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xenaproject.bsky.social

@xenaproject.bsky.social
829 followers 26 following 121 posts
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xenaproject.bsky.social @xenaproject.bsky.social · 05/12/2025
Boris Alexeev writes on how he's been experimenting with AI to solve Erdos Problems: xenaproject.wordpress.com/2025/12/05/f...
xenaproject.wordpress.com
Formalization of Erdős problems
[This is a guest post by Boris Alexeev. Now over to Boris.] I’m here to tell you about various exciting developments centering on Erdős problems, especially involving the formalization of old and n…
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xenaproject.bsky.social @xenaproject.bsky.social · 15/11/2025
It's funny how mathematicians sometimes confuse 0 and infinity. We say that the characteristic of a field can be 0, but that the order of an element in a group can be infinity. These are two different conventions expressing the same idea. 1/2
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xenaproject.bsky.social @xenaproject.bsky.social · 14/11/2025
ooh hello
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xenaproject.bsky.social @xenaproject.bsky.social · 06/11/2025
Congratulations to Floris van Doorn and Christian Thiele for their new ERC grant for formalization of analysis in Lean www.mathematics.uni-bonn.de/en/news/will...
mathematics.uni-bonn.de
Will mathematical research results be verified by computers in the future?
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xenaproject.bsky.social @xenaproject.bsky.social · 26/10/2025
Here's the statement in Lean. How little can one get away with importing in order to prove this? Can it be proved by induction on max(l)-min(l) for example, avoiding the reals completely?
If L is a list of naturals, then its length to the power of its length, multiplied by its product, is at most its sum to the power of its length.
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xenaproject.bsky.social @xenaproject.bsky.social · 26/10/2025
Fermat's Last Theorem is a famous example of a question which can be stated using only naturals and whose proof requires a lot of machinery. But in fact the AM-GM inequality, just for ℕ, can be stated purely using ℕ (clear denoms, raise everything to n'th power). Is there a simple proof avoiding ℝ?
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xenaproject.bsky.social @xenaproject.bsky.social · 22/10/2025
xenaproject.wordpress.com/2025/10/22/f... A chat around what's been happening in the world of AI and Erdos problems, and what it highlights.
xenaproject.wordpress.com
Formal or not formal? That is the question in AI for theorem proving.
So it’s an interesting time for computers-doing-mathematics. A couple of interesting things happened in the last few days, which have inspired me to write about the question more broadly. Fir…
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xenaproject.bsky.social @xenaproject.bsky.social · 09/10/2025
ItaLean : formal maths and AI in Italy (Bologna), Dec 2025. Lectures, hands-on tutorials, research talks from academia and industry etc. Register here pitmonticone.github.io/ItaLean2025/
pitmonticone.github.io
ItaLean 2025
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xenaproject.bsky.social @xenaproject.bsky.social · 03/10/2025
My talk at the Simons Foundation last week is now up on YouTube youtube.com/watch?v=K5w7VS2sxD0 . It is a hopefully-comprehensible general audience talk about what I think is a big decision which mathematicians will have to decide whether to back or not.
youtube.com
Kevin Buzzard - Where is Mathematics Going? (September 24, 2025)
YouTube video by Simons Foundation
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xenaproject.bsky.social @xenaproject.bsky.social · 27/09/2025
My colleague Jon Mestel pointed out to me that whether you use the US 09272025 date system or the pretty-much-everywhere-else-in-the-world-and-far-saner 27092025 system, today's date is a perfect square, as is the current month and the year! Will this ever happen again??
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xenaproject.bsky.social @xenaproject.bsky.social · 18/09/2025
Renaissance Philanthropy have announced the first 29 grants they've given from their AI For Math fund www.renaissancephilanthropy.org/ai-for-math-... . Interesting to see that around half of the funded proposals mention Lean.
renaissancephilanthropy.org
AI for Math Winners Page — Renaissance Philanthropy – A brighter future for all through science, technology, and innovation
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xenaproject.bsky.social @xenaproject.bsky.social · 22/08/2025
The Mathlib Initative is hiring! www.renaissancephilanthropy.org/careers/math... (part-time contractor, helping to solve the "2000 PRs" issue, note the required qualifications) and www.renaissancephilanthropy.org/careers/devo... (full-time, solving distributed systems challenges). 14 Sept deadline.
renaissancephilanthropy.org
Mathematical Research Engineer — Renaissance Philanthropy – A brighter future for all through science, technology, and innovation
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Reposted by @xenaproject.bsky.social
emilyriehl.bsky.social @emilyriehl.bsky.social · 07/08/2025
@sciam.bsky.social gave me the opportunity to share some personal thoughts about the recently reported AI results from the #imo2025: www.scientificamerican.com/article/math...
scientificamerican.com
AI Crushed the Math Olympiad—Or Did It?
