HN user
1) How do you know this structure is the correct one a priori
2) You are starting at 10^500 possibilities. "Much" smaller is not enough, the order of magnitude of the order of magnitude needs to be changed.
3) You still need all of the other assumptions, which were completely unfounded
Impossible.
Honestly just try it. You'll figure out the problem very quickly.
This is not true at all. The parameter space is absolutely MASSIVE. The counterexample is a degree 7 polynomial in 3 variables, which means 360 coefficients. There's no particular way to bound these coefficients or even the degree or number of variables apriori, but assume you somehow did. Also assume you were confident that it would work with integer coefficients bounded from -12 to 12. Now you have to iterate over 360 degrees of freedom, verify that the Jacobian is a nonzero constant, and somehow show uninvertibility of the transformation, which is not a particularly simple task.
If you searched for coefficients from -12 to 12, this would be 25^360 = 2 * 10^503 different possibilities. A common reference point is that there are 10^80 atoms in the observable universe. Sure you could probably reduce this a bit with clever tricks, but the starting point makes the method completely unviable, even with the knowledge: A) a counterexample exists, B) it's in 3 variables, C) it's in degree 7 or less, D) it's in integer coefficients, E) those coefficients are 12 or lower.
Perhaps there was something in the prompt or settings preventing this, but I'm surprised (and slightly disappointed) that none of the models approached this the way I would: download an image of the Mona Lisa, run all of the drawing functions many times to construct a forward model of the drawing implements, and attempt to solve some kind of explicit inverse problem through either ML or a classical algorithm to minimize some difference metric. Were they just restricted from running code or are the models unindustrious without a very specific prompt?
That is exclusive to engineering PhDs, entirely irrelevant to the discussion of math PhDs.
As someone who has met a lot of math majors and a lot of CS majors, I am skeptical of your supposition that CS majors are better at finding and applying novel abstractions than math majors who know how to code.
I didn't watch it myself, but there was a recent Netflix documentary on the subject where Magnus claims he was misled by chess.com into believing that they had more concrete evidence than they did.
From Cambridge dictionary:
obscure (adjective)
not known to many people:
- an obscure island in the Pacific
- an obscure 12th-century mystic
Why does its use in production matter? Perhaps the syntax itself is obscure, but we're not discussing syntax but general awareness. Anyway, the most common "real" use of brainfuck is to prove Turing completeness of other things by finding a way to compile them into brainfuck.
What? Brainfuck is the single least obscure esoteric programming language. It's the most famous example of a simple Turing complete language and its provocative name gets it a fair amount of media coverage outside its niche.
This is true, but the crushing response to this scandal is clearly disproportionate. Millions of views on videos making crude sexual jokes about a 19 year old is already an incredibly unfortunate situation, and his career got completely halted for years due to (what are now clearly) false accusations.
he probably did cheat in this particular game
I have no idea why this continues to be a popular opinion among laypeople. Even at the time actual cheating experts using computer analysis determined it to be likely fair play. His accuracy was rather pedestrian, Magnus just had on off day and played terribly. There is no proposed mechanism for how he could even HAVE cheated. He has continued to perform at a similar level under much tighter security enforcement. The primary accusation seems to be that he's poor at explaining the reasoning behind his moves, but anyone who's ever watched a Hans stream can tell you that the man simply cannot speak.
Here's a fun compilation of him getting cooked by 12 year olds and then immediately reporting them:
Regarding general knowledge, it's a pretty well known phenomena within the community. Here's a video with the three players who spent the longest time at #2 in the world (see [0]) behind Magnus Carlsen answering basic trivia questions[1].
[0] https://www.reddit.com/r/chess/comments/1uk3wa3/world_no_2s_...
A lot of players actually do go to college, although likely a minority. I know that Maxime Vachier-Lagrave in particular has a math degree. Ding Liren has a law degree. Daniel Naroditsky himself, while not quite a top grandmaster by the typical definition, had a bachelors in history.
So at least the user who submitted it to HN was a human (or perhaps a very scheming LLM attempting to appear it?)
Slight mistake in equation (1) (or maybe it's supposed to be a narrative decision?), the inner product of Av_i with itself should end up being s_i^2 and not 1. The vectors u_i are orthonormal, but Av_i = s_i u_i, not just u_i.
Same transformation. Same map on every actual vector. But now it looks like an arbitrary tangle of scaling, shearing, and sign flips — you’d never guess it was just “stretch x by 3.”
I have a very hard time imagining a human writing this if they weren't intentionally attempting to sound like an LLM.
