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Posts by Terence Tao

Title image of the comic "The music of the Spheres" by Dr. Terence Tao and Zach Weinersmith.

Title image of the comic "The music of the Spheres" by Dr. Terence Tao and Zach Weinersmith.

First 2 panels of the comic "The music of the Spheres." A man is narrating the comic, he is the comic representation of the quoted author, Dr. Terence Tao. He says "When I tell people at parties that I'm a mathematician, there's often an awkward pause in the conversation, or the obligatory..." A tall character next to him chimes in "Oh, I was sooooo bad at Math in school!" In the second panel, the narrator continues "though occasionally, you run into a math and science enthusiast who wants to discuss a recent development they heard in the news..." The narrator looks deeply touched, as a young woman is talking to him, she is saying : "oh my gosh, my friends and I cannot stop talking about reconstructing cryptographic protocols from quantum principles and... Do you want to move this conversation to a whiteboard?"

First 2 panels of the comic "The music of the Spheres." A man is narrating the comic, he is the comic representation of the quoted author, Dr. Terence Tao. He says "When I tell people at parties that I'm a mathematician, there's often an awkward pause in the conversation, or the obligatory..." A tall character next to him chimes in "Oh, I was sooooo bad at Math in school!" In the second panel, the narrator continues "though occasionally, you run into a math and science enthusiast who wants to discuss a recent development they heard in the news..." The narrator looks deeply touched, as a young woman is talking to him, she is saying : "oh my gosh, my friends and I cannot stop talking about reconstructing cryptographic protocols from quantum principles and... Do you want to move this conversation to a whiteboard?"

Panels 3 to 6 of the comic "The music of the Spheres." The narrator is putting a reassuring hand on a sad man's shoulder. The narration reads "...or someone who actually had a good experience in their math classes and was somewhat wistful about not pursuing it." The saddened man says "I'll always think of Hadwiger's graph theory conjecture as... the one who got away." In the next panels, the narrator states "those are good moments. But, in general, the public have very little idea what mathematics is, and what mathematicians actually do. Popular culture gives us some caricature portrayals of mathematicians"

Panels 3 to 6 of the comic "The music of the Spheres." The narrator is putting a reassuring hand on a sad man's shoulder. The narration reads "...or someone who actually had a good experience in their math classes and was somewhat wistful about not pursuing it." The saddened man says "I'll always think of Hadwiger's graph theory conjecture as... the one who got away." In the next panels, the narrator states "those are good moments. But, in general, the public have very little idea what mathematics is, and what mathematicians actually do. Popular culture gives us some caricature portrayals of mathematicians"

Panels 7 and 8 of the comic "The music of the Spheres." Both panels show a caricature of a mathematicians from pop culture. The first is a tortured genius, represented by a woman holding a piece of chalk saying "I cannot know love, but by god I *will* know if every polyomino with an area divisible by six can tile and hexagon!" The narration specifies that "torturedness rates among mathematicians are, in fact, average." The second example is the savant with strange mental powers, represented by a man surrounded by equations that obscure his vision. The narration specifies that "if you see equations floating before your eyes, please consult an ophthalmologist."

Panels 7 and 8 of the comic "The music of the Spheres." Both panels show a caricature of a mathematicians from pop culture. The first is a tortured genius, represented by a woman holding a piece of chalk saying "I cannot know love, but by god I *will* know if every polyomino with an area divisible by six can tile and hexagon!" The narration specifies that "torturedness rates among mathematicians are, in fact, average." The second example is the savant with strange mental powers, represented by a man surrounded by equations that obscure his vision. The narration specifies that "if you see equations floating before your eyes, please consult an ophthalmologist."

Does this change my imaginary Erdos number to a complex number?

Click the link to read the full comic on the site!

COMIC ◆ www.smbc-comics.com/comic/sphere...
PATREON ◆ www.patreon.com/ZachWeinersm...
STORE ◆ smbc-store.myshopify.com

1 week ago 150 26 9 7
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Instagram Create an account or log in to Instagram - Share what you're into with the people who get you.

A #cosmicdistanceLadder post on the many ways we project our planet onto a plane. No projection can faithfully reproduce *all* the geometric features of a sphere, so each projection is a compromise; but some projections are still preferred for specific applications. www.instagram.com/p/DVC9SvxkXDs

1 month ago 33 5 1 0
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Six Math Essentials The “Mozart of mathematics” invites readers on a brief tour of six core ideas—numbers, algebra, geometry, probability, analysis, and dynamics—that ca...

We’re thrilled to announce that Terence Tao (@teorth.bsky.social)’s SIX MATH ESSENTIALS is available for preorder: us.macmillan.com/books/978037.... A whirlwind tour through six core ideas that have guided mathematicians from antiquity to the frontiers of what we know today. Pubs October 27, 2026.

