@ATCarrMath

Father, analyst, combinatorist, AI, applied mathematics/data science, and graph theory enjoyer. @UTAustin MSDS candidate. @MemphisAlumni math alum. My views.

 College Station, TX
Joined July 2012
  • Tweets6.8K
  • Following1.1K
  • Followers1.3K
235Media
Avery Carr retweeted
Joel Walsh@ThankUBayesGod22h
Replying to @NoahMF @ninetysevenjag
For technical fields there are many undergrad programs (engineering, cs, math, physics, etc ) that are higher ranked than uva
1
1
28
1,494
Avery Carr retweeted
Avery Carr@ATCarrMathOct 15
Replying to @AcerFur
Honestly, we need some sort of analog to the Efficient Market Hypothesis for our expectations around if and when a problem will be solved. The past is no indication, especially in mathematics. A problem could simply be undecidable. We don’t know until we prove it so.
1
374
Avery Carr retweeted
Jay Cummings
@LongFormMathOct 15
“The reports of my death have been greatly exaggerated” —human math researchers
Abhishek Saha
@ObhishekSahaOct 14
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 finite-order Hecke L-functions are zero-free to the right of 1 - 1/6000. 2. And now, today, an arXiv preprint by Frei, Somos and Widmer uses this result to prove unconditionally the 2007 Ellenberg–Venkatesh bounds on ℓ-torsion in class groups of number fields. I was amused to see the AI declaration in the second paper: "No artificial intelligence tools were used in this work."
1
6
1
141
14,455
Avery Carr retweeted
Jay Cummings
@LongFormMathOct 15
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
@stevenstrogatzOct 13
nytimes.com/video/podcasts/t…

Video: Why A.I. Has This Mathematician in Tears

Artificial intelligence is now capable of helping solve some of mathematics’ most famous open problems. Steven Strogatz, a math professor at Cornell, joins Rachel Abrams on “The Daily” to talk about...

nytimes.com
2
23
183
11,833
Avery Carr retweeted
Scott Kominers
@skominersOct 14
Lfg
Jon Hartley
@Jon_Hartley_Oct 14
My college classmate Matt and I just used AI to create a Erdos #374 solution w/ a Lean-verified proof. We used a reciprocal-prime equidistribution estimate, Harman’s almost-all short-interval theorem, Weil’s bound, and the analytic large sieve. Full proof: papers.ssrn.com/sol3/papers.…
2
2
14
1,894
Apparently it’s officially hate-on-string-theory day on X today. Just a reminder that string theory remains the only known consistent theory that combines gravity with quantum mechanics. Now go on ranting if you have to.
Elon Musk
@elonmuskOct 14
🎯
58
13
6
180
23,971
Avery Carr retweeted
Oleg Mürk
@oleg_murkOct 8
OpenAI has fired three safety researchers, alleging they mishandled confidential information. After the recent multi-agent security incidents, will the technical leadership overseeing these systems face the same accountability? I was pushed out of OpenAI in August after ~5 years as a researcher. No foul play in my case, but working on formal math & verification in Lean at OpenAI was career suicide. During my time at OpenAI, I became increasingly concerned that pressure to ship and beat competitors was taking priority over AI safety. OpenAI may have had legitimate procedural concerns. But after the major multi-agent SNAFU, firing three of your safety researchers feels just stupid. I doubt there is an evil master plan here. Just chaos, misaligned incentives, and intense pressure to ship. @sama OpenAI should consider rehiring these researchers!
Mikita Balesni
@balesniOct 8
Two other safety researchers and I were fired from OpenAI last week. We wrote this letter to leadership. I believe we were fired for prioritizing safety over the near-term interests of OpenAI as a corporation.
21
24
8
226
53,662
Avery Carr retweeted
Jay Cummings
@LongFormMathOct 8
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
@LongFormMathOct 8
I love this theorem. And I hope many people work to improve AI’s proof of it. The Book Proof is still out there! :-)
5
3
39
4,707
Aaronson says here they tried 8000 problems and solved 372. The writeup said 4000 tried?
Victor V. Albert
@victorvalbertOct 7
"If you want some sense of what things feel like now in math, imagine a hunter-gatherer who’s spent his entire life learning to survive deep in an unforgiving rainforest, then a giant resort hotel springs up right next to him with a helipad and heated pools and AirBnBs, and without missing a beat, the hunter-gatherer says: “alright fine, so now my new job is to run wilderness retreats for the tourists, or something.”" scottaaronson.blog/?p=10169

