delhanty

Joined 12 years ago

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Making DOG’s ModeLer (#DOGML)

dogml.eth - expiration date: 2072.09.14 at 17:07 (UTC+09:00)

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Comment · 3 months ago

It seems that AIs are really good at finding counterexamples now.

Even if progress by AIs in proving conjectures lags, it seems likely that AIs collectively will, in the next few years, find counterexamples to nearly all the Erdős (and other) conjectures that are actually false and also provably false.

That means we will able to assume that nearly all the remaining conjectures are either true or undecidable.

Surely, that's good for folks who just want to know where the truth boundaries in mathematics lie.

It's obviously causing a lot of soul-searching amongst professional mathematicians.

Arguably, they should have given less weight for the last 100 years to Hardy's view in 'A Mathematician's Apology' [0]:

> It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done.

Rota takes a much more balanced view in 'Indiscrete Thoughts' [1].

"Problem Solvers" take Hardy's view:

> ... The mathematical concepts required to state mathematical problems are tacitly assumed to be eternal and immutable. Mathematical exposition is regarded as an inferior undertaking. ...

While for "theorizers":

> Mathematical exposition is considered a more difficult undertaking than mathematical research.

If professional mathematicians can reinvent themselves, there will be plenty of work left to do to explain the results of AIs to other humans.

There probably needs to be a new career path into professional pure mathematics other than doing novel research in a PhD.

[0] https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology

[1] https://ncatlab.org/nlab/show/Gian-Carlo+Rota

https://ncatlab.org/nlab/show/Gian-Carlo+Rota

Comment · 6 months ago

2026-04-15 (10 days ago) Millennium Prize Problems Lecture posted yesterday on YouTube - watched 10 minutes so far - seems good level for HN - non-trivial but also no need to be a specialist in analytic number theory

Peter Sarnak – The Riemann Hypothesis [video] youtube.com

4 delhanty 6 months ago 1 comments

Comment · 7 months ago

> Mordel's conjecture implies as a special case that for all n>=4 there are only a finite number of solutions to Fermat's equations with relative prime numbers

I just learnt that fact from Wikipedia's article on Mordel's conjecture (now Faltings' theorem), was curious whether the theorem could be strengthened to obtain a full proof of Fermat’s Last Theorem (FLT) that is genuinely different from the Taylor–Wiles proof (or its later variants) and so asked an AI (in this case Grok via Twitter).

Grok correctly told me "no it's not possible", but then surfaced (as an aside) a nice expository article on the Taylor–Wiles proof by Faltings from AMS notices in July 1995, which I thought I'd share here:

https://www.ams.org/notices/199507/faltings.pdf

Comment · 7 months ago

Oh, these are really nice Andrei! Thanks for posting them.

Comment · 1 year ago

Thank you for the reply - appreciated.

Comment · 1 year ago

For the vertex biconnected components can you say how your implementation compares technically with Boost Graph library's `biconnected_components` and `articulation_points`?

https://www.boost.org/library/latest/graph/

https://www.boost.org/doc/libs/latest/libs/graph/doc/biconne...

Am I correct to suppose both are C++ implementations of Tarjan's algorithm?

Comment · 1 year ago

Thank you very much for that concise explanation.

Comment · 1 year ago

Congratulations!

Can you say how the it's similar and how it's different to superficially similar sounding work?

(1) https://github.com/linebender/vello , dual Apache/MIT, by Raph Levien et al

(2) https://sluglibrary.com/ , proprietary, by Eric Lengyel (Terathon)

Comment · 1 year ago

> They introduced a feature that took me hours and hours to disable (the file not downloaded until you try to open it thing). One bit of documentation pretty much lied about turning it off. Turned out it had to be disabled in more than one place.

Are you able to say what the relevant settings are? (I would like to be able to do that too ...)

Comment · 1 year ago

As someone who has been mitigating and managing chronic pain for 25 years, with respect IMO your expectation is unrealistic.

There isn't a "solution" - you're looking at a life-long mitigation and management strategy that will not be "brief".

The time commitment typically goes up as one ages. I could spend 40 hours a week on nutrition, exercise and relaxation if I was trying to optimize for chronic pain reduction.

But then nothing else would get done.

Comment · 1 year ago

>Becoming a book publisher wasn’t on my bingo card when I started Shapr3D. Yet here we go! For now, it’s only available to select customers—but if there’s enough interest, we’ll make it accessible to the public. The book spans 860 pages and weighs approximately 3 kg—just as heavy as CAD is.

Become a select customer of Shapr3D and their CEO István Csanády might send you one.