Discussed at the time: https://news.ycombinator.com/item?id=47774494
Exceedingly unlikely. This was one of the more discussed Erdos problems, and multiple experts have attested to the technique's novelty. If you're referring to the lack of comments on the erdosproblems website, that doesn't really mean much. From its own blog[0], the site was only started in 2023 and only really gained momentum as a place to discuss AI solving attempts, you aren't going to see serious mathematicians discussing the problems there even if there have been significant efforts to solve it.
The reason plants capture energy from this range is because that's where most of sunlight's energy is concentrated, which is going to drop this quite a bit further. Glancing at a solar radiation spectrum curve makes it look a lot closer to ~1.5x. Combine that with inefficiencies of both the panel and the LEDs and it really doesn't look that good.
abs(x) = sqrt(x*x), no?
This preprint was written by a researcher at an accredited university with a PhD in physics. I'm sure they know what a vector valued function is.
The point of this paper is not to revolutionize how a scientific calculator functions overnight, its to establish a single binary operation that can reproduce the rest of the typical continuous elementary operations via repeated application, analogous to how a NAND or NOR gate creates all of the discrete logic gates. Hence, "continuous mathematics" as opposed to discrete mathematics. It seems to me you're being overly negative without solid reasoning.
Elementary function is a technical term that this paper uses correctly, not a generic prescription of simplicity.
This is an incredibly ironic comment. "Freestyle" chess was an attempt to do exactly this with Magnus's support, and it failed to secure funding after its initial run. This event is them running back to FIDE in shambles to salvage their tour. Kasparov attempted something similar in the 90s, making his own world championship title, and similarly failed horribly.
The stability of a 100+ year old international organization that's led by serious politicians with connections in every major country is hard to contend with. FIDE's current president was Russia's Deputy Prime Minister for 6 years.
Also his current rating is higher than either Karpov’s or Kasparov’s were when they first won the title. His rating when he first won was about the same as Fischer’s when Fischer first won.
This doesn't really mean anything. Rating is a purely relative system, as in the other thing that matters when performing Elo calculations is the difference in Elo between the two players. The absolute value of an Elo rating carries no real meaning and drifts over time based on the volume, skill level, and initial rating of lower level players. Since these change frequently, it's pretty much useless to compare ratings separated in time by more than a decade or so, maybe less. 50+ years is certainly far too long.
His record in bullet in the Speed Chess Championship against Carlsen is rather unremarkable, although that is 1+1. Perhaps he would fair better at 1+0.
He's up there for sure, but not clearly the best. According to him both he and Magnus think Alireza Firouzja is the best in longer matches of multiple bullet games.[0] I suspect he would give the edge to Magnus in a shorter match, but I haven't found evidence for this.
Obviously a board game will be easier for a child to compete at than a physical sport. Tons of Rubik's cube world records are held by 9 year olds. I don't see why any of this is relevant in answering the question "is it impressive to be winning at 35 in chess?"
Is your point that young kids have an advantage in chess, making it harder to keep up as an adult? They clearly don't. No 12 year old has ever been able to seriously compete with top players, at best they can hold a few draws or win a blitz game here and there. As far as I'm aware Judit Polgar was the only 12 year old to even break into the top 100, and she's an outlier among outliers. Right now the top 3 players in the world are all in their 30s, and there's only one player in the top 50 who's younger than 18.
To be clear, "came last in Speed Chess Championship" actually means he came in 4th out of 16. He still made it to the semifinals. Even then he barely lost to Alireza, who is pretty universally considered a top 3 speed chess player. The loss to Lazavik was a lot worse, but it was still a close match against a strong player. He hasn't won a Titled Tuesday this year but he hasn't scored worse than 8/11 and he's still made the top 10. That's not as much of a slump as you imply IMO.
No, even the best prodigies typically aren't winning super tournaments until 17 or 18, and we haven't really had one of those since Gukesh won candidates last cycle. The youngest player in this event was a 20 year old who placed last. (Though to be fair to the youngsters, 3rd and 4th place are both 21 years old.)
Generally speaking it's expected that chess players will peak around their late 20s and slowly decline from there, with sharp declines around age 50. It's unusual but not unheard of for players in their 40s to win major tournaments. 42 year old Levon Aronian won several last year, but it was considered a notable example of longevity every time he won.
In terms of raw numbers, there are currently 30 players in their 30s, 15 players in their 40s, 4 players in their 50s, and no players older that in the top 100. The youngest is 14-year old Yagiz Kaan Erdogmus, who is considered the greatest chess prospect of all time.