2 months ago 50 16 3 1
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Climbing the cosmic distance ladder Climbing the cosmic distance ladder Tanya Klowden and Terence Tao in preparation This project is based on a public lecture on the cosmic distance ladder that I have given on occasion. Working with …

Tanya Klowden and I have uploaded a further sample chapter to our "cosmic distance ladder" book: terrytao.wordpress.com/books/climbi... . See also the blog post terrytao.wordpress.com/2025/11/21/c...

4 months ago 41 8 1 0
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Mathematical exploration and discovery at scale AlphaEvolve is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines ...

A new paper with Bogdan Georgiev, Javier Gomez-Serrano, and Adam Zsolt Wagner: "Mathematical exploration and discovery at scale" arxiv.org/abs/2511.02864. Further discussion is at terrytao.wordpress.com/2025/11/05/m...

5 months ago 123 27 0 3

Calling Bay Area math enthusiasts interested in weekly sessions doing rigorous foundational mathematics the modern way - with computer-verified proofs in Lean.

(An experiment in rigorous math education outside traditional academia)

6 months ago 41 8 5 2
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List of crowdsourced math projects actively seeking participants I believe that with the advent of modern online collaboration platforms (such as Github), proof assistant languages (such as Lean), and (potentially) AI tools, there are many emerging opportunities...

I started a crowdsourced meta-project to list all the other crowdsourced mathematical research projects that are currently active and seeking participants: mathoverflow.net/questions/50...

6 months ago 94 26 3 4
Terence Tao (@tao@mathstodon.xyz) Here is a first proof-of-concept demonstration of an actual outcome for the erdosproblems/OEIS linkage project. There are a number of Erdos problems relating to irrationality of specific series. I ask...

A first proof-of-concept outcome for the erdosproblems.com - OEIS linkage project: with a useful assist from AI, the OEIS was used to locate a proof in the literature for an Erdos problem that was previously marked as "open". mathstodon.xyz/deck/@tao/11...

7 months ago 73 10 3 0
Erdős Problems

Thomas Bloom and I are launching a crowdsourced project to link up Thomas's erdosproblems.com site with the #OEIS, by systematically calculating the various integer sequences associated with the Erdos problems and crosschecking them against the OEIS database: terrytao.wordpress.com/2025/08/31/a...

7 months ago 65 13 1 2
Simons Laufer Mathematical Sciences Institute (SLMath) 
- AxIOM Month-Long Programs: Call for Proposals for Spring 2027 and beyond
- PROOF and LATTICE summer research for teams: Call for Applications for Summer 2026

Simons Laufer Mathematical Sciences Institute (SLMath) - AxIOM Month-Long Programs: Call for Proposals for Spring 2027 and beyond - PROOF and LATTICE summer research for teams: Call for Applications for Summer 2026

SLMath (MSRI) announces three new research initiatives in Berkeley, California: Call for Proposals for AxIOM month-long programs to begin in Spring 2027, and applications for Summer 2026 PROOF and LATTICE independent research groups. Learn more at www.slmath.org/news-and-eve....

7 months ago 12 4 0 0
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I’m an award-winning mathematician. Trump just cut my funding. The “Mozart of Math” tried to stay out of politics. Then it came for his research.

I wrote an op-ed on the world-class STEM research ecosystem in the United States, and how this ecosystem is now under attack on multiple fronts by the current administration: newsletter.ofthebrave.org/p/im-an-awar...

8 months ago 792 325 21 32
Terence Tao (@tao@mathstodon.xyz) The current administration in the US has, through various funding agencies such as the NSF and NIH, has recently suspended virtually all federal grants to my home university, UCLA (including my own p...

I have some related posts on this at mathstodon.xyz/@tao/1149568... and mathstodon.xyz/deck/@tao/11...

8 months ago 38 6 0 0

#IPAM (the institute for pure and applied mathematics) is facing a critical shortfall for operating expenses due to an unexpected suspension of NSF funding www.ipam.ucla.edu/news/nsf-fun... . Donations for emergency continuity of operations funding can be made at

giving.ucla.edu/Campaign/Donat

8 months ago 128 39 5 7
Terence Tao (@tao@mathstodon.xyz) It is tempting to view the capability of current AI technology as a singular quantity: either a given task X is within the ability of current tools, or it is not. However, there is in fact a very wid...

My thoughts on the crucial importance of methodology on self-reported AI performance on mathematics competitions, and my policy on commenting on such reports going forward: mathstodon.xyz/@tao/1148814...

9 months ago 232 52 2 10
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Salem Prize About

The #SalemPrize for 2025 is now accepting nominations until September 15th. www.ias.edu/math/activit... (I am the chair of the Scientific Committee for the prize.) A bit more information in my blog post on this: terrytao.wordpress.com/2025/07/08/s...

