MATHEMATICS NEWS
Q&A: The political calculus—and actual math—of gerrymandering
on May 7, 2026 at 20:40
On April 29, the U.S. Supreme Court struck down Louisiana’s voting map on the basis that the state had illegally used race as a consideration when it created a new majority-Black district. Observers say the ruling could have major implications across the country for how future district boundary decisions are made under the Voting Rights Act. Meanwhile, ahead of the November midterms, lawmakers in several states have been redrawing their district maps to favor one party or the other, or are considering such reconfigurations.
Theoretical framework can predict how complex networks behave
on May 7, 2026 at 20:00
The University of Hong Kong (HKU) has spearheaded an international research collaboration to develop a pioneering theoretical framework that deciphers the predictability of complex networks. A research team including Professor Qingpeng Zhang’s group at the HKU Musketeers Foundation Institute of Data Science (HKU IDS) and the HKU Li Ka Shing Faculty of Medicine, together with researchers from Zhejiang University and Sapienza University of Rome, has developed a new theoretical framework to understand the predictability of complex networks.
Study warns cost-cutting use of generative AI could increase cyber-attack risks
on May 3, 2026 at 18:30
Newly published research from a leading computer scientist warns that the use of generative AI to design, train, or perform steps within a machine learning system could increase serious risks. Michael Lones, professor at Heriot-Watt University’s School of Mathematical and Computer Sciences, has argued in a new paper that generative AI could expose organizations and the public to unintended harm.
AI tackles one of math’s most brutal problems: Inverse PDEs
on May 1, 2026 at 15:20
Penn Engineers have developed a new way to use AI to solve inverse partial differential equations (PDEs), a particularly challenging class of mathematical problems with broad implications for understanding the natural world.
on April 30, 2026 at 16:00
A physics-inspired model calibrated on 40 years of US congressional data pinpoints a spending threshold of roughly 1.8 million USD at which campaigns stop influencing who wins and start fueling polarization instead.
Western music is getting simpler and more repetitive by the day and data prove it
on April 29, 2026 at 18:00
Ever had that moment when a song comes on and it feels strangely familiar, like it reminds you of another song that came out just a few months ago? If you feel this phenomenon has become more frequent, then you are not imagining it. Science agrees with you. A recent study found that Western music is not only starting to sound more alike but is also becoming less structurally complex than in the past.
How can opinions be maximally influenced? New research offers insights
on April 28, 2026 at 18:00
Who should you target, and when, to maximize the impact of your message? New research uses mathematical models to show that targeted influence is significantly more effective than random persuasion. In social networks, certain individuals play a key role at specific moments in how ideas spread and how polarization arises.
Universal patterns emerge across 22 languages, mapping how vocabularies evolve
on April 26, 2026 at 16:40
Human languages are known to have grown and changed considerably over the course of history, often reflecting technological, cultural, and societal shifts. Studying the evolution of languages can thus offer valuable insight into how human societies and cultures have transformed over time.
We think norms spread by imitation, but one deceptively simple rule tells a more human story
on April 23, 2026 at 22:10
A paper appearing in Proceedings of the National Academy of Sciences offers a strikingly simple answer to a longstanding question: How do people learn and settle on shared social conventions, from everyday habits to workplace norms? Researchers from the CUNY Graduate Center, the University of Pennsylvania, and Stanford University have found that people do not primarily learn by copying others or by calculating the most likely choice. Instead, they follow a two-stage process—sampling behaviors at first, then committing once enough evidence accumulates.
What Can We Gain by Losing Infinity?
by Gregory Barber on April 29, 2026 at 14:54
Ultrafinitism, a philosophy that rejects the infinite, has long been dismissed as mathematical heresy. But it is also producing new insights in math and beyond. The post What Can We Gain by Losing Infinity? first appeared on Quanta Magazine
Why Math’s Final Axiom Proved So Controversial
by Gregory Barber on April 29, 2026 at 14:50
Zermelo-Fraenkel set theory is so widely accepted that modern mathematicians hardly think about it. But believing in its core principles didn’t come easily. The post Why Math’s Final Axiom Proved So Controversial first appeared on Quanta Magazine
A Powerful New ‘QR Code’ Untangles Math’s Knottiest Knots
by Erica Klarreich on April 22, 2026 at 14:49
With a newly discovered mathematical tool, researchers are hoping to gain unprecedented insight into the structure of complex knots. The post A Powerful New ‘QR Code’ Untangles Math’s Knottiest Knots first appeared on Quanta Magazine
The AI Revolution in Math Has Arrived
by Konstantin Kakaes on April 13, 2026 at 14:54
AI is being used to prove new results at a rapid pace. Mathematicians think this is just the beginning. The post The AI Revolution in Math Has Arrived first appeared on Quanta Magazine
In Math, Rigor Is Vital. But Are Digitized Proofs Taking It Too Far?
