(s)}&fg=000000$ is defined in the region $latex {\hbox{Re}(s)>1}&fg=000000$ by the absolutely convergent series $latex \displaystyle \zeta(s) = \su…
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Climbing the cosmic distance ladder: Terence Tao book announcement
Several years ago, I developed a public lecture on the cosmic distance ladder in astronomy from a historical perspective (and emphasising the role of mathematics in building the ladder). I previous…
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Illustration Beyond Proof
[This is a guest post by Kate Stange and Edmund Harriss. This blog post was initially written in a different file format and converted using AI. — T.] In January a group of mathematicians, hi…
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A review of probability theory
In preparation for my upcoming course on random matrices, I am briefly reviewing some relevant foundational aspects of probability theory, as well as setting up basic probabilistic notation that we…
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Jean Bourgain
I have just learned that Jean Bourgain passed away last week in Belgium, aged 64, after a prolonged battle with cancer. He and Eli Stein were the two mathematicians who most influenced my early ca…