Research Blogs

Peter Cameron

Complete mappings

# Complete Mappings: An Elegant Dance Between Algebra and Combinatorics A complete mapping is a special kind of bijection defined on a group. Specifically, it is a function that m...

Terence Tao

AI, Mathematics, Education, and a public goods problem

Here is a 3-paragraph summary for mathopen.com: A student's visit to office hours sparked an important conversation about the recently announced Navier-Stokes result, prompting de...

Peter Cameron

CFSG, checked

Here is a 3-paragraph summary for mathopen.com: The Classification of Finite Simple Groups (CFSG) is one of the greatest collective achievements in the history of mathematics. Spa...

Terence Tao

On the diameter and distribution of Sidon sets

Here is a 3-paragraph summary of the research blog post: A new paper titled "On the Diameter and Distribution of Sidon Sets" has been uploaded to arXiv by Daniel Carter, Kevin O'B...

Gil Kalai

Election Day 2026

This blog post is less of a traditional math research entry and more of a brief personal note from the author. They mention that it is Election Day in Israel and share that they ar...

Terence Tao

The quasi-Riemann hypothesis

I'd be happy to help summarize this blog post, but the content provided is quite minimal. It only mentions that Maksym Radziwill will be giving a hybrid talk on the quasi-Riemann h...

Terence Tao

247A, Notes 3: Singular integral operators

Here is a 3-paragraph summary of the blog post for mathopen.com: Singular integral operators sit at a fascinating crossroads in mathematical analysis. Unlike standard integral ope...

Scott Aaronson

Podcasts about the Topic: Part II

Here is a 3-paragraph summary of the blog post for mathopen.com: This post highlights a podcast conversation between the blog's author and Curt Jaimungal. The episode covers a wid...

Scott Aaronson

Vote! (Israeli edition)

Here is a 3-paragraph summary for mathopen.com: This blog post shares a personal exchange between the author and an Israeli journalist working on a piece about people living abroa...

Terence Tao

Disadvantages of Designating Mathematicians for AI Output Releases

Here is a 3-paragraph summary of the blog post for mathopen.com: The Advisory Group on Mathematics and Artificial Intelligence published a guest post addressing concerns about how...

John Baez

Counting Primes

Here is a 3-paragraph summary of the blog post on counting primes: Prime numbers become rarer as numbers grow larger, but mathematicians have developed powerful ways to estimate j...

Gil Kalai

Busy Week Ahead!

Here is a 3-paragraph summary for mathopen.com: The mathematics community is preparing for a packed and eventful week during October 25 to 29, 2026. The blog post highlights a bus...

Terence Tao

oai-math-revised: a community hub for revising OpenAI’s math write-ups

Here is a three-paragraph summary of the blog post: A team of mathematicians, including Abhinav Nellore, Johannes Schmitt, Soledad Villar, and Rachel Ward, has launched a communit...

Terence Tao

IAS applications for membership in the school of mathematics

Here is a 3-paragraph summary of the blog post for mathopen.com: The Institute for Advanced Study (IAS) has opened its application page for membership in the School of Mathematics...

Terence Tao

Simple and critical zeros of the Riemann zeta-function

Here is a 3-paragraph summary for mathopen.com: The Riemann Hypothesis is one of mathematics' most famous unsolved problems, and researchers approach it from many different angles...

Tanya Khovanova

Sleeping Beauty and ChatGPT

Here is a 3-paragraph summary of the blog post "Sleeping Beauty and ChatGPT": The Sleeping Beauty problem is a classic probability puzzle that goes like this: Sleeping Beauty is p...

Peter Cameron

Windrush

Here is a 3-paragraph summary of the blog post for mathopen.com: The blog post titled "Windrush" serves as a warm and heartfelt introduction from a new member joining a community ...

John Baez

The Quasi-Riemann Hypothesis

# The Quasi-Riemann Hypothesis: A Near-Miss That Still Shakes Mathematics An AI company recently released a proof of something called the "quasi-Riemann hypothesis," and the math ...

Scott Aaronson

AI Alignment Theory Course: Readings and Rapporteur Reports!

# AI Alignment Theory Course: Readings and Rapporteur Reports A professor at UT Austin is currently teaching a brand new course called AI Alignment Theory, and the subject matter ...

Scott Aaronson

Vote!

Here is a 3-paragraph summary of the blog post for mathopen.com: The author of this math research blog takes a brief detour from their usual content to encourage American readers ...

