Reprinted from Communications in Pure and Applied Mathematics, Vol. 13, No. I (February 1960). New York: John Wiley & Sons, Inc. Copyright © 1960 by John Wiley & Sons, Inc.
Mathematical Beauty, Truth and Proof in the Age of AI | Quanta Magazine
Mathematicians have started to prepare for a profound shift in what it means to do mathematics.
Tony Feng on Twitter / X
I am a mathematician but I avoided commenting on this because the problems are (far) outside my domain. Even if I sat down to read the technical details (which I have not), it would be hard to appreciate the context of prior work, etc. But I've gotten enough sense of things… https://t.co/VZzosBYFto— Tony Feng (@tonylfeng) August 5, 2026
The End of Mathematics — Daniel Litt
I'm currently returning to Toronto from a summit on the future of mathematics, at OpenAI. Sebastian Bubeck asked me to talk a bit about the future we'd all like to avoid, where humans are mathematically disempowered. Jacob Tsimerman advised us to try to prioritize detail over correctness, and I have no doubt that I succeeded in deprioritizing correctness.
fenc.es — be wrong on the internet, productively
Trace the map of reasonable disagreement. Break arguments into statements, rate confidence and importance, and find the crux.
Mathematical Thinking Isn’t What You Think It Is | Quanta Magazine
The mathematician David Bessis claims that everyone is capable of, and can benefit greatly from, mathematical thinking.
Mathematics in the age of AI
An essay, based on a public lecture delivered at the 2026 International Congress of Mathematicians, on how the mathematical community might respond to the arrival of artificial intelligence tools that are capable of performing research-level mathematical tasks. Rather than debating the capabilities of such tools, we condition on the hypothesis that these capabilities will arrive, and examine instead a question that is orthogonal to it: what the goals and values of mathematical research actually are. The problem-solving component of mathematics is used as a case study.
The Unreasonable Effectiveness of Recurrent Neural Networks
Musings of a Computer Scientist.
Kill Math
The power to understand and predict the quantities of the world should not be restricted to those with a freakish knack for manipulating abstract symbols.
The Unreasonable Sufficiency of Protocols Web
The Unreasonable Sufficiency of Protocols Venkatesh Rao, Tim Beiko, Danny Ryan, Josh Stark, Trent Van Epps, and Bastian Aue 1. Introduction Complex coordination problems have an air of doomed intractability about them. We speak in fatalistic terms of economics being a “dismal” science, of sociological phenomena being dominated by the
Using spaced repetition systems to see through a piece of mathematics
By Michael Nielsen, January 2019
Terence Tao: AI companies are harming mathematics | New Scientist
archived 9 Sep 2026 16:47:49 UTC
Talia Ringer 🕊🪬 on Twitter / X
Poured my heart and soul into advocating for formal proof with AI assistance in a mathematical setting because of the large collaborations I thought it could empower. (1/3)— Talia Ringer 🕊🪬 (@TaliaRinger) September 10, 2026
Misperception of Exponential Growth: Are People Aware of Their Errors?
Previous research shows that individuals make systematic errors when judging exponential growth, which has harmful effects for their financial well-being. This study analyzes how far individuals are aware of their errors and how these errors are shaped by arithmetic and conceptual problems. Whereas arithmetic problems could be overcome using computational assistance like a pocket calculator, this is not the case for conceptual problems, a term we use to subsume other error drivers like a general misunderstanding of exponential growth or overwhelming task complexity. In an incentivized experiment, we find that participants strongly overestimate the accuracy of their intuitive judgment. At the same time, their willingness to pay for arithmetic assistance is too high on average, often much above the actual benefits a calculator provides. Using a multitier system of task complexity we can show that the willingness to pay for arithmetic assistance is hardly related to its benefits, indicating that participants do not really understand how the interplay of arithmetic and conceptual problems shape their errors in exponential growth tasks. Our findings are relevant for policymaking and financial advisory practice and can help to design effective approaches to mitigate the detrimental effects of misperceived exponential growth.
Causality
Written by one of the preeminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, economics, philosophy, cognitive science, and the health and social sciences. Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations. Cited in more than 2,100 scientific publications, it continues to liberate scientists from the traditional molds of statistical thinking. In this revised edition, Judea Pearl elucidates thorny issues, answers readers' questions, and offers a panoramic view of recent advances in this field of research. Causality will be of interest to students and professionals in a wide variety of fields. Dr Judea Pearl has received the 2011 Rumelhart Prize for his leading research in Artificial Intelligence (AI) and systems from The Cognitive Science Society.
OpenAI accused of stealing math proof from expert Andreas Thom | Valerio Capraro posted on the topic | LinkedIn
BREAKING: OpenAI might have stolen another major proof. In a detailed Mathstodon post, which I report in full in the comments, Andreas Thom presents several pieces of evidence suggesting that OpenAI may have trained Astra on conversations in which he and Gábor Kun were working on Gromov’s soficity conjecture, one of the ten problems OpenAI later announced Astra had solved. I know Andreas. We met several times early in our careers. He is an exceptional mathematician, a leading expert on sofic and hyperlinear groups, and one of the most respected scholars in the field. He has spent two decades working on this problem. If his account is correct, this is not a minor dispute over attribution. It would mean that unpublished human work was absorbed into a model and then presented to the world as a breakthrough by the model itself. And if the allegations raised by Levent Alpöge, Tristan Buckmaster, and now Andreas Thom are all substantiated, we are no longer looking at isolated incidents. We may be looking at one of the greatest intellectual scandals in the history of science. AI is not discovering new mathematics. AI is stealing human discovery. | 201 comments on LinkedIn