AI models supposedly did well on International Math Olympiad problems, but how they got their answers reminds us why we still need people doing math
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xenaproject.bsky.social @xenaproject.bsky.social · 04/08/2025
NSF announces funding for ICARM: the Institute for Computer-Aided Reasoning in Mathematics, based in Carnegie-Mellon . Amazing! Carnegie-Mellon press release here: www.cmu.edu/news/stories... www.nsf.gov/news/nsf-inv...
nsf.gov
NSF invests over $74 million in 6 mathematical sciences research institutes
The U.S. National Science Foundation is investing over $74 million in six research institutes focused on the mathematical sciences and their broad applications in all fields of science, technology and...
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xenaproject.bsky.social @xenaproject.bsky.social · 03/08/2025
Sunday afternoon.
A level from the computer game "Baba is you"
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xenaproject.bsky.social @xenaproject.bsky.social · 03/08/2025
Thoughts on AI and the IMO. xenaproject.wordpress.com/2025/08/03/a...
xenaproject.wordpress.com
AI at IMO 2025: a round-up
Setting the scene The 2025 International Mathematics Olympiad has come and gone. Reminder: this is an exam for high-school kids across the world (each country typically sends six kids), comprising …
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xenaproject.bsky.social @xenaproject.bsky.social · 31/07/2025
Featuring a sorry-free proof that 2+2=6
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xenaproject.bsky.social @xenaproject.bsky.social · 28/07/2025
Why is this a worthwhile project? 1) It will create a hard dataset for autoformalization AI's; 2) It will force us to formalize the definitions of mathematical objects which are being used today in the top journals, thus making Lean's mathematics library more relevant to modern math researchers.
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xenaproject.bsky.social @xenaproject.bsky.social · 28/07/2025
I am advertising for 4 post-docs to come to Imperial and formalize, in Lean, *statements* of theorems from recent issues of the top generalist pure mathematics journals. www.imperial.ac.uk/jobs/search-... Positions are for 2 years, start date 1st Oct this year. Deadline 15th August.
imperial.ac.uk
Description
Please note that job descriptions are not exhaustive, and you may be asked to take on additional duties that align with the key responsibilities ment...
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xenaproject.bsky.social @xenaproject.bsky.social · 24/07/2025
A new "Mathlib initiative" focussed around Lean's mathematics library has been announced. Thanks to the generosity of Alex Gerko and XTX Markets, there is finally an official entity focussed on growing this 21st century way of doing mathematics. www.renaissancephilanthropy.org/news-and-ins...
renaissancephilanthropy.org
Lean FRO and Mathlib receive $10M from XTX Markets Founder Alex Gerko to further advance the use of AI for mathematical research — Renaissance Philanthropy – A brighter future for all through science,...
FOR IMMEDIATE RELEASE July 24, 2025 Contact: media@renphil.org ; richard.hillary@xtxmarkets.com ; pr@convergentresearch.org
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xenaproject.bsky.social @xenaproject.bsky.social · 19/07/2025
Floris van Doorn and his team at Bonn have finished formalizing both the classical theorem of Carleson (Fourier series converges almost everywhere) and a far-reaching generalisation (still unpublished) on doubling metric measure spaces. leanprover.zulipchat.com#narrow/chann...
leanprover.zulipchat.com
Public view of Lean | Zulip team chat
Browse the publicly accessible channels in Lean without logging in.
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xenaproject.bsky.social @xenaproject.bsky.social · 15/07/2025
Terry Tao has translated his "Analysis I" textbook into Lean! github.com/teorth/analy... Projects like this are tough to pull off, and need users to play through the levels and find and eliminate things which the formalization is making artificially hard. Fork the repo and give the exercises a try!
github.com
GitHub - teorth/analysis: A Lean companion to Analysis I
A Lean companion to Analysis I. Contribute to teorth/analysis development by creating an account on GitHub.
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xenaproject.bsky.social @xenaproject.bsky.social · 15/07/2025
First volume of new diamond open access journal "Annals of Formalized Mathematics" just dropped: afm.episciences.org/volume/view/...
afm.episciences.org
Annals of Formalized Mathematics - Volume 1
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xenaproject.bsky.social @xenaproject.bsky.social · 06/07/2025
Markus Himmel has written a blog post about how to write a simple imperative program in Lean and then how to verify that the program is bug-free. markushimmel.de/blog/my-firs...
markushimmel.de
My first verified (imperative) program
One of the many exciting new features in the upcoming Lean 4.22 release is a preview of the new verification infrastructure for proving properties of imperative programs. In this post, I’ll take a fir...
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xenaproject.bsky.social @xenaproject.bsky.social · 20/06/2025
Some fundamental progress in formalized category theory in Lean including Freyd-Mitchell embedding.
