@QuantaBks publisher; @QuantaMagazine founding editor; former @nytimes, @ScienceWriting; author list: Terence Tao, David Tong, Kevin Hartnett
New York City
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It was an intellectual joyride working with Terry Tao on his first popular math book SIX MATH ESSENTIALS. In stores Oct 27, now available for preorder: quantabooks.org
We’re thrilled to announce that Terence Tao’s SIX MATH ESSENTIALS is available for preorder: us.macmillan.com/books/97803…. A whirlwind tour through six core ideas that have guided mathematicians from antiquity to the frontiers of what we know today, the book pubs October 27, 2026
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Watch this terrific video about Lean by @MLStreetTalk: piped.video/IRJDwtAreB4
Then read @KSHartnett’s definitive account of Lean’s origin story: quantabooks.org/books/the-pr…
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The AI-assisted video edit is cool, but the real gem is Po’s simple, elegant (and natural) explanation for why e is natural. In other words, Claude Code saved time, but the video’s true value lies in the mathematical beauty, wonder, and joy that Po inspires.
An easier way to explain why e is natural: video finally released! piped.video/03n3SQBAUrs
I actually recorded this last year. But none of us had time to edit the footage. Then I built a full video editing pipeline in Claude Code. Amazing what can be done now! (All real footage)
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Thomas Lin retweeted
Are you a college journalist looking to work in one of the country’s great local newsrooms next summer? Come work with me at The Dallas Morning News.
FAQ = bit.ly/4dBASLR
Apply by Nov. 6, 2026 = dallasnews.com/internships
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A wonderful @newscientist review of Terence Tao’s SIX MATH ESSENTIALS (naturally called Six Maths Essentials in the UK), publishing Nov 10 in the U.S. by @QuantaBks. Makes a perfect gift for the holidays: quantabooks.org/books/the-pr…
Terence Tao, one of the world's great mathematicians, urges us to find empowerment in numbers in his new book Six Maths Essentials. Karmela Padavic-Callaghan is convinced newscientist.com/article/259…
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Thomas Lin retweeted
1/ Two really fun reviews just landed back to back in Current Biology, both on a question I never get tired of: why did animals take over when they did? One argues animals engineered their own world. The other argues oxygen and temperature had to line up first.
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Thomas Lin retweeted
"We recognize the power of new technologies for mathematical reasoning and appreciate what they can contribute to the subject we know and love. We are generally optimistic about the role AI can play, but we are deeply concerned by some recent calls to formalize everything as quickly as possible. If done well, a large-scale, coordinated formalization effort could enormously expand mathematical exploration and discovery. Done poorly, it will be, at best, a waste of resources; more likely, it will do lasting damage."
A guest post on xenaproject by Jeremy Avigad, Kevin Buzzard, Johan Commelin, Rémy Degenne, Kim Morrison, Oliver Nash and Adam Topaz
xenaproject.wordpress.com/20…
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We broke this story in @QuantaMagazine in 2013. quantamagazine.org/yitang-zh…
In April 2013, a 58-year-old mathematician named Yitang Zhang submitted a paper to the prestigious Annals of Mathematics.
At the time, he was virtually unknown in the mathematical community.
After earning his PhD from Purdue University in 1991, Zhang struggled to find a permanent academic position.
For years, he worked outside academia, including at a Subway sandwich shop, before eventually becoming a lecturer at the University of New Hampshire, where he taught undergraduate mathematics.
Yet throughout those difficult years, he continued pursuing his own mathematical research, particularly the mysteries of prime numbers.
In July 2012, while visiting a friend in Colorado, Zhang was sitting quietly in the backyard when an idea came to him. He had spent three years working on a problem involving the gaps between prime numbers, and suddenly he saw a way past an obstacle that had frustrated some of the world's leading number theorists.
Over the following months, he carefully developed that insight into a rigorous mathematical proof.
On April 17, 2013, he submitted his manuscript to the Annals of Mathematics.
The response was remarkable. Within just three weeks, the referees had delivered an unusually enthusiastic report, recognizing the work as a landmark achievement. The paper was formally accepted on May 21.
For centuries, mathematicians had wondered whether infinitely many pairs of prime numbers could occur within some fixed distance of one another.
The famous twin prime conjecture predicts that infinitely many pairs differ by exactly 2, such as 11 and 13 or 17 and 19.
Zhang did not prove the twin prime conjecture itself. Instead, he established something that had never been proved before: there are infinitely many pairs of consecutive primes whose difference is less than 70 million.
Seventy million might seem enormous when compared with 2. But the crucial breakthrough was that the gap was bounded by a fixed number, no matter how far along the number line one went.
It was the first proof that bounded gaps between consecutive primes occur infinitely often.
His discovery opened an entirely new chapter in number theory, inspiring mathematicians around the world to improve his bound. In 2014, Zhang received a MacArthur Fellowship in recognition of his extraordinary achievement.
