Jay Cummings @LongFormMath

Math prof. Author of long-form textbooks on proofs (https://t.co/YqXnxDmOe0), real analysis (https://t.co/3IGQ6BIx5Z) & math history (https://t.co/KkXMGTxCDK). longformmath.com Sacramento, CA Joined July 2019

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Jay Cummings @LongFormMath

2 hours ago

The kiddo continues to be into math this weekend. Found a free spot on dad’s blackboard to solve some problems. Working on 5+100 right now.

Jay Cummings @LongFormMath

22 hours ago

My son asked me what infinity plus ten equals. I’ve been training for this moment my whole life.

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Jay Cummings @LongFormMath

19 hours ago

@CharleySeymour6 Maybe some day! But not soon. Got other things in the list first :-) Btw I clicked your profile and saw that you taught high school math in Tucson. That’s great, I have family there. My cousin’s daughter graduated from Tanque Verde High School.

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Jay Cummings @LongFormMath

22 hours ago

My son asked me what infinity plus ten equals. I’ve been training for this moment my whole life.

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Jay Cummings @LongFormMath

19 hours ago

Chill, it’s only been 3 hours. He’s 5 years old so it takes time. Anyways, we started with bijections and cardinality, moved on to countable versus uncountable infinities, Cantor’s diagonal argument, Hilbert’s Hotel, ordinal arithmetic and transfinite induction. I’m trying to get to the aleph hierarchy before bedtime, but he’s really struggling with the axiom of choice and Zorn’s lemma. I think I’ll wait until the morning to cover the continuum hypothesis—don’t want to give him bad dreams, ya know.

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Jay Cummings @LongFormMath

2 days ago

“The reports of my death have been greatly exaggerated” —human math researchers

Abhishek Saha @ObhishekSaha

4 days ago

Some fascinating developments following OpenAI's shock breakthrough proof of the Quasi-Riemann Hypothesis, which was released publicly on October 6: 1. Building on OpenAI's proof, a recent Hexagon preprint (released on October 12) by Cureton and Thorner establishes that ALL

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OpenAI @OpenAI

2 days ago

We want to support the mathematics community in turning progress in AI into deeper human understanding and new discoveries. To support that goal, we are contributing $5 million to a new Simons Foundation initiative to help mathematicians examine, understand, and build on results produced by AI, including the results we recently published. The funding, managed and awarded by the @SimonsFdn will support workshops, conferences, and special programs. We will also provide access to our models and computing resources to Simons Foundation-supported researchers.

Simons Foundation @SimonsFdn

2 days ago

How can the math community forge the best path forward in the AI age? We're committing $15M to workshops and initiatives — plus free AI computing resources for foundation-supported researchers — through new partnerships with @AnthropicAI and @OpenAI: bit.ly/4zpfIbW

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Jay Cummings @LongFormMath

2 days ago

I love math, and I thought this was a beautiful interview. My mom is allergic to math, and she thought this was a beautiful interview. So I think many people will find value in this conversation. I listened to it yesterday, but I suspect the video version will be more poignant

Steven Strogatz @stevenstrogatz

4 days ago

nytimes.com/video/podcasts…

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Jay Cummings @LongFormMath

3 days ago

@sujoyrc I think AI can help guide a student’s vague questions toward interesting pastures. But I agree it will be imperfect.

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Jay Cummings @LongFormMath

6 days ago

During K-12 school, I didn’t particularly like math. It was only when I took college-level math courses that I fell in love with the subject. Now that AI is making the fun and fascinating parts of math much more accessible, I hope far more people will also come to love math.

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Jay Cummings @LongFormMath

3 days ago

@Satyaki_R @golchha_J It’s mostly silly stories IIRC, but I also think that’s the book that comes closest to what you’re after. (Please let me know if you find a better one!)

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uguu @removeanime

5 days ago

you could be living in sacramento you could be sacramentomaxxing we have the the kings, old sac, the waterfront you will build your life in sacramento, california

Alessandro Palombo @thealepalombo

5 days ago

America’s most livable cities, at local median salary and local tax rate. New York: this is probably the reason why Mamdani won

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Ruben Sanders @RubenSanders28

6 days ago

Just getting started on @LongFormMath’s Proofs, already much more lively than how proofs were taught in high school. Looking forward to the rest of it!

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Jay Cummings @LongFormMath

5 days ago

@RubenSanders28 I hope you enjoy it!!

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David Bessis @davidbessis

5 days ago

10 remarks on AI and math that can be true all at once: 1. The recent progress is stunning and exciting. 2. The Quasi-Riemann Hypothesis is arguably Fields-medal level. 3. Mathematics is being transformed and there is no way back. 4. OpenAI doesn't give a fuck about the future of mathematics. 5. Half-baked unreadable preprints claiming major results can effectively stall mathematical progress. 6. Some mathematicians are responding with naive, overly defensive comments. 7. The social-media wankers framing this as "OpenAI tramples gatekeeping" have no experience of mathematical research. 8. The product of mathematics is clarity and understanding. Not theorems, by themselves. 9. Mathematics is a critical infrastructure of human cognition. The human need for understanding isn't obsolete and it can't be offloaded to machines. 10. We haven't "solved" mathematics and we won't get there before the Sun burns out.

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Jay Cummings @LongFormMath

6 days ago

For examples of how AI might do this:

Jay Cummings @LongFormMath

6 days ago

@theonlymolnar A younger me would have been very interested in learning about advanced topics in math, but nobody around me knew those topics or had time to share them with me. If I had AI to chat with, I very likely would have asked it to teach me things. Similarly, for many people in the

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Jay Cummings @LongFormMath

6 days ago

A younger me would have been very interested in learning about advanced topics in math, but nobody around me knew those topics or had time to share them with me. If I had AI to chat with, I very likely would have asked it to teach me things. Similarly, for many people in the world, even buying math books and other resources is challenging. Also, people who love to teach math now have new resources to do a better job at it. Lastly, AI will be discovering new and beautiful things. Which both increases the quantity of fun, fascinating things to study, and also produces a lot of new things which in some ways is more exciting than studying very old math

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Jay Cummings @LongFormMath

a week ago

@Mathenvarghese Seems possible. But also seems too early to say.

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Jay Cummings @LongFormMath

a week ago

Very exciting prospects for applied math! And AI holds the promise of enabling scientists to more capably work with these deeper areas of math. I hope OpenAI leans much more in this direction, where the benefits extend to humanity more broadly.

Ole Lehmann @itsolelehmann

a week ago

“okay, so what? it’s just math.” no, you don't get it. here’s what OpenAI’s math breakthroughs could eventually help make possible in the real world: Vlasov–Maxwell → stronger foundations for fusion research, whose ultimate prize is virtually limitless clean energy to power

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Jay Cummings @LongFormMath

a week ago

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.

Jay Cummings @LongFormMath

a week ago

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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Jay Cummings @LongFormMath

a week ago

@archernikov The friend is Zach Norwood btw. Do you know him?

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Jay Cummings @LongFormMath

a week ago

I think that partially depends on you. For some people, learning the old-fashioned way might still be best. For some people learning through a very extended and ongoing conversation with AI might be best. I heard one professor tells his PhD students to alternate between one week being all-AI and one week no AI. That sounded pretty good too!