Research Blogs

Tanya Khovanova

Recreational Mathematics in the Age of AI

Here is a 3-paragraph summary of the blog post for mathopen.com: Artificial intelligence is rapidly transforming the world of mathematics, affecting everyone from seasoned researc...

Terence Tao

Why I do mathematical research

Here is a 3-paragraph summary of the blog post for mathopen.com: Emily Riehl, a mathematician and guest contributor, opens by reflecting on what first drew her to mathematics as a...

Terence Tao

Happy, those able to know the causes of things

I'm unable to summarize this blog post because the content provided is too incomplete. Only a brief excerpt, author credit, and keyword list were shared, with the actual body of th...

Terence Tao

“Deep theorems were scarce and difficult and so became an effective mechanism to identify deep thought. AI has broken this system.”

Here is a 3-paragraph summary of the blog post for mathopen.com: For generations, mathematicians have used theorems as the primary measure of mathematical ability and success. A d...

Terence Tao

After Math

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Terence Tao

Wimbledon, the U.S. Open, and the future of mathematics

Here is a 3-paragraph summary of the blog post for mathopen.com: Steven Strogatz, a well-known mathematician, recently made headlines when WIRED reported that he was moved to tear...

Scott Aaronson

9/11 in Berkeley

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Gil Kalai

Jesús A. De Loera, Ethan X. Fang, Shengtao Guo, Junwei Lu, and Hailun Zheng Proved the Simplex–Cube Conjecture for Simple Polytopes.

Here is a 3-paragraph summary for mathopen.com: A major open problem in combinatorial geometry has finally been solved. Jesús A. De Loera, Ethan X. Fang, Shengtao Guo, Junwei Lu, ...

Terence Tao

A Severe Misalignment of AI in Mathematics

Here is a 3-paragraph summary of the blog post for mathopen.com: A group of 25 Fields Medallists, the most prestigious award winners in mathematics, have come together to sign a f...

Terence Tao

On the Hodge conjecture

Here is a 3-paragraph summary of the blog post for mathopen.com: The Hodge conjecture is one of the most famous unsolved problems in mathematics, and it sits at a fascinating inte...

Tanya Khovanova

Cats and Sausages

It looks like the full content of the blog post was cut off after the opening anecdote. Only the introduction about the cat and the backup camera was included, and the actual mathe...

Terence Tao

Crowdsourcing a list of general resources on AI and mathematics

Here is a 3-paragraph summary for mathopen.com: The math research community is taking a closer look at the growing intersection of artificial intelligence and mathematics, and one...

Terence Tao

Stable singularity of the Euler equations on R^3

Here is a 3-paragraph summary for mathopen.com: One of the most famous open problems in mathematics and fluid dynamics concerns whether the 3D Euler equations can develop a singul...

Gil Kalai

Overtaken

# Overtaken: A Hike That Leads to a Surprising Math Problem What begins as a nostalgic story quickly turns into a fascinating mathematical puzzle. In the early 1970s, math economi...

Terence Tao

Finite time blowup with smooth forcing term for the incompressible porous medium, Boussinesq, and incompressible Euler equations

Here is a 3-paragraph summary of the blog post for mathopen.com: Recent exciting work by mathematicians Alpöge and Buckmaster, building on earlier results by Córdoba and Martínez-...

John Baez

The E6 Root Polytope

Here is a 3-paragraph summary of the blog post about the E6 root polytope: The blog post explores the E6 root polytope, a fascinating geometric object connected to the exceptional...

Gil Kalai

Amazing: There is no Percolation at the Critical Probability in all Dimensions. (Solved by AI via a conjecture of Gady Kozma and Shahaf Nitzan.)

Here is a 3-paragraph summary of the blog post for mathopen.com: One of the most famous open problems in probability theory has finally been resolved. The conjecture that θ(p꜀) = ...

Gil Kalai

Annotated Slides – Micha A. Perles 90th Birthday Meeting

# The Cascade Conjecture: A 50-Year-Old Problem Gets New Attention The Cascade Conjecture is a fascinating open problem in combinatorial geometry that has roots stretching back to...

Scott Aaronson

LLMs and self-referentiality

# LLMs and Self-Referentiality: A Fresh Take on an Old Idea The post opens with a reflection on Douglas Hofstadter's classic book *Gödel, Escher, Bach*, which convinced a generati...

Peter Cameron

Quantum solutions to Euler’s 36 officers

Here is a 3-paragraph summary of the blog post: Euler's 36 Officers Problem is a classic puzzle that has fascinated mathematicians for centuries. The challenge is to arrange 36 of...

