8,933 karma · joined March 16, 2009
That announcement is about exactly this group: https://openai.com/index/advisory-group-on-mathematics-and-a...
This group has been formed to tell OpenAI whether or not (and if yes how) they should release those 100+ problems.
IMO “AI companies are using math to as a PR tool” is not quite it; they are using math problems as a benchmark to evaluate their AIs, but after the prior blowback from the mathematical community, they are happy to sit on the results until the community (this group) tells them how to publish the results.
And as you say, even if they don't publish the results eventually anyone will be able to do this when this model is released, so it's just a matter of time.
I listened to the Odyssey recitation on the channel you shared (https://www.youtube.com/watch?v=KZByDOoDjIM) and to me it doesn't sound much like Sanskrit, but maybe that's just because I'm too familiar with Sanskrit and cannot take an outside view. (I can see how it's similar to other Sanskrit chanting videos on the same channel though.) Anyway as you said, it would make sense for the oldest Indo-European chanting traditions to have some similarities.
4. Some of his best work was done/completed while he was in military prison (ignoring his draft orders to report to World War II duty). IIRC later when he mentioned this to some official, they offered to give him the opportunity again.
(André Weil spent some time in India, previously having apparently taught himself Sanskrit at age 14 and the Bhagavad Gita being described as his constant companion. His autobiography The Apprenticeship of a Mathematician is very interesting.)
A REASON FOR RENUNCIATION
Possessions leave us at the end,
However long they stay;
Then why not cast aside, my friend,
What leaves us anyway?
And if they leave against our will,
The heart takes time in mending;
If given willingly, they fill
That heart with joy unending.
The other two you quoted (https://shreevatsa.net/bhartrhari/web/K084.html https://shreevatsa.net/bhartrhari/web/K085.html) have also been translated, though IMO not as successfully.So at the time my conclusion had been that there was no mistake (interpreting the "repeat" as a loop), but it's arguable… maybe if the person who posted the question had asked Knuth instead, he'd have had a reward check?
For anyone else reading this: make sure you click on the "controls & metrics" at the bottom to try out all the options (such as comparing with your browser's "text-wrap: pretty"); it's really cool!
But obviously multiplying two n-bit binary numbers is not done in O(1) time, so "only counting the number of multiplies" is not a meaningful model, and not the model adopted by the researchers quoted in the article.
Wish this project great success!
(From https://samkriss.substack.com/p/if-you-let-ai-do-your-writin...)
> [2014-01] “Here you’re able to, in combination, use many, many selective antibodies and screen them in a very sensitive manner,” said Mark Rubin, who directs the Institute for Precision Medicine at Weill Cornell Medical College and New York Presbyterian Hospital, and was not involved in the research. https://csb.mgh.harvard.edu/data/wiki_pages/26/thescientist....
> [2018-12] “I think it’s beautiful stuff; I’m really excited,” says Eric J. Schelter of the University of Pennsylvania, who studies lanthanide-dependent enzymes and was not involved in the research. https://axial.acs.org/biological-chemistry-and-chemical-biol...
> [2020-06] The study “adds to the growing appreciation of cells’ responses to bioelectric aspects of their environment,” said Michael Levin, who directs the Center for Regenerative and Developmental Biology at Tufts University and was not involved in the research. https://partnerships.princeton.edu/news/researchers-use-elec...
> [2018-11] Linda Bauld is Professor of Public Health at the University of Edinburgh and a member of the NCRI Cancer Conference Scientific Committee, and was not involved in the research. She said… https://ecancer.org/en/news/15060-doctors-and-nurses-relucta...
> [2019-03] The case provides “solid evidence for remission,”says Hans-Peter Kiem, a physician who studies cell and gene therapy at the Fred Hutchinson Cancer Research Center in Seattle, and was not involved in the research. http://institute.wuhanvirology.org/Newsletter2016/201904/P02...
> [2021-08] ‘I would say there's a lot of potential … now that they have shown that these structures are feasible, they are stable, at least under these conditions,' said Professor Roman Fasel, who heads the nanotech@surfaces Laboratory at the Swiss Federal Laboratories for Materials Science and Technology (EMPA) and was not involved in the research. https://projects.research-and-innovation.ec.europa.eu/en/hor...
> [2011-01] Dr. Kristine Scordo, who heads the Acute Care Nurse Practitioner Program at Wright State University-Miami Valley College of Nursing and Health in Dayton, Ohio, and was not involved in the research, said the results with rosuvastatin are consistent with what she sees in clinical practice. https://webapp2.wright.edu/web1/newsroom/2011/01/18/rosuvast...
> [2022-06] The findings could allow doctors to “focus on the patients we think would truly benefit from chemotherapy and avoid the side effects for patients for whom it’s likely unnecessary,” said Dr. Stacey Cohen of Fred Hutchinson Cancer Center in Seattle, who reviewed the colon cancer findings and was not involved in the research. https://nihfw.ac.in/Doc/Daily%20Health%20News%2020220608.pdf
> [2018-11] Robert Jones is Chair of the NCRI's Advanced Disease Prostate Cancer Clinical Studies Subgroup, Professor of Clinical Cancer Research at the University of Glasgow, and was not involved in the research. He said https://ecancer.org/en/news/15045-men-with-prostate-cancer-w...
> [2022-07] Professor Marielle Pijnenburg is head of the paediatric assembly of the European Respiratory Society and was not involved in the research. She says… https://publications.ersnet.org/press/2022-07-children-close...