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The @WSJ has been 🔥: “One of the deadliest saboteurs in recent military history, Lt. Lev Stupnikov fed troop locations and battle plans to the enemy before making a daring escape.”
wsj.com/world/russian-defect…
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Thomas Lin retweeted
Many people just starting out on Lean formalization have enjoyed playing the Natural Numbers Game. Now Autumn Mapes has produced Visual Lean, isomorphic to the original but playable in a lovely intuitive way with clicking and dragging rather than typing.
leangame.autumnofautumn.com/
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Thomas Lin retweeted
Imagine being in a group chat with 20 Fields Medalists!
Full interview with Terence Tao now on Numberphile.
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Thomas Hales on Terry Tao’s blog: “Mathematicians have been weighing in on what they value about mathematics. For me, what matters is the consistency of math and its unparalleled reliability in support of science and civilization.”
terrytao.wordpress.com/2026/…
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Thomas Lin retweeted
How fun. The podcast I co-host with the great @stevenstrogatz -- The Joy Of Why from @QuantaMagazine -- is nominated for a signal award. Cast your vote. Voting = loving vote.signalaward.com/PublicV…
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“We want to put them in trauma.” Mission accomplished.
As budget director, Russell Vought has often ignored Congress by … not signing the checks.
At other times, he’s been able to take money Congress intended for one thing and use it for something else by justifying it as a “national emergency.”
Listen: propublica.org/podcast/who-i…
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Thomas Lin retweeted
I think of my goal as a mathematician as something like: to better understand the fundamental concepts “shape” and “number,” and to convey that understanding to others. I think this is a valuable goal for many reasons. The primary reason discussed on social media is the (admittedly slow, but I think very real) diffusion of mathematical ideas into technologies that better our lives. There are others, though: production of human capital (which plays some role in this diffusion), and diffusion of mathematical understanding into culture, for example. It is not obvious to me that even the bare technological need for mathematics can be filled without human experts; this seems to me to be a tricky question of institutional design.
For me the most compelling reason is simply that we feel a pressing need to understand. While deep understanding is largely limited to professional mathematicians, the existence of mathematicians and of the institutions they make up is a huge part of what makes mathematical understanding available to those who want it. I believe that the capacity to understand mathematics (and the universe as a whole) is part of a good life, and we should try to provide people with a good life.
We operationalize the goal of understanding in a number of ways, problem-solving and theorem-proving among them. My own research is oriented around certain open questions that I believe measure our lack of understanding (of numbers, shapes and so on), and I think resolving those is genuinely important. I would welcome a solution with any provenance. But I think proof is only a measure of progress—what actually matters (for technology, human capital, culture, a good life) is a bit harder to get at.
Crucially it is very hard to measure progress—plausibly theorem-proving is used in large part because it is easy to measure rather than because it is a perfect proxy for what we care about. I worry a bit that we may automate many easy-to-measure things without automating the correlates we care about for which they are proxies. This presents a clear problem for the design of institutions aimed at achieving progress.
In part because I think problem-solving is a proxy for something else, I don’t feel that my goal of understanding “shape” and “number” is particularly threatened by a machine that is good at problem solving. I expect that machine to be a substantial boon, instead. Ultimately I think we will operationalize mathematical progress in better ways. But how to do this is a difficult question and I think many on here are too quick to dismiss concerns about it.
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Amazon book reviewers are not always known for their concision, but this reader captured @KSHartnett’s THE PROOF IN THE CODE (@QuantaBks/@fsgbooks) in two sentences:
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Thomas Lin retweeted
Out today in @nature.com: our review on how single cells evolve into multicellular organisms, with Ozan Bozdag, @kai_tong_mc25, Peter Yunker, and Matt Herron.
rdcu.be/9ZuiKow9twKa
For an overview, check out the video below.
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Thomas Lin retweeted
Terence Tao has a Fields Medal, a MacArthur Fellowship, and a reputation as the greatest living mathematician.
None of it lets him skip a single step.
"Doesn't matter how famous you are or how much of a reputation you have, you can't just say I've proven something, trust me."
I asked Terry what changed after his Fields Medal in 2006. Invitations to embassies. Seats on committees. Suddenly everyone wanted his opinion. What kept him grounded was the work itself. Every step of a proof has to be validated, and if you don't have the proof, you don't have the proof.
Then he said something every PhD student should hear: "I know more problems that I can't solve than the problems I have solved."
He also told me about his grad school years at Princeton. He'd spend hours on a problem his advisor had assigned, try every crazy idea he had, and come back each week with a list of failures. His advisor would look at the blackboard for 10 or 15 seconds, pull out one preprint, and say: read this. It solved the problem every time.
That wasn't magic. It was experience. His advisor knew exactly who had already hit the same wall, and how they got past it.
Now Terry pulls the same trick on his own students. Full circle.
Three lessons I keep coming back to as a professor:
1. Credentials buy you attention, not truth. The work still has to stand on its own.
2. A long list of problems you can't solve isn't a weakness. It's a map.
3. The best mentors don't hand you the answer. They hand you the paper.
Watch the clip: piped.video/5BRMqYLOH0Y
What's the most useful thing a mentor ever handed you?
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