traes

> 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:

https://www.youtube.com/watch?v=Gg5LSOoYoPs

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_...

[1]: https://www.youtube.com/watch?v=sXyLJaaLEpE

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.

[0]: https://www.erdosproblems.com/forum/thread/blog:1

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.

See https://en.wikipedia.org/wiki/Elementary_function.

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.

[0]: https://www.youtube.com/watch?v=yKXV9-dTq1I&t=2674s

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.

I suspect Magnus draws a similar level of attention regardless, it's probably closer to half the viewer base

For some concrete numbers, there are only four players over 50 years of age in the top 100 at the moment by live ratings[0]. They are ranked #13 (age 56), #89 (age 53), #95 (age 54), and #97 (age 57). In their primes these players were ranked #1, #10, #4, and #3 respectively.

[0]: https://2700chess.com/?per-page=100

Candidates prep and also the entire Freestyle chess experiment has been a bit of a mess. Here's what he told chess.com[0]:

A few months ago I was invited to the first leg of the 2026 Freestyle Tour with the same format and prize fund. I let everyone know that I'd be playing there.

Just a few days ago I received news that there will be no year-long tour for Freestyle. The format for the only event to be held will be only three days and only rapid formats. Instead of the tour that was planned, Freestyle has joined forces with FIDE and are now calling it a World Championship. I think it might hold the record for most rushed arrangement for a World Championship title in history.

I truly enjoyed the first event in Weissenhaus in 2025, and it's a shame that the classical length format wasn't continued. Furthermore, this all feels like a hastily arranged tournament with less than 1/3rd the prize fund it originally had, and now it's attached to FIDE, which isn't a positive development in my opinion.

Despite many phone calls and messages from the organizer, I have decided to decline my slot in this event. I have an important tournament in the end of March/April to focus on, and that is where my attention will be.

[0] https://www.chess.com/news/view/freestyle-chess-fide-world-c...

I understand not watching a 3 hour video before leaving a comment, but this is a disrespectful reaction to a very well thought out video by a professional physicist giving a nuanced opinion about Feynman's legacy. She acknowledges many times in the video that Feynman was a great physicist who deserved his Nobel prize. The central topic of the video is dissecting his public image and the many books published under his name that he did not in fact write, including Surely You're Joking and indeed the Feynman Lectures, as well as criticizing misogynistic behaviors celebrated in those books that has left a negative impact on the culture of physics.

(And also, "cutting him a tiny bit of slack" is pretty lax language considering the behavior being criticized includes beating his wife.)

There seems to be a mistake in the "Building the Transition Matrix" section of this article. Instead of showing the diagonal matrix D with the normalization coefficients it instead shows the normalized Markov matrix M, incorrectly claiming it is equal to the unnormalized matrix C.

Come on now. You know he's not talking about small machine learning models or protein folding programs. When people talk about AI in this day and age they are talking about generative AI. All of the articles he links when bringing up common criticisms are about generative AI.

I too can hypothetically conceive of generative AI that isn't harmful and wasteful and dangerous, but that's not what we have. It's disingenuous to dismiss his opinion because the technology that you imagine is so wonderful.

Sure, but there clearly wasn't much concern if an American got 2/3rds of the vote on day 2. They didn't have to elect a new pope this quickly.

That would mean deactivating all discounts. Honey actively scrapes for them, so as soon as a discount is available on the internet it will find it. Not an impossible solution, but not a popular one.

You could probably be clever and come up with a more complicated discount scheme that's not so easy for Honey to take advantage of, but that adds complexity for users as well.

The entire 3blue1brown series[0] on linear algebra is well worth watching, it has really intuitive graphical explanations of a bunch of concepts. Here's the one on determinants in particular[1].

TL;DW the determinant represents how much you scale the area/volume/hypervolume (depending on dimension) of a shape by applying a matrix transformation to each point.

[0] https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQ...

[1] https://www.youtube.com/watch?v=Ip3X9LOh2dk&list=PLZHQObOWTQ...

Something that seems to be frequently lacking in discussions of convergence in introductory texts on Taylor series is the possibility that the series DOES converge, but NOT to the approximated function. It's not sufficient to conclude that the derived Taylor series must converge to cos(x) because it always converges, since any of the infinitely many functions that match cosine's derivatives at x = 0 will have the same Taylor expansion. How do you know cos(x) is the one it will converge to?