> [2022-08] “Alcoholism is hard to treat, so any success is noteworthy,” Boris Heifets, who studies psychedelics at Stanford University and was not involved in the research, tells STAT News’ Olivia Goldhill. https://www.smithsonianmag.com/smart-news/psychedelic-magic-...
It's really a common format, and gathering quotes from independent sources is pretty much what all journalism is about.
In particular writing like this is just annoying:
> Perfect foresight doesn’t save you, because the discounting doesn’t care whether you were correct. It cares that you sequenced the cost ahead of the return. The gap between the two is the loss, and you opened the gap on purpose.
(Bruce Edgar), who was (on (102 not out)), was stuck at (the (non-striker's end)) the entire (over).
• An “over” consists of six opportunities to hit the ball and score “runs”. (A “run” is the basic unit of scoring.)
• "102 not out" indicates how many runs the player had personally contributed to the team's score. The number is large enough to suggest that this was the player who was playing particularly well in that match.
So the sentence is saying that the player who could be expected to make good use of whichever of those six opportunities he got, did not get any of them.
I think as with most cases of unfamiliar jargon, the sentence can be confusing not because of unusual words but because of everyday words being used with technical meanings ("not out", "end", "over").
• The Wikipedia page from before the reference to Chen's article was added: https://en.wikipedia.org/w/index.php?title=Chip%27s_Challeng... — it cites two sources for "coded by Tony Krueger" ("About box from the game") and for "written [by Krueger] in a single summer" (a forum post).
• Chen's article mentions "Tony Krueger is remembered in Wikipedia as the person who ported…", then adds a footnote: “Probably not as widely documented is that he accomplished this without the source code: He reverse-engineered the MS-DOS version and then reimplemented it for Windows.”
• The Wikipedia article then cites Chen's article for this additional information.
It's all fine and proper. I've just edited the citation to make this clear again.
Also for anyone else reading this, Frank Liang's thesis "Word Hy-phen-a-tion by Com-put-er" (https://tug.org/docs/liang/) is a great read, and the data structure it uses (packed tries) is clever too. The section of the TeX program that describes hyphenation is also an interesting read, and Knuth added a further twist (what we may call a hash-packed trie) in his frequent-words literate program for Bentley's column.
So whether “only 17%” is interesting or not depends on whether you see it as a stand-in for “less than half”, or “a number close to 0”.
(Posting this comment mainly to correct an error in my previous comment: in both places that I wrote “n=2^64” I should have instead written “n=2^32”.)
| n | factorization | products of two numbers
|-----|----------------|------------------------------------
| 50 | 2 * 5^2 | 1x50, 2x25, 5x10
| 60 | 2^2 * 3 * 5 | 1x60, 2x30, 3x20, 4x15, 5x12, 6x10
| 70 | 2 * 5 * 7 | 1x70, 2x35, 5x14, 7x10
| 75 | 3 * 5^2 | 1x75, 3x25, 5x15
| 80 | 2^4 * 5 | 1x80, 2x40, 4x20, 5x16, 8x10
| 84 | 2^2 * 3 * 7 | 1x84, 2x42, 3x28, 4x21, 6x14, 7x12
| 90 | 2 * 3^2 * 5 | 1x90, 2x45, 3x30, 5x18, 6x15, 9x10
| 96 | 2^5 * 3 | 1x96, 2x48, 3x32, 4x24, 6x16, 8x12
| 98 | 2 * 7^2 | 1x98, 2x49, 7x14Here's the multiplication table up to 9 (so for n=10 in place of n=2^64), and it already contains only 37 distinct products among its 100 entries:
× | 0 1 2 3 4 5 6 7 8 9
---+------------------------------
0 | 0 0 0 0 0 0 0 0 0 0
1 | 0 1 2 3 4 5 6 7 8 9
2 | 0 2 4 6 8 10 12 14 16 18
3 | 0 3 6 9 12 15 18 21 24 27
4 | 0 4 8 12 16 20 24 28 32 36
5 | 0 5 10 15 20 25 30 35 40 45
6 | 0 6 12 18 24 30 36 42 48 54
7 | 0 7 14 21 28 35 42 49 56 63
8 | 0 8 16 24 32 40 48 56 64 72
9 | 0 9 18 27 36 45 54 63 72 81
That is, in decimal, only 37% of (up to) two-digit numbers can be written as products of two one-digit numbers. This fraction, which drops to 28% at n=100, only drops to 17% at n=2^64 (per the article). So it decreases VERY slowly, and it's nontrivial that it actually goes to 0.Do they? To check, I tried to find a recent publication of Agatha Christie, and found the collection “Country Christie: Twelve Devonshire Mysteries” which says “First published by HarperCollins Publishers Ltd 2025”. It still has British-style punctuation (throughout the book), and times like “1.30”, “9.30”, “11.30”, “7.30 a.m.”, “12.30 p.m.”, and “8.30”. I checked a couple of other recent publications and admittedly they do modernize (though not in phrases like “every one of you”), but again I found the collection “The Last Seance: Haunting Tales from the Queen of Mystery” (2019) which does not. So it seems mixed.
In any case, I think it's fine to do what Standard Ebooks does, and if it were instead called something like “Modernized Ebooks with American punctuation”—if readers would know before picking one up—it would be totally unobjectionable. The name “Standard” gives the wrong impression. It's a bit like colorizing old black-and-white movies (or dubbing foreign-language movies instead of subtitling them): yes possibly even a majority of people may prefer it, but IMO it would be good to be more explicit what has been done.