Julian Külshammer

[Alvaro Lozano-Robledo @mathandcobb]

I had a long conversation with a journalist today (for a piece that may show up on Sunday) and he asked me about something that many here also misunderstand:

"Why wouldn't mathematicians want solutions to famous open problems if they are found by or with the aid of AI/LLM's??"

And the answer is that **we absolutely want to know the solutions** to the riddles that have "haunted" math for so long! But not *at any cost*. Not at the cost of the future of our profession. Not in a hurry just to make headlines before an IPO.

It is undeniable that the LLM's are clearly amazing tools and they can be harnessed to aid and accelerate mathematical discoveries. And I fully expect these tools are here to stay, and they will be incredibly helpful in some arenas. But as many others have already said, math is built by humans for humans and it's built on *understanding* and *absorbing* (slowly, because it takes humans a long time to distill the essence of a new proof, the main ideas) of the ideas and techniques that we invent and discover.

When a huge result is proved by an LLM and a 100+ page paper is produced, and no one associated with that particular company/paper can actually explain what are the key new mathematical ideas that have made the proof possible, then there is very little to gain from that paper/result. At least until a human mathematician takes the time to read it, digest it, and distill the key ingredients so that the rest of us can digest it and hopefully apply it to other settings. Such a paper is the equivalent of the pop-culture answer "42" to the ultimate question of life, the universe, and everything.

But what if we get a 100+ proof every week, that no one understands and the LLM companies make little effort to make understandable? How do we process all of these "would be" advancements? I say would-be because they are not advancements until the *community* is able to advance with the new knowledge!

The thing is that there is a viable alternative: the LLM companies give up their arms race (which is in essence adversarial not just to each other but also to the math community) and actually become scientific partners of the community. How so? Suppose OpenAI wanted to prove Navier-Stokes and get credit for it (which of course they did want). Then six months ago they could have invited the top 10 fluid dynamics researchers (including Córdoba, Zoroa, etc) to form a team to solve it using their products. OpenAI gives funding to each faculty member for a course release, and they fund a number of grad students for the semester to work on this too (and be trained in LLM-aided research in the process). OpenAI provides resources and the community provides expertise. Eventually they prove (or make progress) on this important problem and there are several positive outcomes:

1) OpenAI gets credit for propelling scientific progress, and their tool is solidified as a terrific tool for team work on advanced research.

2) The researchers understand how the proof was built, and they are able to write a human-readable paper that peers can use to advance knowledge. They can give talks about this work and help the community digest the new insights, and advance the field.

3) The experts know the literature and they can identify when an LLM is using a piece that is due to a certain person. They can identify the correct references and *give deserved credit* to the work being used. Or even better, invite those researchers to join the project at that point, since their work is heavily used by the LLM. In other words: stop or try to minimize scientific plagiarism and dishonest practices.

4) Grad students get to learn material, new techniques, understand the capabilities of what LLM's can and can't do, and participate in a new model of research collaboration (plus they get funding).

[Trefor Bazett @TreforBazett]

I'm worried about learning. Last year, 42% of my students evidently used AI for a particular problem. Fine. But those that used AI did 22 percentage points worse on their test than those that didn't. I'm not anti-AI, but I'm very worried...1/2

[Emily Riehl @emilyriehl]

At the #ICM2026, I moderated a panel on "AI for mathematics" with the following abstract:

AI has the potential to transform mathematical research practices. After surveying some notable recent uses of AI in mathematical research, we will turn to broader questions.

[Hadas Weiss @weiss_hadas]

the most annoying shift i've experienced in academia

[Julian Külshammer @kuelshammer]

My department at Uppsala University, Sweden, is advertising 4 PhD positions in Mathematics, Applied Mathematics, and Statistics. The topic can be in any research area represented at the Department. For details see https://t.co/EeV5ZISK3C

[Julian Külshammer @kuelshammer]

https://t.co/xtn4dxNUF4

[Julian Külshammer @kuelshammer]

Postdoc position in my group out. Contact me for questions.

[Julian Külshammer @kuelshammer]

Joined an editorial board.

[Communications in Algebra @CommsAlg]

We are delighted to announce that Prof. Julian Külshammer from the Uppsala University in Uppsala, Sweden, is joining our board. A leading expert in representation theory, Prof. Külshammer brings valuable expertise to our team. Welcome, Prof. Külshammer, to our Editorial Board!

[Julian Külshammer @kuelshammer]

Our department advertises PhD positions in mathematics. Feel free to share and/or apply yourself: https://t.co/Wgi5DJlzb2

[Julian Külshammer @kuelshammer]

@TonyTheLion2500 As others have said probably Swedish for gcd, största gemensamma delare.

[Julian Külshammer @kuelshammer]

@TonyTheLion2500 1) Not knowing what a function is. 2) Underestimating the usefulness of being able to check your answer without relying on an answer sheet.

[Matteo Capucci @mattecapu]

can't help but Stan everything Leinster writes, today it's this beautifully simple analysis of injections and their duals in Set

[Lean @leanprover]

Proud to see Lean being used at https://t.co/ZPYpqp9AOV

[Timothy Gowers @wtgowers @wtgowers]

Have you ever thought about starting an open access mathematics journal? If so, you may be interested in a project that has just been announced to provide such journals with startup funds of up to $10,000, as well as advice from experienced people.

https://t.co/q0evWGwF6W

[Anders Eklund @wandedob]

Bra med mer pengar till forskning, men eftersom man inte ens justerat för inflation de senaste 10-20 åren så är det snarare en återgång till hur finansieringen såg ut för 10-20 år sen.

Dessutom vill man återigen mest satsa på de bästa forskarna. Jag tror inte att det bästa för Sverige är att ösa ännu mer pengar på forskargrupper som redan är stora och har mycket finansiering. Man borde snarare identifiera mindre forskargrupper som har potential att relativt snabbt växa till större grupper.

[PhD Voice - Independently Run @PhDVoice]

A PhD is all about becoming better at research.

So, it’s normal to look back on your earlier work and see flaws in it.

That’s a sign that you’ve improved.

#PhDvoice @PostdocVoice

[tagesschau @tagesschau]

"Für Christen nicht wählbar": Oberster Bischof Bätzing warnt vor Wahl der AfD https://t.co/pwRNwpbvSS #Landtagswahlen2024 #DeutscheBischofskonferenz #GeorgBätzing

[Len Thomas @len_thom]

Congratulations to my fantastic PhD student @EmpacherFa for defending her thesis this week, and thank-you to co-supervisor @KenNewm20028163 of @BioSScotland and @EdinUniMaths for all his help. Go Fanny!

[Julian Külshammer @kuelshammer]

@Quasilocal At Uppsala University there is KoF, not sure how it is at other universities https://t.co/eckXTxDS96
For mathematics specifically there was https://t.co/502kcV2aPN in 2010.