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xenaproject.bsky.social

@xenaproject.bsky.social
831 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
Yes exactly! It's easy to get the "divides" ordering confused with the "less or equal to" ordering becase a | b usually implies a <= b. But everything divides zero, whereas everything is less than infinity.
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xenaproject.bsky.social @xenaproject.bsky.social · 15/11/2025
If we said that infinite groups had "order 0" (i.e. "order" meant "size if it's finite, and 0 if not"), and elements of infinite order also had order 0, then the standard theorems about order of the element/subgroup dividing the order of the group would be true even in the infinite case.
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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 · 28/10/2025
Apparently so: 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 · 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 · 22/10/2025
xenaproject.wordpress.com/2025/08/03/a... is a summary of what happened in 2025.
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 · 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 · 04/10/2025
Good question. They're available on my hard drive but Simons never asked for them. I've uploaded them to the Lean Zulip here 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 · 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
Of course Barbara! Thanks for asking!
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xenaproject.bsky.social @xenaproject.bsky.social · 18/09/2025
Amongst the projects funded is my project www.renaissancephilanthropy.org/a-dataset-of... to create what in 2025 is a super-hard dataset of pairs (informal hard proof, formal statement) of recent results from top journals. The challenge for machine is to formalise the rest of the paper.
renaissancephilanthropy.org
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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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xenaproject.bsky.social @xenaproject.bsky.social · 12/08/2025
Mathematics is also incomplete (assuming it's consistent) and that hasn't stopped lean from engaging with it at research level
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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 · 06/08/2025
Could you ever envisage lean being useful to verify nontrivial code written in common programming languages or is this asking too much?
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xenaproject.bsky.social @xenaproject.bsky.social · 04/08/2025
I absolutely agree; IPAM is the notable absentee from the list. I organised a conference there in 2023 www.ipam.ucla.edu/programs/wor... bringing together people from mathematics and machine learning and formal methods, and it was a fascinating week!
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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 · 04/08/2025
Lol that was me a few years ago
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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
I did read parts of Langlands document about defining local epsilon factors locally and it was just page after page of representation theory (so it looked like groups acting on vector spaces)
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xenaproject.bsky.social @xenaproject.bsky.social · 31/07/2025
I have never read the algebraic proof of the first inequality in global class field theory, I've just heard that it exists. I read the analytic proof last week though :-) The elementary proof of the prime number theorem still has plenty of basic real analysis in it.
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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 · 30/07/2025
The construction of local epsilon factors in the Langlands program was done by Langlands in an unpublished document which is hundreds of pages long. Then Deligne discovered a global construction which uses L-functions at some point and which fits into 30 pages
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xenaproject.bsky.social @xenaproject.bsky.social · 30/07/2025
The fact that there exists a class formation for global fields (this is a higher reciprocity statement in number theory) boils down to proving two inequalities and traditionally one of them was done analytically (using L-functions like PNT) but now purely algebraic proofs are known.
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xenaproject.bsky.social @xenaproject.bsky.social · 28/07/2025
Thanks for asking Barbara. The salary range is £48,056 - £56,345 per annum. I made some enquiries and the visa question is infinitely more complicated because there are a gazillion different kinds of visas depending on the applicant. The price could range from hundreds to thousands.
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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
Note that no official IMO markers were involved in the marking of the solutions. I am also unclear about whether many solutions were generated and then humans chose the ones most likely to be correct, or whether the machine gave one "final answer" to each question with no human intervention.
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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 · 18/07/2025
Urysohn's lemma. Where do the numbers come from?
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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 · 19/05/2025
They're worth a read! I was fortunate enough that their release was at a time when they were perfect material to read to my kids.
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xenaproject.bsky.social @xenaproject.bsky.social · 18/05/2025
One of the questions is still open: whether there exists a finite magma with (some property) but not (some other peoperty); out of all the 44 million questions attacked by the project it is the only one which remains.
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xenaproject.bsky.social @xenaproject.bsky.social · 18/05/2025
Yes, and this was one of the harder ones, so the question was which machines can solve it and how quickly and how efficiently.
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