Teenager solves stubborn riddle about prime number look-alikes • Hacker News Board

Re: Teenager solves stubborn riddle about prime number look-alikes

#81

Post by sudosysgen » Thu, Oct 13, 2022, 8:38 PM UTC

ok_dad wrote: post #43

I knew a guy in high school that carried around a sub-compact notebook and one day in science class we were learning about how to factor quadratic equations (a review of old math we should know) and this guy was not paying attention at all, just typing away. The teacher asked him what he was doing that was so important that he couldn't listen, and to please come up and solve the problem. This kid walked straight up t…

I wrote a similar program in those years about when we were first learning of quadratics. It's not really that I'm very smart, my parents were just math teachers and they'd force me to go through more advanced math books where I learned stuff, and I'd get bored in math class.

My algorithm was slow garbage though, so I'm sure your friend's was much better.

Re: Teenager solves stubborn riddle about prime number look-alikes

#82

Post by selimthegrim » Thu, Oct 13, 2022, 8:38 PM UTC

MikePlacid wrote: post #25

BaseballPhysics wrote: post #17

Earlier quoted context omitted.

> I would rather guess that it is some genetic defect in the brain causing a person to prefer playing with abstract problems to booze, smoke and sexual gratification. But I doubt that having such a guess is allowed. Understandable given it's a comically elitist point of view. Fun fact: Richard Feynman experimented with both LSD and Ketamine, among other things. Shame, imagine how much he could have achieved if he had…

Elitist?? I doubt that any American family has a lower standard of living, than a Soviet math post-graduate student, single mother of two. We have no permanent beds only folding ones, I made my studies on a drawing board put over a sewing machine (do you know what sewing machine is for? It’s to repair your old clothing) our apartment was shared by two families, it has no hot water and water itself was de facto ration…

Come to New Orleans and after I am done giving you tour of some neighborhoods let's see what you say.

Re: Teenager solves stubborn riddle about prime number look-alikes

#83

Post by misterprime » Thu, Oct 13, 2022, 8:45 PM UTC

dekhn wrote: post #75

I've known quite a few families where both parents are scientists or software engineers or quantitative engineers. Very frequently, their children will have a scary intuitive understanding of concepts that took my many years to understand (I'm a slow learner; didn't really understand hash tables until my 30s) and then apply their abilities to be in the higher echelons at science in a very young age. I see a similar t…

Agreed, but this brings up the topic of nature vs. nurture, and perhaps even the previously (~90 years ago now?) popular concept of eugenics.

I think society settled on a response of "yeah, but we shouldn't actively do anything about it as a group." It seems to be best left to individuals to seek out parental partners and enjoy the outcomes on a personal level.

Re: Teenager solves stubborn riddle about prime number look-alikes

#84

Post by phaedrus » Thu, Oct 13, 2022, 8:52 PM UTC

JadeNB wrote: post #74

ok_dad wrote: post #43

I knew a guy in high school that carried around a sub-compact notebook and one day in science class we were learning about how to factor quadratic equations (a review of old math we should know) and this guy was not paying attention at all, just typing away. The teacher asked him what he was doing that was so important that he couldn't listen, and to please come up and solve the problem. This kid walked straight up t…

> Since then, I don't feel bad if someone achieves more than me, because clearly there are some people out there that are born to solve certain classes of problems (maybe their brain structure is better for those, or something, who knows). As a math teacher, I very much like every part of your comment except for this. There are way too many people who decide never to try mathematics because they weren't born to it. I…

What's funny is I was that guy (not literally the same guy, but did similar things) as GP describes who could type in a program implementing the math lesson in the time it took the teacher to describe it.

And. I. Struggled. So. Much. with math classes.

Could never get homework done because I couldn't focus due to undiagnosed (and thus unmedicated) ADHD. On tests it'd take me the whole hour to do three problems out of twenty because I had to re-derive every equation and lemma from first principles before I convinced myself I was doing it right. And then (probably again due to the undiagnosed ADHD) I'd transpose symbols while working the problem or make other working-memory errors.

The best math class experience I had (later in life) was with a professor at a community college who was a military veteran (mentioned because it influenced his attitude toward teaching). He said, "I'm going to spend hardly any time explaining things; we're just going to work the problems." And that's what we did; we just worked problems.

You'd think I'd be bored with that, but it was the opposite. As I think about it now to try to explain why, I realize that other math classes I'd been in the expectation was lecture was for explaining the concepts, homework was for self-directed working the problems, and tests were for demonstrating that. But if you're bright and have ADHD you're quickly bored with the explanation and completely UNable to self-direct working the problems. So the class time was wasted and homework sessions were hell. So this professor using class time to work the problems was just what I needed.

Re: Teenager solves stubborn riddle about prime number look-alikes

#85

Post by nominusllc » Thu, Oct 13, 2022, 8:54 PM UTC

misterprime wrote: post #83

dekhn wrote: post #75

I've known quite a few families where both parents are scientists or software engineers or quantitative engineers. Very frequently, their children will have a scary intuitive understanding of concepts that took my many years to understand (I'm a slow learner; didn't really understand hash tables until my 30s) and then apply their abilities to be in the higher echelons at science in a very young age. I see a similar t…

Agreed, but this brings up the topic of nature vs. nurture, and perhaps even the previously (~90 years ago now?) popular concept of eugenics. I think society settled on a response of "yeah, but we shouldn't actively do anything about it as a group." It seems to be best left to individuals to seek out parental partners and enjoy the outcomes on a personal level.