Peter Cameron

Complete mappings of semigroups

Here is a 3-paragraph summary of the blog post on complete mappings of semigroups: A magma is simply a set equipped with a binary operation, and a complete mapping is a special ki...

Terence Tao

Rotating needles in space: the road to the Kakeya conjecture, and why it matters

Here is a 3-paragraph summary of the blog post: The International Congress of Mathematicians (ICM) has a tradition of commissioning accessible, non-technical articles about each o...

John Baez

The Mantle

# The Mantle Earth's interior is far from static. As you travel deeper beneath the crust and into the mantle, increasing pressure and temperature force minerals to continuously re...

Scott Aaronson

Anthropic’s LLM watermarking

Here is a 3-paragraph summary of the blog post for mathopen.com: Anthropic has announced that it is now watermarking the outputs of its Claude AI models. The watermarking scheme t...

Terence Tao

Mathematical Discourse

Here is a 3-paragraph summary of the blog post for mathopen.com: Mathematical Discourse is an exciting new online journal dedicated to publishing peer-reviewed mathematics researc...

Scott Aaronson

Better than gold

Here is a 3-paragraph summary of the blog post for mathopen.com: The blog post, titled "Better than Gold," highlights an extraordinary act of defiance at the International Olympia...

Terence Tao

Quantitative bounds for sets lacking polynomial progressions with shifted prime difference

Here is a 3-paragraph summary of the research blog post for mathopen.com: A new paper by Ben Krause, Hamed Mousavi, Joni Teräiväinen, and Terence Tao has been uploaded to arXiv, t...

Terence Tao

Palomar – a registry of Lean verified mathematics

Here is a 3-paragraph summary of the blog post for mathopen.com: The rise of AI-generated mathematical proofs has created an exciting but complicated landscape for researchers and...

Scott Aaronson

Michael Rabin memorial conference

Here is a 3-paragraph summary of the blog post for mathopen.com: A memorial conference called Mind-IL is being organized at Tel Aviv University on October 26 in honor of Michael O...

Gil Kalai

Test Your Intuition 59 : The Conclave Process

Here is a 3-paragraph summary of the blog post for mathopen.com: The conclave is the centuries-old process used to elect a new pope. Cardinal-electors gather in the Sistine Chapel...

Tanya Khovanova

Permutation-Based Labeled Chip-Firing

Here is a 3-paragraph summary of the blog post for mathopen.com: Labeled chip-firing is a fascinating combinatorial process that plays out on an infinite directed binary tree. The...

John Baez

Three Generations in E7

Here is a 3-paragraph summary of the blog post for mathopen.com: One of the longest-standing puzzles in particle physics is why nature contains exactly three generations of quarks...

Terence Tao

A digestion of the proof of Sendov’s conjecture

Here is a 3-paragraph summary of the blog post for mathopen.com: Sendov's conjecture is a elegant problem in complex analysis that asks about the relationship between the roots an...

Tanya Khovanova

Killer Puzzle

# Killer Puzzle A math teacher ended the year with a memorably dark logic puzzle for their students. The setup involves a kidnapper who presents each victim with two identical pil...

Tanya Khovanova

AT, BAT, and CAT

I notice that the blog post content appears to be incomplete. Only the title "AT, BAT, and CAT" and a brief introduction mentioning it was posted by Konstantin Knop on Facebook are...

Scott Aaronson

Enough with all the world-historic milestones

I notice the blog post content appears to be cut off, with most of the actual mathematical content missing after the introductory sentences. I only have access to a brief excerpt t...

Gil Kalai

Snapshots from ICM2026

# Snapshots from ICM2026 The International Congress of Mathematicians 2026 in Philadelphia brought together mathematicians from around the world for a vibrant celebration of both ...

Terence Tao

A partial digestion of the HRT counterexample

Here is a 3-paragraph summary of the blog post: The blog post explores a fascinating concept in harmonic analysis involving functions of one variable that can be manipulated in tw...

Tanya Khovanova

ChatGPT Jokes About ChatGPT

Here is a 3-paragraph summary of the blog post for mathopen.com: The blog post "ChatGPT Jokes About ChatGPT" takes a lighthearted look at artificial intelligence by turning the le...

Peter Cameron

Arnold on mathematics

# Arnold on Mathematics V. I. Arnold was one of the most colorful and opinionated mathematicians of the 20th century, and his 1981 book on catastrophe theory offers readers far mo...