Gil Kalai

Progress on Borsuk’s Problem and Answer to TYI 60.

# Progress on Borsuk's Problem Borsuk's Problem is a classic question in combinatorial geometry that asks how many pieces a shape must be divided into so that each piece has a sma...

Terence Tao

An experimental AI-math challenge: using tenth discriminant bounds to explore arguments ruling out Siegel zeroes

Here is a 3-paragraph summary for mathopen.com: Mathematician Terence Tao has proposed an experimental challenge that sits at the intersection of artificial intelligence and numbe...

Terence Tao

Mathematics is a subject for the young

I don't have access to the full content of the blog post beyond what you've shared. The excerpt you provided only includes the title, a brief editorial note, and the beginning of a...

Terence Tao

Some of my recent talks and interviews

I'm sorry, but the content you've shared appears to be truncated, ending mid-sentence with "The […]". There isn't enough detail in the post for me to write a full, accurate three-p...

Terence Tao

Starting a new journal

Here is a 3-paragraph summary of the blog post for mathopen.com: Mathematician Shaoming Guo announced in a guest post that he and several colleagues are in the process of launchin...

Tanya Khovanova

Returning Soldier Effect

## The Returning Soldier Effect The "Returning Soldier Effect" refers to a well-documented statistical phenomenon in which the proportion of male births increases during and immed...

Terence Tao

How to Formalize All of Mathematics

Here is a 3-paragraph summary for mathopen.com: A fascinating new blog post titled "How to Formalize All of Mathematics" has been written by a team of prominent mathematicians and...

Terence Tao

SAIR Open Math OS released

Here is a 3-paragraph summary of the blog post for mathopen.com: The SAIR Open Math OS has officially entered its soft launch phase, following an announcement made a few weeks pri...

Peter Cameron

Graphs on topological spaces

Here is a 3-paragraph summary for mathopen.com: At the AAA108 conference in Vienna, mathematician Peter Cameron explored a natural extension of his work on graphs associated with ...

Peter Cameron

Read this!

I'd love to help summarize this article, but I only have access to the brief blog post you shared, which doesn't include the actual content of Tanswell's article "The Enshittificat...

Terence Tao

Simons Foundation Launches $15M Effort To Help Mathematicians Navigate AI Era

# Simons Foundation Invests $15M to Prepare Mathematics for the AI Era The Simons Foundation has announced a major $15 million initiative aimed at helping mathematicians adapt to ...

Terence Tao

Why are we even doing all this?

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Terence Tao

First Proof, Third Batch webinar

I don't have enough content from this blog post to write a full, accurate three-paragraph summary. The post is quite brief, essentially just announcing a webinar where First Proof ...

Terence Tao

Call for stories: human–AI collaboration in recent mathematics

Here is a 3-paragraph summary of the blog post for mathopen.com: Artificial intelligence is becoming an increasingly meaningful partner in mathematical research. Recent preprints ...

Tanya Khovanova

An Asteroid Walk: The Answer

Here is a 3-paragraph summary of the blog post for mathopen.com: This post revisits a fun geometry puzzle originally shared in 2016 called "An Asteroid Walk." The setup involves s...

John Baez

Liverworts

I'm only seeing a partial excerpt of the blog post, with the content cutting off mid-sentence. Could you share the full text of the post? That way I can give you an accurate and co...

Scott Aaronson

Podcasts about the Topic

Here is a 3-paragraph summary of the blog post for mathopen.com: The blog post rounds up a collection of podcasts centered on what the author playfully calls "the Mathocalypse," a...

Gil Kalai

The Most Outrageous Conjecture in the World

# The Most Outrageous Conjecture in the World This post dives into one of the most provocative questions in mathematics: what is the most outrageous conjecture ever proposed? The ...

Terence Tao

2026 AMS Committee on Education Workshop Report

Here is a three-paragraph summary of the blog post for mathopen.com: The American Mathematical Society recently released a report from its Committee on Education workshop, focusin...

Terence Tao

Additional recent pieces on math and AI

Here is a 3-paragraph summary of the blog post for mathopen.com: This blog post serves as a curated collection of recent writings on the intersection of mathematics and artificial...

Terence Tao

This is normal bad work

I notice the blog post content appears to be cut off after "At minimum you need" and only contains an introduction/metadata. I don't have access to the full text of the post. Coul...