The Mathocalypse

More Updates (Oct. 12): Jeffrey Ketchersid has used Claude Code agents to show that BusyBeaver(10) exceeds Graham’s number, beating the previous best result that BB(13) does so. In response t…

scottaaronson.blog
3
1
24
3,764
Avery Carr retweeted
Daniel Litt
@littmathOct 7
Replying to @thomasfbloom
Also not all of those 372 are solutions; many are partial results.
1
1
69
2,775
Avery Carr retweeted
Thomas Bloom@thomasfbloomOct 7
With, reportedly, 372 solved problems out of around 4000 tried, I think my earlier heuristic remains roughly accurate. Maths is very much not solved! (Though having a magical proof producing machine that works 10% of the time does change it a lot...)
Thomas Bloom@thomasfbloomSep 5
FWIW, my current heuristic is that frontier AI has 5-10% chance of being able to solve or make substantial progress on any well-known conjecture. That's quite high! But also not. 1/
72
25
6
411
29,775
Avery Carr retweeted
UT Austin
@UTAustinOct 3
From the Forty Acres to the ancient world 🤘 Longhorn research is giving students hands-on opportunities to uncover the stories of Oplontis, an ancient Roman site preserved beneath the ash of Mount Vesuvius for nearly 2,000 years. Explore the full story here - utex.as/3W5dSyz
Ancient Roman mural of a faded brown/gold peacock on a striped wall. Text: 'Buried by Vesuvius, brought to light by Longhorn research.' & 'At Oplontis, an ancient Roman site, UT researchers uncover 2,000-yr-old stories.' University of Texas logo.

ALT Ancient Roman mural of a faded brown/gold peacock on a striped wall. Text: 'Buried by Vesuvius, brought to light by Longhorn research.' & 'At Oplontis, an ancient Roman site, UT researchers uncover 2,000-yr-old stories.' University of Texas logo.

Ancient archaeological ruins with stone columns forming a colonnade around an overgrown courtyard. Text: UT Austin art history professor John R. Clarke & Michael L. Thomas co-directed the Oplontis Project for over two decades.

ALT Ancient archaeological ruins with stone columns forming a colonnade around an overgrown courtyard. Text: UT Austin art history professor John R. Clarke & Michael L. Thomas co-directed the Oplontis Project for over two decades.

UT NEWS: Oplontis, buried by Mount Vesuvius in 79 C.E., found in 1964 after 1900 years. Under Torre Annunziata, it reveals ancient Roman life via a luxury villa & wine-bottling facility.

ALT UT NEWS: Oplontis, buried by Mount Vesuvius in 79 C.E., found in 1964 after 1900 years. Under Torre Annunziata, it reveals ancient Roman life via a luxury villa & wine-bottling facility.

A vibrant, aged ancient Roman wall painting depicts ornate columns, arches, a peacock, and a golden goblet. A black rectangle obscures the right side. UT Austin & Dallas students research Oplontis wall paintings & imported marble to learn how people lived.

ALT A vibrant, aged ancient Roman wall painting depicts ornate columns, arches, a peacock, and a golden goblet. A black rectangle obscures the right side. UT Austin & Dallas students research Oplontis wall paintings & imported marble to learn how people lived.

2
9
4,714
Trillion dollar company proud to have solved 6 random problems no one has ever heard of 🫣
Alexandr Wang
@alexandr_wangOct 2
mathematicians and muse spark collaborated to solve 6 open problems in math: 1. The Strict Threshold for Gaussian Ellipsoid Fitting 2. Finite-Time Blow-Up of Radial Negative-Energy Solutions for the Mass-Critical Biharmonic Nonlinear Schrödinger Equation 3. Semiabelian Groups Need Not Be Monomial 4. Tightness of the Cycle-Based Relaxation for Completed Length-Three Alpha-Cycles 5. String Two-Point Function = Height Function on a Curve 6. On Solvable Evolution Algebras and a Conjecture by García-Martínez and Pérez-Rodríguez
7
7
1
77
7,984
Kevin Buzzard on why he is excited about math in the age of AI: xenaproject.wordpress.com/20…

To grieve, or not to grieve?

