Terence Tao

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, …

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…

There’s more to mathematics than rigour and proofs

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…

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…

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&…

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 …

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…

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…

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…

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…