HeyJaredTerence Tao
- Indexed articles, last 90 days
- 7
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- Sep 25, 2026
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- Jul 11, 2026
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We’re gonna need a lot more mathematicians (opens the original)
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[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 several students who felt that the pace at which the top students could understand new math concepts was far too fast for them. They, too, could understand the ideas, but it would take them much longer. Eventually, almost all of these students gave up their dream of pursuing research mathematics and found s
After Math (opens the original)
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[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 for Advanced Studies IUSS Pavia) Eamon Duede (Princeton University and Purdue University) On September 8th, 2026, OpenAI announced that it had produced an AI-generated solution to the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems. The announcement kicked off debat
Palomar – a registry of Lean verified mathematics (opens the original)
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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 that a given Lean repository actually proves the claimed statement is somewhat non-trivial, especially for an audience which is not expert in the use of Lean: one has to first check that the claimed formal Lean statements have proofs that typecheck, that the proofs do not contain any “cheats” such as addi
A digestion of the proof of Sendov’s conjecture (opens the original)
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This post concerns the following conjecture of Sendov, as well as its strengthening by Phelps–Rodriguez: By applying a rotation around the origin, we can normalize to be a real number with . From the work of Rubinstein, both conjectures were already established in the case, so one can restrict to the case. Both of these conjectures then follow from All three of these conjectures were established for (in a sequence of papers culminating in this paper of Brown and Xiang) and for sufficiently large
A partial digestion of the HRT counterexample (opens the original)
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A function of one variable can be translated in space by a spatial shift to obtain a new function Some functions obey finite linear relations between their time-frequency shifts. For instance, a sinusoid obeys the relation A special case of the HRT conjecture, which was also open, makes the additional assumption that was Schwartz. Many positive results towards this conjecture were known. I will mention only a few here. A simple case is when we only have frequency shifts rather than spatial shift
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