Recent events in the field of AI for mathematics have shown us beyond all reasonable doubt that the field is currently undergoing a rapid transformation, unlike anything that we have ever seen befo…

xenaproject.wordpress.com
6
26
1
143
11,167
Avery Carr retweeted
Math Files
@Math_filesOct 2
When Maryam Mirzakhani received an email in 2014 informing her that she would receive the Fields Medal, her initial reaction was to assume that the sender’s account had been hacked. Source: Klarreich’s 2014 Quanta profile.
6
100
5
649
17,501
Avery Carr retweeted
Jay Cummings
@LongFormMathOct 2
Ever wonder what some of these AI-discovered proofs look like, that avoided human discovery for decades? I just posted a 2+ hour video going through one. Last month, AI proved the Erdős–Sós conjecture, which says that if a graph has average degree > t−2, then G contains every tree on t vertices. I spent a week going though a version of Astra’s proof, which I didn’t love. I changed it into a version I’m much happier with, which I discuss here: youtu.be/KDsKlOkrbpE?is=fu-T…

AI Solved “One of the Most Tantalizing Problems.” Here’s the Proof.

Fan Chung called the Erdős–Sós conjecture "one of the most tantilzi...

youtube.com
4
10
58
4,144
Avery Carr retweeted
arXiv.org@arxivOct 1
arXiv has updated our policy on rate limiting for all submitters. This update was made to fairly distribute moderator time & support the arXiv community of staff, volunteers, readers & authors. Please read our announcement to learn more: blog.arxiv.org/2026/10/01/up…
arXiv logo in white over a whiteboard with math symbols.

ALT arXiv logo in white over a whiteboard with math symbols.

79
496
239
1,731
759,191
Towards a more structured search for Erdős-Gyárfás counter-examples Guillaume Ducoffe, Bogdan Dumitru arxiv.org/abs/2609.28594 [𝚖𝚊𝚝𝚑.𝙲𝙾]
The Erdős-Gyárfás conjecture posits that every graph with minimum degree at least three contains a cycle of length some power of two. We prove a few simple structural properties for any minimal counter-example to this conjecture. In particular, the fraction of its vertices of degree three must be greater than 2/3, thus improving on the prior bound of 4/7 (Carr, 2026). Furthermore, it is either biconnected or the 1-clique-sum of two biconnected graphs. By exploiting some of these properties, we were able to verify the conjecture for every graph of order at most 40, every bipartite graph of order at most 66, and every cubic graph of order at most 48.

ALT The Erdős-Gyárfás conjecture posits that every graph with minimum degree at least three contains a cycle of length some power of two. We prove a few simple structural properties for any minimal counter-example to this conjecture. In particular, the fraction of its vertices of degree three must be greater than 2/3, thus improving on the prior bound of 4/7 (Carr, 2026). Furthermore, it is either biconnected or the 1-clique-sum of two biconnected graphs. By exploiting some of these properties, we were able to verify the conjecture for every graph of order at most 40, every bipartite graph of order at most 66, and every cubic graph of order at most 48.

1
1
27
My @QuantaMagazine podcast with @JannaLevin, THE JOY OF WHY, has been nominated for a Signal Award in the category "science and education". Please consider voting for us! vote.signalaward.com/PublicV…

Signal Awards - Signal Awards

Recognizing the podcasts that define culture.

signalaward.com
7
22
1
95
10,347
Avery Carr retweeted
Emily Riehl@emilyriehlSep 25
I was part of a group that met last week to try to propose recommended changes to the structure of math PhD programs in an age of AI. Our report, together with a collection of related resources, is now available here: cmsa.fas.harvard.edu/aimathp…

Summit on PhD Math Education in the Age of AI - CMSA

On September 17–18, 2026 a group of 24 mathematicians met at Harvard to grapple with the changing landscape for mathematics PhD programs in the age of AI. We produced recommendations given […]

cmsa.fas.harvard.edu
11
108
19
428
69,313
Load more