Math prof. Author of long-form textbooks on proofs (amzn.to/3oZrMNu), real analysis (amzn.to/2kjvMwh) & math history (a.co/d/8pLSo0C).
Sacramento, CA
Based in United States
- Tweets 6,988
- Following 600
- Followers 51,976
- Likes 29,837
Decades worth of “progress” can now be accomplished in 3 weeks using a single model.
The era of theorem abundance is here.
We’re working with an independent advisory group of mathematicians to help OpenAI responsibly share advances in AI and mathematics.
The group will advise on how we assess and communicate new mathematical results, uphold academic and professional standards, and build tools that support mathematical research and learning.
Through this work, we want mathematicians to be at the center of shaping how AI supports mathematical understanding and how its benefits reach the wider community.
openai.com/index/advisory-gr…
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The Bernoullis were more than a family of mathematicians; they formed a remarkable mathematical dynasty.
Across several generations, Jacob, Johann, Daniel, and others made important contributions to mathematics and mathematical physics during the 17th and 18th centuries, alongside figures such as Newton, Leibniz, and Euler.
Their story also includes one of the most famous rivalries in mathematical history. Jacob and Johann initially collaborated in studying Leibniz’s calculus, but their relationship gradually deteriorated into a bitter and very public competition, with the brothers challenging and criticizing each other over mathematical problems and priority.
Whether this rivalry actually fueled their achievements is difficult to establish. What is clear is that their intense competition existed alongside work of lasting importance, and their family became one of the most influential mathematical lineages in early modern Europe.
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“Whew. Big day of math news. But that’s enough math twitter for today. Let’s just flip over to my politics twitter account and see what everyone’s talking about over there—”
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And now he’s off to kindergarten 🥹🥹
How’s this timing: It’s the 1st day of fall semester, my 1st class starts in 15 mins, and this morning my wife went into labor.
Logging into Zoom from the hospital to tell my students the news and then dismiss class.
Wife is doing amazingly! Maybe 3-5 hours until baby arrives!
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"If I were to awaken after having slept for a thousand years, my first query would be: Hey Claude, please solve the Riemann hypothesis and make no mistakes." - David Hilbert
Wow, what a genius. So ahead of his time! 🤩
We asked an unreleased research version of Claude to take a stab at the Riemann hypothesis.
It didn’t solve it, but it did make strides on a related problem: it increased the lower bound for the fraction of zeros of the Riemann zeta function that satisfy the hypothesis from 41.6% to 67.2%.
anthropic.com/research/riema…
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Are AI developers the first people to think there’s like a 10% chance they get added to this list but they plough ahead anyways?
Breaking News: Scientists have used A.I. to create new viruses for the first time, raising hopes for medical advances while also raising the possibility that the technology could someday be used to invent dangerous pathogens. nyti.ms/4bxx7Wy
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In today’s YouTube video, I discuss inflection points in math history and the Erdős unit distance problem.
piped.video/g80IBdGQ1k8
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“Sir, another counterexample has been found. Our conjectures are under attack.”
Dinitz-Garg-Goemans conjecture is false. This graph theory problem was open for ~30 years.
The graph below has fractional flow cost 58. Any unsplittable flow (with capacity violation <=15) has cost at least 60.
Chat with GPT 5.6 Pro where this was found: chatgpt.com/share/6a60b2eb-0…
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New book in the “Counterexamples in” series is available on a subscription plan for $400/month
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Today’s video is a fake proof that the harmonic series converges. Check it out here!
piped.video/ZmTO1v8rsBk?is=OrZS…
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Wow! Just came across this. Looks like someone made a LFM shadow object to celebrate Long-Form Math textbooks🤩
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Btw I have slowly but surely been making videos over the content of my Proofs book. This week I began chapter 4. Check it out and subscribe if you’re interested! Eventually I will go through all the other books too.
Proofs by Induction and Dominoes:
piped.video/X2IgwuKlIVs
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Students like this warm my heart. It’s effortless to be dishonest, and yet they make an honest effort anyways!
Friends don't let friends continue to give exams and papers that are not adapted to the current AI landscape (this is AFTER 27 bailed so the reality is even worse)
PS Props to students 1, 22, and 31
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Btw on July 4, 1776, Leonhard Euler was 69 years old, was almost completely blind, and was still writing over one paper a month at a very high quality.
