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Eigenvectors from eigenvalues
Peter Denton, Stephen Parke, Xining Zhang, and I have just uploaded to the arXiv the short unpublished note “Eigenvectors from eigenvalues”. This note gives two proofs of a general eige…
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
Math & Algorithms 41Science & Space 29Life, Learning & Writing 10AI & Machine Learning 8Career & Management 6Society, Policy & Culture 3
2
If math is more than proof, we need to better celebrate the rest of it
[This is a guest post by Grant Sanderson. This blog post was initially written in a different file format and converted using AI. — T.] A sentiment echoing throughout the mathematics communit…
3
We're gonna need a lot more mathematicians
[This is a guest post by Amit Sahai. This blog post was initially written in a different file format and converted using AI. — T.] When I was an undergraduate student, I remember talking with…
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Mathematics has changed. Let's act like it
[This is a guest post by Frank Calegari. This blog post was initially written in a different file format and converted using AI. — T.] Why we should not be sad The release by OpenAI on Octobe…
5
A digestion of the Jacobian conjecture counterexample
The notorious Jacobian conjecture can be formulated concretely over the complex numbers as follows. Conjecture 1 (Jacobian Conjecture) Let $latex {F:{\bf C}^n \rightarrow {\bf C}^n}&fg=000000$ …
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Six Math Essentials
Just a brief announcement that I have been working with Quanta Books to publish a short book in popular mathematics entitled “Six Math Essentials”, which will cover six of the fundament…
7
Masterclass on mathematical thinking
About a year ago, I was contacted by Masterclass (a subscription-based online education company) on the possibility of producing a series of classes with the premise of explaining mathematical ways…
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Why do we need human mathematicians anymore?
[This is a guest post by Po-Shen Loh, crossposted from his blog, where an illustrated version appears. This blog post was initially written in a different file format and converted using AI. —…
9
A Lean companion to Analysis I
Almost 20 years ago, I wrote a textbook in real analysis called “Analysis I”. It was intended to complement the many good available analysis textbooks out there by focusing more on foun…
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Mathematical exploration and discovery at scale
Bogdan Georgiev, Javier Gómez-Serrano, Adam Zsolt Wagner, and I have uploaded to the arXiv our paper “Mathematical exploration and discovery at scale”. This is a longer report on…
11
What mathematicians should know about the Lean Theorem Prover: reliability & AI
[This is a guest post by Thomas Hales. This blog post was initially written in a different file format and converted using AI. — T.] Mathematicians have been weighing in on what they value ab…
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Why are we even doing all this?
[This is a guest post by Rikab Gambhir. This blog post was initially written in a different file format and converted using AI. — T.] First, they came for the artists, and I did not speak out…
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Problem solving strategies in a graduate real analysis course (2010)
This is going to be a somewhat experimental post. In class, I mentioned that when solving the type of homework problems encountered in a graduate real analysis course, there are really only about a…
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There's more to mathematics than rigour and proofs (2007)
The history of every major galactic civilization tends to pass through three distinct and recognizable phases, those of Survival, Inquiry and Sophistication, otherwise known as the How, Why, and Wh…
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Palomar: A registry of Lean verified mathematics
In recent months there has been a proliferation of AI-generated proofs of various old and new results, some of which have been formalized in the proof assistant language Lean. However, checking tha…
16
Gamifying propositional logic: QED, an interactive textbook
About six years ago on this blog, I started thinking about trying to make a web-based game based around high-school algebra, and ended up using Scratch to write a short but playable puzzle game in …
17
Egoless Mathematics in the AI Era
[This is a guest post by Karthik C. S., Amit Sahai, and Jie Xue. This blog post was initially written in a different file format and converted using AI. — T.] This is a good time for mathemat…
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A pilot project in universal algebra to explore new ways to collaborate
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…
19
A mathematical formalization of dimensional analysis (2012)
Mathematicians study a variety of different mathematical structures, but perhaps the structures that are most commonly associated with mathematics are the number systems, such as the integers $late…
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How to assign partial credit on an exam of true-false questions?
Note: the following is a record of some whimsical mathematical thoughts and computations I had after doing some grading. It is likely that the sort of problems discussed here are in fact well studi…
21
What should we tell our students?
[This is a guest post by Álvaro Lozano-Robledo. This blog post was initially written in a different file format and converted using AI. — T.] TL;DR: Keep calm and carry on studying math. I wo…
22
The Advisory Group on Mathematics and Artificial Intelligence
[This is a guest post by the Advisory Group on Mathematics and Artificial Intelligence. This blog post was initially written in a different file format and converted using AI. — T.] We would …
23
Erdős Problem #1026
Problem 1026 on the Erdős problem web site recently got solved through an interesting combination of existing literature, online collaboration, and AI tools. The purpose of this blog post is to try…
24
AI for math resources, and erdosproblems.com
This post contains two unrelated announcements. Firstly, I would like to promote a useful list of resources for AI in Mathematics, that was initiated by Talia Ringer (with the crowdsourced assistan…
25
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 …
26
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…
28
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…
29
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…
30
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…