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xenaproject.bsky.social @xenaproject.bsky.social · 19/06/2025
Last chance to see @emilyriehl.bsky.social at the LMS next month!
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xenaproject.bsky.social @xenaproject.bsky.social · 14/06/2025
I have a gig in Southampton next week! www.turnersims.co.uk/whats-on/mat... Thurs 19th June 2025, 4pm, tickets are free but need to be booked in advance, I'll be explaining what I learnt this week in Cambridge about where we are with AI and mathematics, and summarising for a general audience.
turnersims.co.uk
Mathematics and AI: Generating the Future How will AI change mathematics? - Turner Sims
There’s no shortage of headlines proclaiming that AI will soon revolutionise everything — including mathematics — and leave no profession untouched. But what’s really happening behind the scenes? In t...
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xenaproject.bsky.social @xenaproject.bsky.social · 12/06/2025
I'm at Big Proof this week. Bhavik Mehta's talk (video not yet up) contained a big surprise at the end: one of the references in a paper he's formalizing is an old 4-page paper about bounds for the ABC conjecture, and the paper has been completely *autoformalized* by Morph Labs' AI model "Trinity".
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xenaproject.bsky.social @xenaproject.bsky.social · 10/06/2025
I'm teaching a computer a proof of Fermat's Last Theorem. Here's my talk from yesterday at the Newton Institute in Cambridge explaining how it's going. www.youtube.com/live/r-Vu_4s...
youtube.com
Big proof: formalizing mathematics at scale | Monday 09th June
YouTube video by INI Seminar Room 1
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xenaproject.bsky.social @xenaproject.bsky.social · 16/05/2025
@profkinyon.bsky.social you might like this one
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xenaproject.bsky.social @xenaproject.bsky.social · 16/05/2025
Let G be a magma (i.e a set equipped with a multiplication and no further axioms). Can you prove that if ∀ x y z, x = x(y((zx)y)) then ∀ x y z, x = x(y(z(xz)))? You can use a theorem prover, a language model, a SAT or SMT solver or even pencil and paper. Terry Tao is collecting proofs of this! 1/2
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xenaproject.bsky.social @xenaproject.bsky.social · 13/05/2025
I think Courtney knows as well as I do what's going on here. A CS friend of mine told me that they'd set a homework problem about a family tree containing Homer, Marge, Bart, Lisa and Maggie, and some of the solutions she got had answers referring to other Simpsons characters not in the question.
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xenaproject.bsky.social @xenaproject.bsky.social · 12/05/2025
Great Exhibition Road Festival 7th and 8th June, come play me at dots and boxes
Pic of previous GERF Festival, Exhibition Road, South Kensington, text says "One month to go"
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xenaproject.bsky.social @xenaproject.bsky.social · 09/05/2025
Dang we should have youtube videos for every tactic www.youtube.com/watch?v=y6p0...
youtube.com
Canonical
YouTube video by Chase Norman
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xenaproject.bsky.social @xenaproject.bsky.social · 16/04/2025
The US's National Science Foundation advisory committee for Mathematical and Physical Sciences has just been disestablished, by Presidential executive order. www.nsf.gov/executive-or...
nsf.gov
NSF Implementation of Recent Executive Orders
Information for the NSF community regarding executive orders.
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xenaproject.bsky.social @xenaproject.bsky.social · 14/04/2025
The final proof in Tao's "Equational theories" Lean project has just been formalized! See Tao's blog post here github.com/teorth/equat... . All 22,028,942 theorems are now formally verified in Lean. A place to start reading about the project is here teorth.github.io/equational_t... .
github.com
Terence Tao's personal log
A project to map out the relations between different equational theories of Magmas. - teorth/equational_theories
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xenaproject.bsky.social @xenaproject.bsky.social · 13/04/2025
Lean's maths library finally has the Lie algebra of a Lie group! github.com/leanprover-c... The library has been used to formalize research level mathematics but there are still a few things missing which I learnt as an undergrad, and this was one. Still no de Rham cohomology though...
github.com
[Merged by Bors] - feat: the Lie algebra of a Lie group over a general field by sgouezel · Pull Request #18396 · leanprover-community/mathlib4
We construct the Lie algebra of a Lie group, where the bracket is given by the vector field bracket of invariant vector fields associated to an element of the Lie algebra, i.e., the tangent space a...
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xenaproject.bsky.social @xenaproject.bsky.social · 07/04/2025
They're doing affine group schemes along the way -- useful for FLT! Why doesn't Sophie Morel get a mention though? She's working on diagonalisable group schemes for the project.
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xenaproject.bsky.social @xenaproject.bsky.social · 05/04/2025
Proving Fermat's Last Theorem in the Roundhouse Camden whilst listening to Jem Finer's Longplayer en.wikipedia.org/wiki/Longpla...