I wish this could be discussed more openly. I feel the same way.

Re: Teenager solves stubborn riddle about prime number look-alikes

#86

Post by r00fus » Thu, Oct 13, 2022, 8:55 PM UTC

RC_ITR wrote: post #54

Vt71fcAqt7 wrote: post #51

Earlier quoted context omitted.

And, to add to this, we need to find and nurture these minds so they don't get bored and can grow at their natural speed.

>Throughout high school, Kaczynski was ahead of his classmates academically. Placed in a more advanced mathematics class, he soon mastered the material. He skipped the eleventh grade, and by attending summer school he graduated at age 15. Kaczynski was one of his school's five National Merit finalists and was encouraged to apply to Harvard.[17] While still at age 15, he was accepted to Harvard and entered the univers…

For those who, like me, were wondering - this excerpt is from the Wikipedia page [1] about the Ted Kaczynski, aka the Unabomber.

[1] https://en.wikipedia.org/wiki/Ted_Kaczynski

Re: Teenager solves stubborn riddle about prime number look-alikes

#87

Post by zeroonetwothree » Thu, Oct 13, 2022, 8:55 PM UTC

phkahler wrote: post #41

renewiltord wrote: post #22

Summary: 1. Fermat's Little Theorem: if p is prime, then b^p = b (mod p) for all integers b. i.e. b^p - b is always a multiple of p. 8^3-8 = 512-8 = 504 = 168 x 3. 2. Is the inverse true? Does b^n - b = 0 (mod n) mean that n is prime? No. Sometimes n is non-prime (like n=561, divisible by 3). We call these n, Carmichael numbers. 3. Okay, so these numbers exist. How common are they? For primes we know they're common.…

But from the article: >> In fact, Larsen’s argument didn’t just allow him to show that a Carmichael number must always appear between X and 2X. And yet the Wikipedia page says 2821 and 6601 are the 5th and 6th Carmichael numbers, which means there are not between 3000 and 6000 (X and 2X). So is his result actually that one must always exist between X and 2.5X or some other small multiple? If so, what multiple did he…

It’s true for x sufficiently large. So there will be some small counterexamples.

Re: Teenager solves stubborn riddle about prime number look-alikes

#88

Post by zeroonetwothree » Thu, Oct 13, 2022, 8:56 PM UTC

bibanez wrote: post #44

phkahler wrote: post #41

Earlier quoted context omitted.

But from the article: >> In fact, Larsen’s argument didn’t just allow him to show that a Carmichael number must always appear between X and 2X. And yet the Wikipedia page says 2821 and 6601 are the 5th and 6th Carmichael numbers, which means there are not between 3000 and 6000 (X and 2X). So is his result actually that one must always exist between X and 2.5X or some other small multiple? If so, what multiple did he…

I only read the abstract and the result is in the same spirit but doesn't say exactky between X and 2X. It's between some more complicated expressions (using logs like usual in number theory)

The bounds are tighter than n and 2n. So he actually proved a stronger result.

Re: Teenager solves stubborn riddle about prime number look-alikes

#89

Post by gcanyon » Thu, Oct 13, 2022, 8:57 PM UTC

phaedrus wrote: post #84

JadeNB wrote: post #74

Earlier quoted context omitted.

> Since then, I don't feel bad if someone achieves more than me, because clearly there are some people out there that are born to solve certain classes of problems (maybe their brain structure is better for those, or something, who knows). As a math teacher, I very much like every part of your comment except for this. There are way too many people who decide never to try mathematics because they weren't born to it. I…

What's funny is I was that guy (not literally the same guy, but did similar things) as GP describes who could type in a program implementing the math lesson in the time it took the teacher to describe it. And. I. Struggled. So. Much. with math classes. Could never get homework done because I couldn't focus due to undiagnosed (and thus unmedicated) ADHD. On tests it'd take me the whole hour to do three problems out of…

I was on my high school's math team. For three years I was in a special class where all we did was look at math problems selected from competitions and solve them. On the one hand, it was great and fun. On the other hand, trig problems were in short supply, and I came out with a less than excellent grasp of trig, especially identities.

Re: Teenager solves stubborn riddle about prime number look-alikes

#90

Post by zeroonetwothree » Thu, Oct 13, 2022, 8:57 PM UTC

strikelaserclaw wrote: post #60

paulpauper wrote: post #39

Earlier quoted context omitted.

it's not like everyone can win the IQ lottery. Superior ability is unequally distributed.

people should measure themselves by how best they utilized their gifts and circumstances to live a life that they are happy with. No point in comparing yourself to some kid who probably inherited an amazing mathematical brain through no conscious effort, moral superiority etc.. of his own.

Ability to maximize your own talent is a talent in itself.