by Leila Sloman on March 25, 2026 at 14:53
The quest to make mathematics rigorous has a long and spotty history — one mathematicians can learn from as they push to formalize everything in the computer program Lean. The post In Math, Rigor Is Vital. But Are Digitized Proofs Taking It Too Far? first appeared on Quanta Magazine
Primitive sets and von Mangoldt chains: Erdős Problem #1196 and beyond
by Terence Tao on May 4, 2026 at 02:49
Boris Alexeev, Kevin Barreto, Yanyang Li, Jared Duker Lichtman, Liam Price, Jibran Iqbal Shah, Quanyu Tang, and I have just uploaded to the arXiv our paper Primitive sets and von Mangoldt chains: Erdős Problem #1196 and beyond. This paper (which is a work in progress) represents our efforts to digest and document the recent flurry
Products of consecutive integers with unusual anatomy
by Terence Tao on March 31, 2026 at 17:06
I’ve just uploaded to the arXiv my paper “Products of consecutive integers with unusual anatomy“. This paper answers some questions of Erdős and Graham which were initially motivated by the study of the Diophantine factorial equation where and are positive integers. Writing , one can rewrite this equation as where denotes the squarefree part of
Mathematical methods and human thought in the age of AI
by Terence Tao on March 30, 2026 at 02:56
Tanya Klowden and I have uploaded to the arXiv our preprint “Mathematical methods and human thought in the age of AI“. This is an unabridged version of a solicited article for a forthcoming Blackwell Companion to the Philosophy of Mathematics. I rarely write article-length essays of a philosophical nature (perhaps the last one was in
Local Bernstein theory, and lower bounds for Lebesgue constants
by Terence Tao on March 24, 2026 at 04:30
I’ve just uploaded to the arXiv my paper “Local Bernstein theory, and lower bounds for Lebesgue constants“. This paper was initially motivated by a problem of Erdős} on Lagrange interpolation, but in the course of solving that problem, I ended up modifying some very classical arguments of Bernstein and his contemporaries (Boas, Duffin, Schaeffer, Riesz,
Mathematics Distillation Challenge – Equational Theories
by Terence Tao on March 14, 2026 at 03:33
Mathematical research traditionally involves a small number of professional mathematicians working closely on difficult problems. However, I have long believed that there is a complementary way to do mathematics, in which one works with a broad community of mathematically minded people on problems which may not be as deep as the problems one traditionally works
by Terence Tao on February 27, 2026 at 16:05
[This post is written in my capacity as Vice-Chair of the Board of Trustees of SLMath. -T.] SLMath, formerly MSRI, has launched the search for the next Deputy Director. This key position is a close advisor to the Director and shares in the internal management of the scientific team and programs at SLMath. This position is
by Terence Tao on February 16, 2026 at 16:59
Just a brief announcement that I have been working with Quanta Books to publish a short book in popular mathematics entitled “Six Math Essentials“, which will cover six of the fundamental concepts in mathematics — numbers, algebra, geometry, probability, analysis, and dynamics — and how they connect with our real-world intuition, the history of math
IPAM industrial short course in generative AI algorithms – deadline for applications closing soon
by Terence Tao on February 2, 2026 at 22:32
(Sharing this in my capacity of director of special projects at IPAM.) IPAM is holding an Industrial Short Course on Generative AI Algorithms on March 5-6, 2026. The short course is aimed at people from industry or government who want to get started in deep learning, apply deep learning to their projects, learn how to
A crowdsourced repository for optimization constants?
by Terence Tao on January 23, 2026 at 03:24
Thomas Bloom’s Erdös problem site has become a real hotbed of activity in recent months, particularly as some of the easiest of the outstanding open problems have turned out to be amenable to various AI-assisted approaches; there is now a lively community in which human contributions, AI contributions, and hybrid contributions are presented, discussed, and