Constantin Kogler

Mathematician, Postdoc at @the_IAS
to be an AI optimist

[Timothy Gowers @wtgowers @wtgowers]

An interesting perspective (as one would expect) from Kevin Buzzard.

https://t.co/BtrxXLA2Sn

[Constantin Kogler @ConstantinKogl]

I'm excited too (which is why I made my first post on Wednesday)! The entire value-system, job security, journal system etc. will change immediatly and this will be extremely disruptive. Many people feel affected by that and so I want to share my more optimistic viewpoint as a contrast.

I disagree that the models have no truely new ideas and only solve low-hanging fruits. I had a very significant problem solved with an outstanding idea (that will come out soon and that is much better than Odlyzko-Poonen, which is also not a low-hanging fruit). So I believe the AIs will be able to do everything at some point – even invent schemes if they want to!

[Constantin Kogler @ConstantinKogl]

I think it’s a great idea of the arXiv to limit the number of monthly papers to two!

Math journals should immediately do the same, possibly even restricting to only submit one paper every six months! Let’s discuss what would best!

https://t.co/tYr3MoQKot

[Constantin Kogler @ConstantinKogl]

@cockytenuki Agree with most of what you say! The math world should defintely coordinate, but it is in such crisis mode that it might be difficult to act. And it is of course withful thinkinging the labs would provide something...

[Constantin Kogler @ConstantinKogl]

@cockytenuki Good point! I believe the arXiv should stay human focused while there should be other platforms for the AIs to go crazy. Problem of course is that there is no "industry standard" where all these papers would go. Would be cool if the big labs collaborated to provided one.

[Constantin Kogler @ConstantinKogl]

@cockytenuki 🤣 Most people will fully agree with this. I don't care that much about the cookies, except for the dark chocolate ones, which come like once a fortnight.

[Constantin Kogler @ConstantinKogl]

One of the best things about the present mathematical culture is the respect we have for our peers. All distinguished mathematicians I have met were open-minded to hear new perspectives no matter where they came from – and they even might take notes during your talk.

This is a culture worth preserving.

[Constantin Kogler @ConstantinKogl]

The math on the board was initially trivial. It came up with this when I asked for deeper math without specifying from what area. I thought the model would take math from my area to please me again, but it didn't at all. So maybe I do indeed look generic.

[Constantin Kogler @ConstantinKogl]

The picture, by the way, is obviously AI-generated. The guy looks kind of like me. So either I look generic, or the model stalked my looks and wanted to please me (a bit scary).

[Giulio Tiozzo @tiozzo_giulio]

2020 leftists: society does not understand exponential growth
2026 libertarians: society does not understand exponential growth

[Constantin Kogler @ConstantinKogl]

@tiozzo_giulio Uff - maybe I would even pay that for a month!

[Giulio Tiozzo @tiozzo_giulio]

Hear me out new OAI subscription tier where for $10k a month you can see the counterexample to Hodge

[Constantin Kogler @ConstantinKogl]

@CRGreathouse Very cool! I feel a bit strange with “Kogler proves…” as the proof was found by AI. On could rather write “It was proved in …” But your call how to quote this 😊 Anyhow, thanks a lot for this!

[Constantin Kogler @ConstantinKogl]

@kennyxiexie But an AI oral interview could actually be fun - I like the idea!

[Constantin Kogler @ConstantinKogl]

@kennyxiexie That’s an interesting idea and some journals may require something like that soon. A problem would be if the interviewer is a person, we loose referee anonymity. Another option is to just require a talk upload.

[Constantin Kogler @ConstantinKogl]

@originaldint Cool - nice disagreement then! Just to understand: You believe in so rapid recursive self-improvement of the models that there will be no boundary of what we know and don’t know?

[Constantin Kogler @ConstantinKogl]

I always enjoy reading Kevin Buzzards thoughts!

https://t.co/GxvyQrvwb5

I’m also overall an AI optimist, despite everything will change. Will share more about my optimism soon!

[Daniel Litt @littmath]

Interesting that arXiv monthly submissions were exponential pre-AI; is this just driven by population growth?

[Giulio Tiozzo @tiozzo_giulio]

Very good move overall!
The only issue is Sep-Oct is the time when many young ppl post just before job applications, so that may be a bit trickier even for some legit researchers - but all in all probably not a big deal

[Constantin Kogler @ConstantinKogl]

@originaldint I’m not sure Kevin means that they will come to a natural stop for long periods of time. At least they will be stuck about many things at every given point in time. The models are currently clueless about most problems I care about. Let’s see how quickly that changes!

[Constantin Kogler @ConstantinKogl]

@DvorakJohnN Thanks so much for your nice words! I feel that congratulations rather belong to the model 😊 but I am happy to accept nice words about my writing!

[Constantin Kogler @ConstantinKogl]

I am excited to share that last week I posted my first paper where an AI model entirely came up with a new proof that I spent some time understanding and rewriting.

The proof made me excited about the future of mathematics as the model found a niche but known trick (that I call the twin factorization trick) that led to a rather simple solution of a longstanding question. The proof is also fully formalized in Lean.

https://t.co/ibsP4Pswzv

[Constantin Kogler @ConstantinKogl]

@originaldint He’s definitely refreshing and I find him the most fun math speaker! What do you exactly disagree with? Math is definitely infinite, so no model will solve everything!