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Google researcher, long out of math, cracks devilish problem about sets

quantamagazine.org

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Re: Google researcher, long out of math, cracks devilish problem about sets

#11

Post by triyambakam »

jobs_throwaway wrote: post #7
acctant wrote: post #2

> He also worked with a textbook by his side so he could look up formulas he’d forgotten. “You’d think someone who comes up with a great result shouldn’t have to consult Chapter 2 of Elements of Information Theory, but I did,” Gilmer said. Always enjoy seeing this sentiment reaffirmed. Funny that Gilmer states it in a somewhat self surprised tone. Rings of the Einstein quote: “[I do not] carry such information in my…

"The value of a … education is not the learning of many facts but the training of the mind to think." While anyone with a (good) STEM education knows this to be obviously true, its frightening how many people go through 16+ years of formal schooling where they mostly do rote memorization and regurgitation.

> its frightening how many people go through 16+ years of formal schooling where they mostly do rote memorization and regurgitation.

That's how most education is structure, though. Unless your point is simply that, though it reads as if you're blaming the student.

Re: Google researcher, long out of math, cracks devilish problem about sets

#13

Post by thethirdone »

> “Mike said, ‘Justin, you’re going to get me thinking about this problem again and I don’t want to do that,’” said Gilmer.

This is a very relatable feeling. I often find myself getting trapped into thinking about problems I am unlikely to solve.

Re: Google researcher, long out of math, cracks devilish problem about sets

#14

Post by tester457 »

jobs_throwaway wrote: post #7
acctant wrote: post #2

> He also worked with a textbook by his side so he could look up formulas he’d forgotten. “You’d think someone who comes up with a great result shouldn’t have to consult Chapter 2 of Elements of Information Theory, but I did,” Gilmer said. Always enjoy seeing this sentiment reaffirmed. Funny that Gilmer states it in a somewhat self surprised tone. Rings of the Einstein quote: “[I do not] carry such information in my…

"The value of a … education is not the learning of many facts but the training of the mind to think." While anyone with a (good) STEM education knows this to be obviously true, its frightening how many people go through 16+ years of formal schooling where they mostly do rote memorization and regurgitation.

We can thank the academic system and Goodhart's Law for that.

We measure students with tests, but all we get are people good at taking tests and rote memorization.

Maybe if we had a better way to access actual learning but are teachers even paid enough to truly care?

Re: Google researcher, long out of math, cracks devilish problem about sets

#15

Post by dang »

agar wrote: post #12

The article title has been revised to more accurately reflect the researcher's position (and removes the AI ambiguity): "Google Researcher, Long Out of Math, Cracks Devilish Problem About Sets" Should the title of this HN entry be updated accordingly?

Ok, done. Thanks!

Re: Google researcher, long out of math, cracks devilish problem about sets

#16

Post by kataklasm »

naillo wrote: post #8

The title makes it sound like an AI solved it but he's just a programmer who normally works on AI that happens to have solved it.

> (i.e. clickbait)

It is not clickbait just because you interpreted it wrongly. The AI in the title only aims to demonstrate his state of out-group in regards to math.

Re: Google researcher, long out of math, cracks devilish problem about sets

#17

Post by jobs_throwaway »

tester457 wrote: post #14
jobs_throwaway wrote: post #7

Earlier quoted context omitted.

"The value of a … education is not the learning of many facts but the training of the mind to think." While anyone with a (good) STEM education knows this to be obviously true, its frightening how many people go through 16+ years of formal schooling where they mostly do rote memorization and regurgitation.

We can thank the academic system and Goodhart's Law for that. We measure students with tests, but all we get are people good at taking tests and rote memorization. Maybe if we had a better way to access actual learning but are teachers even paid enough to truly care?

Tests have their place though. The more rigorous maths exams I took in school were some of the most intellectually challenging things I did in school. If written correctly, they require you to apply the things you've learned in novel ways, or to combine the topics you've studied in new ways. Problem is, IME there's very few professors/teachers qualified and devoted enough to develop those sorts of exams, and as soon as you try to 'scale' it by centralizing the test creation, you run into the same issue of students simply learning for the test.

Re: Google researcher, long out of math, cracks devilish problem about sets

#18

Post by koolba »

rkp8000 wrote: post #9

Always cool to see unexpected applications of information theory, especially outside of probabilistic contexts. A related toy example that comes to mind is the puzzle where you're given 12 metal balls and told that one of them is either heavier or lighter than the rest. You're then given a balance/scale and instructed to figure out which ball is different and whether it is heavier or lighter using the balance a maxim…

The 12-ball problem is a fun one and IMO the key revelation is that you do not need to determine whether the ball is lighter or heavier (which isn’t possible anyway). Just which ball is different than the rest. It’s a great exercise in decision trees as you change your strategy based on total information, not just the most recent step.

It’s also fun to scale the problem from 3 balls up to see how the solution evolves.

Re: Google researcher, long out of math, cracks devilish problem about sets

#19

Post by jobs_throwaway »

triyambakam wrote: post #11
jobs_throwaway wrote: post #7

Earlier quoted context omitted.

"The value of a … education is not the learning of many facts but the training of the mind to think." While anyone with a (good) STEM education knows this to be obviously true, its frightening how many people go through 16+ years of formal schooling where they mostly do rote memorization and regurgitation.

> its frightening how many people go through 16+ years of formal schooling where they mostly do rote memorization and regurgitation. That's how most education is structure, though. Unless your point is simply that, though it reads as if you're blaming the student.

Students do share some of the blame, at least once you get to high school and university level. No one forces (university) students to take easy courses that don't require rigor. As long as people are willing to shell out full-price tuition for a degree that doesn't require you to do more than rote memorization and regurgitation, schools will continue to facilitate it.

Re: Google researcher, long out of math, cracks devilish problem about sets

#20

Post by kibwen »

bornfreddy wrote: post #4

GPT, how do I prove that...?

Similarly, I assumed from the headline that he had used the AI to help him determine the proof.

As for using AIs as mathematical proof helpers, I threw it the following softball and can't say that mathematicians should be too worried just yet:

>> Please prove that the first decimal digit of pi is 3.

> The value of pi is an irrational number, which means that it has an infinite number of decimal digits that do not repeat in a pattern. It is not possible to prove that any particular decimal digit is the first decimal digit of pi, because the decimal representation of pi is infinite and does not repeat. However, the first few decimal digits of pi are widely accepted to be 3.14, so the first decimal digit of pi is generally assumed to be 3.

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