Ten advances in mathematics and theoretical computer science
1–10 of 1000 posts
Re: Ten advances in mathematics and theoretical computer science
#2I don’t feel the existential dread of mathematicians is correct. It seems to me in fact these results are bringing math mainstream. I now personally look forward to the interpretations and discussions of the significance of such results by human mathematicians.
Now I understand that it’s mostly the super stars benefitting from the increased attention. Folks who are less established don’t share in that glory. But on the other hand it seems like an exciting time to go even deeper for in various specialties of math by deciding where to focus these powerful tools. For every conjecture defeated some seven or eight new ideas open up. Our path through that combination will be set by creative and curious human mathematicians.
[edit: deleted a distracting comparison to Chess]
Re: Ten advances in mathematics and theoretical computer science
#3I don’t feel the existential dread of mathematicians is correct. It seems to me in fact these results are bringing math mainstream. I now personally look forward to the interpretations and discussions of the significance of such results by human mathematicians. Now I understand that it’s mostly the super stars benefitting from the increased attention. Folks who are less established don’t share in that glory. But on t…
Given that we were nowhere near this state even two years ago, I think it’s a question of velocity more so than just distance.
Re: Ten advances in mathematics and theoretical computer science
#4I'm enjoying learning about these hard problems, but this line about credit made me chuckle:
> We helped prepare the manuscripts and formalize the proofs in Lean, and we take responsibility for their correctness
Offering to take responsibility for the correctness of a proof written in Lean feels like volunteering to be the fall guy in case someone finds a flaw in basic arithmetic, no?
Re: Ten advances in mathematics and theoretical computer science
#5I wonder what the total cost of this research was, including the salary for their mathematicians and engineers.
Re: Ten advances in mathematics and theoretical computer science
#6My main gripe here is the lack of transparency around the total experiment and construction. I doubt that they simply pointed their model at these ten specific problems alone and gave the model one shot; therefore the $2000 number could be completely misleading, similar to P-value hacking by not disclosing the total experimental setup.
I want to know:
1. How many total problems were given to the model, and what percent were left unsolved at what cost before giving up? 2. How many attempts did you give the model at solving these problems? 3. How expensive was the harness, e.g. did the model have access to a job cluster?
Re: Ten advances in mathematics and theoretical computer science
#7I'm enjoying learning about these hard problems, but this line about credit made me chuckle: > We helped prepare the manuscripts and formalize the proofs in Lean, and we take responsibility for their correctness Offering to take responsibility for the correctness of a proof written in Lean feels like volunteering to be the fall guy in case someone finds a flaw in basic arithmetic, no?
No, the correctness isn't for the "inside the Lean proofs", but for the translation of "human language math" and its formal Lean variant.
Re: Ten advances in mathematics and theoretical computer science
#8I'm enjoying learning about these hard problems, but this line about credit made me chuckle: > We helped prepare the manuscripts and formalize the proofs in Lean, and we take responsibility for their correctness Offering to take responsibility for the correctness of a proof written in Lean feels like volunteering to be the fall guy in case someone finds a flaw in basic arithmetic, no?
I'm not an expert at it myself, but my understanding is there are numerous ways to "cheat" in a Lean proof (via `sorry` and similar). They're taking responsibility for fully verifying that none of these cheats were used (and that the theorem statements themselves were all correctly formalized.)
Re: Ten advances in mathematics and theoretical computer science
#9How much do you all think it would cost to "buy" these advances from PhDs, practicing scientists?
Re: Ten advances in mathematics and theoretical computer science
#10I don’t feel the existential dread of mathematicians is correct. It seems to me in fact these results are bringing math mainstream. I now personally look forward to the interpretations and discussions of the significance of such results by human mathematicians. Now I understand that it’s mostly the super stars benefitting from the increased attention. Folks who are less established don’t share in that glory. But on t…
Every time someone makes a comparison to chess I die inside. Chess is a spectator sport primarily funded by a few eccentric billionaires. Players artificially constrain themselves in timed environments knowing that they will never be able to produce better moves than a smartphone because a select few people find it interesting. Only ~30 top professionals actually make enough money to have a full career playing chess, maybe a few hundred more can sustain a meager lifestyle with coaching gigs. I shudder to imagine what will happen to the tens of thousands of non-Fields medalist caliber mathematicians if math goes the way of chess. Perhaps Terence Tao and a few other famous mathematicians will be funded by Peter Thiel to report on how well humanity can keep up with the machines? How do you expect any mathematician to be optimistic about this comparison.