Kevin Buzzard sitting with laptop in Roundhouse in London whilst a performance of Jem Finer's Longplayer is going on
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xenaproject.bsky.social @xenaproject.bsky.social · 01/04/2025
arxiv.org/abs/2503.21934 tl;dr: people think LLMs are getting good at maths because they're being tested on hard questions for which the answer is a number. But when you ask them for proofs (which is what mathematicians *actually* do) they score < 5% on average even at Olympiad (pre-uni) level.
arxiv.org
Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad
Recent math benchmarks for large language models (LLMs) such as MathArena indicate that state-of-the-art reasoning models achieve impressive performance on mathematical competitions like AIME, with th...
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xenaproject.bsky.social @xenaproject.bsky.social · 01/04/2025
I'll be speaking with Leo de Moura in Oxford on the afternoon of 6th May: we're giving the 2025 Strachey Lectures. Register here www.cs.ox.ac.uk/seminars/264...
cs.ox.ac.uk
The Lean Theorem Prover/Will computers prove theorems?
The Lean Theorem Prover/Will computers prove theorems?
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xenaproject.bsky.social @xenaproject.bsky.social · 01/04/2025
I'll be challenging allcomers at dots and boxes at the Great Exhibition Road Festival on 7th/8th June: www.greatexhibitionroadfestival.co.uk/event/maths-...
greatexhibitionroadfestival.co.uk
Maths Exploratorium - The Great Exhibition Road Festival
Come along to our Maths Exploratorium, a playful, hands-on marquee where numbers meet adventure - no maths skills needed, just curiosity!
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xenaproject.bsky.social @xenaproject.bsky.social · 24/03/2025
Maxwell's equations in Lean: github.com/HEPLean/Phys... Part of a project by Joseph Tooby-Smith to formalize various parts of physics in Lean.
github.com
PhysLean/PhysLean/Electromagnetism/MaxwellEquations.lean at master · HEPLean/PhysLean
A project to digitalise results from physics into Lean. - HEPLean/PhysLean
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xenaproject.bsky.social @xenaproject.bsky.social · 18/03/2025
Applications are open for the 2025 Clay Math summer school in Oxford UK, on formalization of class field theory. If anyone knows of PhD students interested in one or more of class field theory, and formalization of mathematics, encourage them to apply! www.claymath.org/events/forma...
claymath.org
Formalizing Class Field Theory - Clay Mathematics Institute
Class Field Theory in its cohomological form is one of the highlights of early 20th century mathematics, and is now understood as the abelian case of the Langlands Philosophy. Although it sounds like ...
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Reposted by @xenaproject.bsky.social
Morgan, the napper @letsgogirls.bsky.social · 16/03/2025
To my fellow screamers:
A poem. White background with black lettering, reads,
Scream
So that one day
A hundred years from now
Another sister will not have to
Dry her tears wondering 
Where in history 
She lost her voice.
- Jasmine Kaur
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xenaproject.bsky.social @xenaproject.bsky.social · 16/03/2025
An update on a (basically failed) attempt of mine to make a database of hard number theory problems on the cheap.
xenaproject.wordpress.com
Think of a number: an update
A month or two ago I wrote this post which expressed my frustration with various issues around private datasets as a way of measuring the mathematical abilities of language models. More generally I was frustrated about the difficulty of being able to judge closed source software owned by a tech company when it's extremely difficult to do science (i.e. perform reproducible experiments) on it.
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xenaproject.bsky.social @xenaproject.bsky.social · 14/03/2025
Just merged and deployed the PR with an Italian translation of the Natural Number Game! Game currently available in English, Italian and Chinese; try it at adam.math.hhu.de#/g/leanprove... if you didn't already have a go. It's all about proving 2+2=4 (and some generalizations of this).
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xenaproject.bsky.social @xenaproject.bsky.social · 14/03/2025
Interesting panel discussion on the new FrontierMath blog post epoch.ai/frontiermath... . Everyone seems to be in agreement that LLMs are going to get good at guessing numerical answers to hard maths qs. People at pains to point out that maths isn't about this. Best part was (1/2)
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xenaproject.bsky.social @xenaproject.bsky.social · 05/03/2025
Quantum harmonic oscillator in Lean: heplean.com/CuratedNotes...
heplean.com
PhysLean: Digitalizing Physics in Lean 4
A project to digitalize results from physics into Lean 4.
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xenaproject.bsky.social @xenaproject.bsky.social · 22/02/2025
Terry Tao speaking on machine-assisted proofs: www.youtube.com/watch?v=5ZII... . This is quite a broad (and general audience) discussion on uses of language models, theorem provers and neural networks in mathematics.
youtube.com
Terence Tao - Machine-Assisted Proofs (February 19, 2025)
YouTube video by Simons Foundation
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