For example, in 1776 Euler wrote his landmark memoir giving the modern formulation of linear and angular momentum in mechanics. And in another paper he introduced and studied double zeta values.
GMOAT things.
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Happy Independence Day US! There's plenty of mathematics in your Declaration. Thomas Jefferson deliberately used a Euclidean "axiom-and-proof" framework for it: the document begins with self-evident truths (axioms) and builds to a logical conclusion. You will find plenty of articles on this, but it's just as well to enjoy the original spring of ideas here aleph0.clarku.edu/~djoyce/ja…
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Noticed a clever pun at the end of this abstract, on whether AI might help to reveal the global structure of mathematics by analyzing the relationships among proofs.
s/o @grok
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I just read that Charles Darwin made Pros-and-Cons list when deciding whether or not he should get married (to his first cousin).
One of the 9 benefits to staying single: “more money for books”
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I was interviewed on the Office Hours podcast. Here it is if you’re interested:
piped.video/watch?v=UcoEBdAS…
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The next summer thriller
Hollywood studios are searching Reddit for short stories and ideas that can be turned into movies following the success of ‘BACKROOMS.’
(hollywoodreporter.com/busine…)
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You just won a 2-week, all-expenses-paid vacation. But there’s a catch: you have to stay within one region the whole time. What are you picking?
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Most of the Ivy League schools have now reinstated SAT/ACT requirements. Yale’s announcement today:
University of California STEM professors want standardized tests back due to severe math deficiencies among students:
“We now observe preparation gaps so severe that instructors must reteach middle school mathematics”
“The current admissions metric, based primarily on GPA & essays, can no longer reliably distinguish readiness for university-level STEM majors in an era of severe grade inflation & AI assisted application essays”
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I have my great-grandparents’ radio. My grandma would sit next to it as a little girl to listen to FDR’s fireside chats.
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My student writes little songs to remember math definitions. What it means to be on open/closed set in R:
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A student seems to have dropped their study sheet for some class and it seems vitally important to get it back to them?? I mean this is a tragic loss, right??
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Today's meme
I'm back to posting YouTube videos on my proofs book. Just started chapter 3, on sets!
piped.video/xUt-2nEacYM?si=BUvJ…
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I'm back to posting YouTube videos on my proofs book. Just started chapter 3, on sets!
piped.video/xUt-2nEacYM?si=BUvJ…
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Two of my students are in a band and they made a cover of my math history song. I love it so much. Check it out:
piped.video/watch?v=RegahzeR…
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I might have a new favorite proof that the harmonic series diverges. It's just so beautiful.
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In the age of AI writing, it is more important than ever to emphasize this to the next generation. Writing is not a simple record of what you think---it is one of the best ways to learn. And it is a means to uncover what you didn't know you believed.
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ICYMI: I wrote a math history song. (And I think it's actually pretty damn good!)
You can watch the music video on YouTube:
piped.video/watch?v=0KrT_Vl3…
Or listen on Spotify:
open.spotify.com/album/3MEbK…
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Little news: I wrote a song! It is a math history version of Billy Joel's "We Didn't Start the Fire."
I then got Tom Bedlam to perform it, and I turned that into a music video.
Check it out! I hope you enjoy it!
piped.video/watch?v=0KrT_Vl3…
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My latest YouTube video discusses why we prove things in math. Check it out!
(And subscribe! I have a math music video that I plan to post next Wednesday that I think you will enjoy! 😃)
piped.video/watch?v=2QcJB-Yl…
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My kiddo and I recently finished our 100th chapter book. :-) It’s been so fun, but I am running low on book ideas.
Do you have recommendations? Ideally we want an early chapter book with lots of pictures, but feel free to suggest others too!
Here’s what we’ve read:
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I am starting a sequence of videos on my YouTube channel in which I will cover the main content of my Proofs book.
In the first video, I argue that learning proofs amounts to a "phase change" in your math eduction.
Please check it out and subscribe!
piped.video/watch?v=HbUagv4n…
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I'm also playing chess with @MathMatize. He beat me in game 1. I beat him in game 2. Tiebreaks incoming.
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