Btw it seems like this one is not completely verified yet with Lean. And many others also seem to not be verified with Lean.
Seems strange that they would release so many where a lean check is doable but not done.
Seems strange that they would release so many where a lean check is doable but not done.
I love this theorem. And I hope many people work to improve AI’s proof of it. The Book Proof is still out there! :-)
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I love this theorem. And I hope many people work to improve AI’s proof of it. The Book Proof is still out there! :-)
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Decades worth of “progress” can now be accomplished in 3 weeks using a single model.
The era of theorem abundance is here.
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…
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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, 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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Need this house just to turn that two-story area into a personal library which I’ll live in forever
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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! 🤩
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.
youtu.be/g80IBdGQ1k8
youtu.be/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…
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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!
youtu.be/ZmTO1v8rsBk?is…
youtu.be/ZmTO1v8rsBk?is…
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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:
youtu.be/X2IgwuKlIVs
Proofs by Induction and Dominoes:
youtu.be/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. introduced and studied double zeta values.
GMOAT things.
For example, in 1776 Euler wrote his landmark memoir giving the modern formulation of linear and angular momentum in mechanics. 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/java/e…
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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
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”
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:
youtube.com/watch?v=UcoEBd…
youtube.com/watch?v=UcoEBd…
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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/business/digit…)
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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 & essably 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!
youtu.be/xUt-2nEacYM?si…
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I'm back to posting YouTube videos on my proofs book. Just started chapter 3, on sets!
youtu.be/xUt-2nEacYM?si…
youtu.be/xUt-2nEacYM?si…
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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:
youtube.com/watch?v=Regahz…
youtube.com/watch?v=Regahz…
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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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