Gil Kalai

ICM 2026: A Magical Saturday Afternoon with Park, Braden and Proudfoot, and Meka

Since the blog post only provides a title and a brief teaser without the full content of the lectures, I can only summarize what is available. If you share the complete text, I can...

Tanya Khovanova

Coin Parity

Here is a 3-paragraph summary of the Coin Parity blog post: This post explores a clever weighing puzzle shared by Konstantin Knop, centered around the ever-popular balance scale. ...

Peter Cameron

Entropy, partitions, groups and AI

# Entropy, Partitions, Groups, and AI This blog post explores a fascinating connection between information theory and abstract algebra, specifically looking at how the concept of ...

Gil Kalai

Various News Items

Here is a 3-paragraph summary of the blog post for mathopen.com: The International Congress of Mathematicians (ICM) 2026 has officially kicked off in Philadelphia, marking a major...

Peter Cameron

AI for the working mathematician

I can see the title and brief introduction of the blog post, but the full content appears to be cut off with "There has been … Continue reading →", meaning I only have access to th...

Peter Cameron

I read the news today, oh boy

I notice that the content of the blog post appears to be incomplete. Only the title "I read the news today, oh boy" and a brief intro mentioning three BBC news items were provided,...

John Baez

Jordan Triples and the Standard Model

Here is a 3-paragraph summary of the blog post for mathopen.com: **Jordan Triples and the Standard Model** Mathematician John Baez is excited about a new paper he co-authored wit...

Terence Tao

A digestion of the Jacobian conjecture counterexample

Here is a 3-paragraph summary of the blog post for mathopen.com: The Jacobian Conjecture is one of mathematics' most famous unsolved problems. It asks a deceptively simple questio...

John Baez

Galilean Limits of Electromagnetism

Here is a 3-paragraph summary of the blog post for mathopen.com: Maxwell's equations, which govern electromagnetism, follow the rules of special relativity and remain unchanged un...

Scott Aaronson

NISQ and quantum supremacy did not fail

Here is a 3-paragraph summary of the blog post for mathopen.com: A recent preprint by philosopher Amit Hagar titled "The NISQ Trap: Eight Years of Demonstrations the Hardware was ...

Gil Kalai

Micha A. Perles 90th Birthday Meeting

# Celebrating 90 Years of Mathematical Excellence: A Tribute to Micha A. Perles The Israeli Mathematical Society recently held a special afternoon session at their Annual Meeting ...

Terence Tao

Two more apps: visualizing the zeta process and the motions of the heavens

Here is a 3-paragraph summary of the blog post for mathopen.com: The author argues that building visualization apps for mathematical and scientific concepts is one of the best way...

Tanya Khovanova

Five Sages

# Five Sages: A Logic Puzzle Worth Pondering A new puzzle from mathematician Nikolai Chernyatiev challenges five blindfolded sages seated in a row. Once their blindfolds are remov...

Tanya Khovanova

Fingers on One Hand

Here is a 3-paragraph summary of the blog post for mathopen.com: This blog post opens with a clever puzzle that was included as part of an entrance test for a STEP mathematics pro...

Peter Cameron

An ABC conjecture proved

Here is a 3-paragraph summary of the blog post: Researchers have proved a conjecture originally proposed by the blog's author alongside Mohammed Aljohani and John Bamberg. The con...

Peter Cameron

From the Old Abbey

Here is a 3-paragraph summary for mathopen.com: The blog post describes a week spent at the Oude Abdij Drongen, a historic old abbey located near Ghent in Belgium. The author acco...

John Baez

Interview with Micah Zarin

Here is a 3-paragraph summary of the blog post for mathopen.com: This post features an interview with Micah Zarin, though the author openly admits some dissatisfaction with how th...

John Baez

Octonions and the Standard Model

Here is a 3-paragraph summary of the blog post for mathopen.com: **Octonions and the Standard Model** Mathematician John Baez and collaborator Paul Schwahn have released a new pa...

Scott Aaronson

Announcing BQP Partners: my and my brother’s new angel-investing venture

This blog post announces that Scott Aaronson and his brother are launching BQP Partners, a new angel-investing venture focused on the quantum computing and AI spaces. The author hu...

Scott Aaronson

Held Prize call for nominations (+ call for postdocs)

The National Academy of Sciences is currently accepting nominations for the Michael and Sheila Held Prize, a prestigious award recognizing outstanding work in combinatorial and dis...