9 months ago 24 6 0 0

If you click on the link and go to the second slide you will see the second part of the sentence (after the ellipsis ...), which mentions the tropic of Cancer.

10 months ago 0 0 0 0
First page of the instagram post

First page of the instagram post

A new #CosmicDistanceLadder post to mark the summer solstice, on how astronomical measurements, from the time of Eratosthenes to the modern day, rely on the tireless (and often unsung) efforts of many careful and precise data collectors. www.instagram.com/p/DLG6a_WIWyb

10 months ago 50 3 4 0

I have just launched a "Lean companion" to my textbook "Analysis I": github.com/teorth/estim... . This gives a Lean translation (or paraphrasing) of the various definitions, theorems, and exercises in the textbook into Lean.

Further discussion at terrytao.wordpress.com/2025/05/31/a...

10 months ago 134 27 0 3
Formalizing a proof in Lean by hand
Formalizing a proof in Lean by hand YouTube video by Terence Tao

A video on an actual formalization task from my Polynomial Freiman Ruzsa (PFR) project, which is sufficiently tricky (and sufficiently far from existing training data of current models) that one still has to largely formalize these proofs by "hand": www.youtube.com/watch?v=6uLX...

10 months ago 59 7 0 1
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The first page of the instagram post on how we measure cosmological durations.

The first page of the instagram post on how we measure cosmological durations.

A new #CosmicDistanceLadder post on how the distance ladder can also be used to measure cosmic durations, as well as cosmic distances. www.instagram.com/p/DJ2ra2soG4j

11 months ago 26 3 1 1
Formalizing a proof in Lean using Github Copilot only
Formalizing a proof in Lean using Github Copilot only YouTube video by Terence Tao

A third video in my occasional series on #Lean4 formalization workflows, this time focusing on how relying extensively on #GitHubCopilot fares against standard "epsilon delta" type problems in analysis. www.youtube.com/watch?v=c1ix...

11 months ago 46 0 0 2
Formalizing a proof in Lean using Claude and o4
Formalizing a proof in Lean using Claude and o4 YouTube video by Terence Tao

A followup to my previous video, in which I now see how #Claude and #o4mini do at formalizing a slightly different proof of the same algebraic implication, after being given the initial informal and formal proofs as reference. www.youtube.com/watch?v=zZr5...

11 months ago 45 3 1 0
Formalizing a proof in Lean using Github copilot and canonical
Formalizing a proof in Lean using Github copilot and canonical YouTube video by Terence Tao

As an experiment, I tried to use automated tools to formalize (in as "mindless" a fashion as possible) a one-page human written proof into Lean. You can watch the results here: www.youtube.com/watch?v=cyyR...

11 months ago 106 11 2 3
SAM.gov

DARPA's "Exponentiating mathematics" (expMath) program, which is launching a challenge to develop and evaluate "AI collaborators" for assist in decomposing and formalizing informal mathematical proofs, is now taking short abstract proposal submissions: sam.gov/opp/869c8d73...

11 months ago 28 6 6 1
The dashboard of the project reports a 100.00% completion rate.

The dashboard of the project reports a 100.00% completion rate.

After 200 days, we finally have 100% completion on the primary goal of the Equational Theories Project to formally resolve >22 million implications between 4694 equational laws, using modern proof assistants, collaboration platforms, and automated theorem provers. teorth.github.io/equational_t...

1 year ago 55 7 1 1
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A new #CosmicDistanceLadder post, on intriguing hints from the DESI survey data that suggests that the cosmological constant (aka "dark energy) might not, in fact, be constant after all. www.instagram.com/p/DIP0yy5oDUu

1 year ago 31 1 1 0
First page of the instagram post

First page of the instagram post

A new #CosmicDistanceLadder post on why lunar and solar eclipses tend to come in pairs (for instance, the solar eclipse next week is paired with the lunar eclipse from last week). www.instagram.com/p/DHkS3EcA40L

1 year ago 30 5 2 0
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Cosmic Distance Calibration xkcd.com/3066

1 year ago 11910 1004 99 43
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First page of the instagram post

First page of the instagram post

A new #CosmicDistanceLadder post, on how the recent lunar eclipse from the vantage point of the Earth becomes a solar eclipse from the vantage point of the Moon: www.instagram.com/p/DHR1tuWonDR/

1 year ago 24 1 1 1

Lunar eclipses, such as the one yesterday, were one of the earliest pieces of scientific evidence that the Earth was basically a round sphere, already known to Aristotle: regardless of the position of the eclipse in the light sky, the shadow of the Earth on the Moon was always circular.

1 year ago 73 15 1 0