Math prof. Author of long-form textbooks on proofs (amzn.to/3oZrMNu), real analysis (amzn.to/2kjvMwh) & math history (a.co/d/8pLSo0C).
Joined July 2019
- Tweets 6,824
- Following 585
- Followers 45,701
- Likes 29,369
1,356 Photos and videos
Pinned Tweet
22 Apr 2025
🧵 My 3rd book is now out! It is on the fascinating history of math.
How did people throughout history think about math?What problems did they care about? How did they express them? How were they solved?
This book includes a lot of historical math.
a.co/d/gsoNKxP
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f(a) = aᵖ⁻¹ (mod p)
Examples of an actor's limited range adding to the performance.
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Jun 12
Andrew Wiles, Évariste Galois, Ada Lovelace, Paul Erdős
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Jay Cummings retweeted
Jun 12
writing a blog post on Sperner's Lemma and god damn Claude Fable 5 can do parallax animations SO well
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Jun 11
𝘛𝘩𝘦 𝘭𝘢𝘴𝘵 𝘍𝘪𝘦𝘭𝘥𝘴 𝘔𝘦𝘥𝘢𝘭𝘪𝘴𝘵 𝘩𝘢𝘴 𝘢𝘭𝘳𝘦𝘢𝘥𝘺 𝘣𝘦𝘦𝘯 𝘵𝘳𝘢𝘪𝘯𝘦𝘥
Jun 11
GPT is 8 years old today. It has 32 years left to win a Fields Medal.
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Jun 11
A short poem:
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Jay Cummings retweeted
Jun 11
Not a cloud in the sky across virtually all of California today.
What a view from space.
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Jun 1
Departing today on a 5-day cruise trip with family.
Hoping cruise ships do NOT make news this week 🙏🏻
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May 30
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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Jay Cummings retweeted
Another major problem, this time in additive combinatorics, has fallen, this time to humans rather than AI, but using methods related to the AI solution to the unit distance conjecture.
A remarkable paper appeared on arXiv tonight by Thomas Bloom, Will Sawin, Carl Schildkraut and Dmitrii Zhelezov. In this paper, they prove that there exists c>0 and arbitrarily large finite sets A of real numbers such that max(|A A|,|AA|)≤|A|^{2-c}. This disproves the well-known sum-product conjecture over the real numbers. The sum-product conjecture considers the two most basic operations: addition and multiplication. A A is the set of all pairwise sums of two elements in A while AA is the set of all pairwise products of two elements in A. (1/5)
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May 28
Most of the Ivy League schools have now reinstated SAT/ACT requirements. Yale’s announcement today:
May 26
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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May 27
I ended my 2025 math history book discussing Erdős and how his conjectures continue to stimulate math research. The book’s final sentence was:
“Of all the dead mathematicians, Erdős is the most alive.”
Given the last couple weeks, I suppose that holds up well? At least for the time being…
May 24
JUST IN: Google DeepMind says its AI solved 9 open Erdős problems — considered among the hardest unsolved questions in mathematics.
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Jay Cummings retweeted
Earlier this month I volunteered at Stanford’s Future of Math symposium, and ever since, I've been puzzling through what it now means to pursue mathematics as a student in the age of AI. I wrote an essay to make sense of it all: apoorvapanidapu.substack.com…
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May 27
Every integer greater than 77 is the sum of integers whose reciprocals sum to 1.
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May 26
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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May 26
AI solves an Erdos problem and the mathematician pope immediately moves to shut the whole program down. We are so back.
May 25
Humanity, created by God in all its grandeur, is today facing a pivotal choice: either to construct a new Tower of Babel or to build the city in which God and humanity dwell together. In Jesus Christ, this humanity in its grandeur becomes the Way, the Truth and the Life, opening the path for each of us to grow toward fullness. #MagnificaHumanitas
vatican.va/content/leo-xiv/e…
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May 26
I have my great-grandparents’ radio. My grandma would sit next to it as a little girl to listen to FDR’s fireside chats.
May 21
DOES ANYONE HERE HAVE SOMETHING IN THEIR HOUSE THAT'S OVER 40 YEARS OLD..
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May 22
First robot tattoo just dropped
Following up on the suggestion from Will Sawin, here is an illustration of the new configurations that disprove Erdos' unit distance conjecture (made with the help of ChatGPT 5.5 Thinking).
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May 22
Prominent mathematicians as recently as the 17th century were proving amazing things, yet were still uncomfortable with negative numbers.
Cardano called them “fictitious.”
Pascal said that subtracting 4 from 0 is “utter nonsense.”
Descartes had mixed feelings but called negative roots “false.”
Leibniz said they are just a tools to guide one’s thinking, or an indication that the question with poorly formed.
May 12
What historical fact sounds fake but is true?
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May 21
GRADES SUBMITTED
Love that as an adult I still get to experience that “first day of summer” joy :-)
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