What's new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
There has been some spectacular progress in geometric measure theory: Hong Wang and Joshua Zahl have just released a preprint that resolves the three-dimensional case of the infamous Kakeya set conjecture! This conjecture asserts that a Kakeya set – a subset of that contains a unit line segment in every direction, must have Minkowski and […]
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 learned (from Svitlana Mayboroda, the director of the collaboration as well as one of the principal investigators) of a remarkable statistic: net electricity consumption by residential customers […]
Grant Sanderson (who creates the website and Youtube channel 3blue1brown) has been collaborating with myself and others (including my coauthor Tanya Klowden) on producing a two-part video giving an account of some of the history of the cosmic distance ladder, building upon a previous public lecture I gave on this topic, and also relating to […]
Timothy Trudgian, Andrew Yang and I have just uploaded to the arXiv the paper “New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach“. This paper launches a project envisioned in this previous blog post, in which the (widely dispersed) literature on various exponents in classical analytic number theory, as well […]
Hamilton’s quaternion number system is a non-commutative extension of the complex numbers, consisting of numbers of the form where are real numbers, and are anti-commuting square roots of with , , . While they are non-commutative, they do keep many other properties of the complex numbers: Being non-commutative, the quaternions do not form a field. […]
I’ve just uploaded to the arXiv the paper “On the distribution of eigenvalues of GUE and its minors at fixed index“. This is a somewhat technical paper establishing some estimates regarding one of the most well-studied random matrix models, the Gaussian Unitary Ensemble (GUE), that were not previously in the literature, but which will be […]
Renaissance Philanthropy and XTX Markets have announced the launch of the AI for Math Fund, a new grant program supporting projects that apply AI and machine learning to mathematics, with a focus on automated theorem proving, with an initial $9.2 million in funding. The project funding categories, and examples of projects in such categories, are: […]
Vjeko Kovac and I have just uploaded to the arXiv our paper “On several irrationality problems for Ahmes series“. This paper resolves (or at least makes partial progress on) some open questions of Erdős and others on the irrationality of Ahmes series, which are infinite series of the form for some increasing sequence of natural […]
Kaisa Matomäki, Maksym Radziwill, Fernando Xuancheng Shao, Joni Teräväinen, and myself have (finally) uploaded to the arXiv our paper “Higher uniformity of arithmetic functions in short intervals II. Almost all intervals“. This is a sequel to our previous paper from 2022. In that paper, discorrelation estimates such as were established, where is the von Mangoldt […]
The day after the election, I found myself struggling with how to approach the complex analysis class I was teaching. Could I ignore the (almost literal) elephant in the room? Would my students be in the right mental state to learn math? Would I be in the right mental state to teach it? I opened […]
I have been collaborating for many years with a long-time personal friend and polymath, Tanya Klowden, on a popular book on astronomy tentatively entitled “Climbing the cosmic distance ladder“, which was initially based on a public lecture I have given on this topic for many years, but which we have found to be a far […]
Almost three weeks ago, I proposed a collaborative project, combining the efforts of professional and amateur mathematicians, automatic theorem provers, AI tools, and the proof assistant language Lean, to describe the implication graph relating the 4694 equational laws for magmas that can be expressed using up to four invocations of the magma operation. That is […]
Traditionally, mathematics research projects are conducted by a small number (typically one to five) of expert mathematicians, each of which are familiar enough with all aspects of the project that they can verify each other’s contributions. It has been challenging to organize mathematical projects at larger scales, and particularly those that involve contributions from the […]
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