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Simple Set Game Proof Stuns Mathematicians

quantamagazine.org

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Re: Simple Set Game Proof Stuns Mathematicians

#21

Post by imglorp »

dhekir wrote: post #9
pnut wrote: post #2

I did really well in school, and am a professional developer now, and my wife utterly destroys me at this game. She can find sets in real time as the cards are being dealt, while singing along with music, it's maddening.

Could it be somehow related to better peripheral vision? I met a woman once who could gather four-leaf clovers nearly instantly, at the same spot where me and my male friends had spent minutes searching. I've seen written in some places (but could not find a worthy source) that women might have better peripheral vision due to food gathering in prehistoric times, but this might just be some old sexist construct (if an…

I bet it's closer to the pattern matching part of the brain that counts objects at a glance. This is a different skill than counting with words.

Re: Simple Set Game Proof Stuns Mathematicians

#22

Post by tokenadult »

A lot of the history of mathematics is summed up in the last paragraph of this very interesting article. "The fact that the cap set problem finally yielded to such a simple technique is humbling, Ellenberg said. 'It makes you wonder what else is actually easy.'" Mathematical progress comes about by some mathematician noticing a pattern that makes solving a formerly difficult problem more easy than solving it used to be. (For this purpose, innovations like place-value decimal numeral notation fit the preceding statement.) Of course the hard thing is being the first human being to figure out the easy way to solve the problem, and then to embed that understanding in a technique that other problem-solvers can learn. But the increasingly rapid collaboration among mathematicians these days (mentioned in a comment posted earlier) speeds the uptake of new techniques and makes more likely that new understanding will rapidly spread among mathematical problem-solvers.

Re: Simple Set Game Proof Stuns Mathematicians

#23

Post by theoh »

imglorp wrote: post #21
dhekir wrote: post #9

Earlier quoted context omitted.

Could it be somehow related to better peripheral vision? I met a woman once who could gather four-leaf clovers nearly instantly, at the same spot where me and my male friends had spent minutes searching. I've seen written in some places (but could not find a worthy source) that women might have better peripheral vision due to food gathering in prehistoric times, but this might just be some old sexist construct (if an…

I bet it's closer to the pattern matching part of the brain that counts objects at a glance. This is a different skill than counting with words.

From https://en.m.wikipedia.org/wiki/Subitizing

"Subitizing is the rapid, accurate, and confident judgement of numbers performed for small numbers of items. [...] The accuracy, speed, and confidence with which observers make judgments of the number of items are critically dependent on the number of elements to be enumerated. Judgments made for displays composed of around one to four items are rapid, accurate and confident."

Re: Simple Set Game Proof Stuns Mathematicians

#25

Post by tgb »

lettergram wrote: post #17
dhekir wrote: post #9

Earlier quoted context omitted.

Could it be somehow related to better peripheral vision? I met a woman once who could gather four-leaf clovers nearly instantly, at the same spot where me and my male friends had spent minutes searching. I've seen written in some places (but could not find a worthy source) that women might have better peripheral vision due to food gathering in prehistoric times, but this might just be some old sexist construct (if an…

I don't know if that's a male/female trait. I literally find four leaf clovers so often/fast that I don't even consciousnessly know how I do it. I'll just reach down and grab them. I'm a male btw

As a kid I would find them all the time. These days if I end up standing around a clover patch with nothing to do, I always look for them but never find them. I can't imagine I had the patience to look for them as a kid for very long, so I feel that my ability must have gone down hill OR that the patches I'm by now just don't have as many of them. I was always convinced that the ones at the house I grew up at had an abundance of four (or higher) leafed clovers and that patches at school, for example, were relatively poor.

Perhaps that ability decline is just my current reluctance to get down on my hands and knees and leaf through them by hand.

Re: Simple Set Game Proof Stuns Mathematicians

#26

Post by guelo »

Xcelerate wrote: post #3

> The paper soon set off a cascade of what Ellenberg called “math at Internet speed.” Within 10 days, Ellenberg and Dion Gijswijt, a mathematician at Delft University of Technology in the Netherlands, had each independently posted papers showing how to modify the argument to polish off the original cap set problem in just three pages. This is a very interesting trend I've noticed. I wanted to cite a few papers on arX…

I'm not familiar with academia but I was surprised that the discovery was made by three mathematicians at three different far flung universities. Is that type of collaboration also being accelerated by the internet?

Re: Simple Set Game Proof Stuns Mathematicians

#27

Post by throwaway676565 »

abritinthebay wrote: post #15
MichaelBurge wrote: post #13

Earlier quoted context omitted.

Building on research seems like it's a form of peer review, especially in math where you'd need to understand the entire proof before making incremental improvements to it.

While this can be true it's also common to have "assuming X is true" where X is some very complicated hypothesis. We saw this with Fermat's Last Theorem and it was with a great sigh of relief that it was finally proven in the 90s. If the inverse was true then entire fields of Mathematics would have collapsed.

> If the inverse was true then entire fields of Mathematics would have collapsed.

Honest question: what would've been the consequences of this?

Re: Simple Set Game Proof Stuns Mathematicians

#28

Post by tgb »

joe_the_user wrote: post #19
jerf wrote: post #5

For those who check the comments first: Not clickbait. Title is literally accurate.

Oh come on, The title and the article seem to be essentially accurate but are written in a breathless "we'll make this math stuff exciting, darn it" tone that some might like but which, as a math person, I find somewhat grating. I think science/math writing of twenty or forty years ago was still reasonably effective and with that, we could get-by with a headline such as "A impressive result in the combinatorics field…

As a grad student in math I read a lot of lifeless papers. Seeing the exact opposite is fun. I thought it was a good article. Why does math need to avoid breathlessness if we seem to embrace it with, say, a million breathless articles about Stephen Curry's latest game? It only seems bad because there's not a culture of excitement over math like there is for basketball, so it stands out. But if we want there to be such a culture, maybe we need to start by taking every bit of excitement we have and stretching it to the fullest.

Re: Simple Set Game Proof Stuns Mathematicians

#29

Post by x1798DE »

jerf wrote: post #5

For those who check the comments first: Not clickbait. Title is literally accurate.

Even if mathematicians were literally or figuratively stunned by the headline, it's a clickbait headline because it gives you no information about the content of the article, while trying to entice you to click through and read it with a big claim.

Example: Clickbait headline: "This underdog just won a major political office!" Regular headline: "Truman defeats Dewey"

Re: Simple Set Game Proof Stuns Mathematicians

#30

Post by cwmoo740 »

pnut wrote: post #2

I did really well in school, and am a professional developer now, and my wife utterly destroys me at this game. She can find sets in real time as the cards are being dealt, while singing along with music, it's maddening.

My family is ultra-competitive and this used to be one of our go to games until my sister mastered it. My brother-in-law wrote an android game to help her practice and after about a month she was down to sub 1 minute clears. We had to give up the game after that.
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