Terence Tao

Illustration beyond Proof

Here is a 3-paragraph summary for mathopen.com: In January, a fascinating interdisciplinary workshop brought together mathematicians, historians, artists, and educators at the Ins...

Gil Kalai

Test Your Human Intuition 60: The Finite and Infinite Borsuk’s Problem

Here is a 3-paragraph summary of the blog post: Borsuk's problem is a classic question in combinatorial geometry that asks how many pieces of smaller diameter are needed to cover ...

Terence Tao

Math 2.0

Here is a 3-paragraph summary of the blog post for mathopen.com: Terence Tao recently delivered a public lecture at Caltech titled "Math 2.0," sharing his slides from the talk wit...

Peter Cameron

A fable

Here is a 3-paragraph summary of the blog post for mathopen.com: OpenAI made waves in the mathematics community this week by releasing a document claiming its AI system had solved...

Terence Tao

What mathematicians should know about the Lean Theorem Prover: questions of reliability and AI

Here is a 3-paragraph summary of Thomas Hales' blog post for mathopen.com: Thomas Hales opens by making the case that mathematics derives its unique value from its consistency and...

Terence Tao

What should we tell our students?

Here is a 3-paragraph summary of the blog post for mathopen.com: **Keep Calm and Carry On: A Message to Math Students** In a guest post on Terence Tao's blog, mathematician Álvar...

Scott Aaronson

The Mathocalypse

Here is a 3-paragraph summary of the blog post for mathopen.com: The post opens with a striking quote from computer scientist Omer Reingold, riffing on the famous Niemöller poem a...

Gil Kalai

Intersection Homology and Combinatorics

Here is a 3-paragraph summary of the blog post for mathopen.com: This post introduces a set of draft lecture notes on the topic of Intersection Homology and Combinatorics, prepare...

Terence Tao

The barriers of perception

# The Barriers of Perception In mathematics and theoretical computer science, progress is often slowed not just by the difficulty of problems themselves, but by the mental barrier...

Terence Tao

AHM Statement on OpenAI’s October 6 Release of Mathematical Documents

Here is a 3-paragraph summary for mathopen.com: The Association for Human Mathematics (AHM) released an official statement responding to OpenAI's October 6th, 2026 release of a co...

Tanya Khovanova

2026 MIT Mystery Hunt

Here is a 3-paragraph summary for mathopen.com: The MIT Mystery Hunt is an annual puzzle competition at MIT, and math blogger Tanya Khovanova has long made it a tradition to revie...

Gil Kalai

Updates: Sharing AI progress on mathematics (amazing!); and my lecture plans

Here is a 3-paragraph summary of the blog post for mathopen.com: OpenAI has reached a remarkable milestone in artificial intelligence and mathematics by successfully solving sever...

Terence Tao

Changes to the Erdős problems web site

Here is a 3-paragraph summary of the blog post for mathopen.com: Thomas Bloom has shared an update about changes coming to the Erdős problems website, a valuable resource dedicate...

Terence Tao

Hexagon

Here is a 3-paragraph summary of the blog post for mathopen.com: Ben Antieau, a mathematics researcher, has launched a new project called Hexagon, a repository designed to host an...

Terence Tao

The Future of Mathematics

Here is a 3-paragraph summary of the blog post for mathopen.com: **The Future of Mathematics: A New Era Takes Shape** Mathematics has always evolved, but rarely as dramatically a...

Terence Tao

Postdoc position on formal verification and algorithm discovery for numerical analysis

Here is a 3-paragraph summary of the blog post for mathopen.com: A postdoctoral position is available at the Chair of Numerical Modelling and Simulation at EPFL, led by Annalisa B...

Tanya Khovanova

Immensely Questionable Tests

Here is a 3-paragraph summary for mathopen.com: Mathematician Tanya Khovanova recently published a research paper titled "Immensely Questionable Tests," a collaborative project bo...

Scott Aaronson

My new course at UT Austin: AI Alignment Theory

Here is a three-paragraph summary of the blog post for mathopen.com: Scott Aaronson is teaching a brand-new graduate course at UT Austin this semester called CS395T AI Alignment T...

Gil Kalai

Quantum Computers and Applied Mathematics at Brown University

Here is a 3-paragraph summary for mathopen.com: Brown University recently hosted a visit centered on the exciting intersection of quantum computing and applied mathematics. The vi...