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Teenager solves stubborn riddle about prime number look-alikes

quantamagazine.org

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

#61

Post by jbverschoor »

vorticalbox wrote: post #32
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.…

Thanks for this. I find articles like this super hard to read due to the mixing of the topic and all the "back ground". It does sometimes feel like it's only there to bulk out the article.

Lazy writers and/or who get paid per word.

The writer can fix the article, or let every reader fix it in his mind.

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

#62

Post by wingmanjd »

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 wasn't as cool as this kid, but I wrote a binomial expansion program in TI BASIC back in high school that I was pretty proud of. Teacher said it was neat, but then banned calculators on our tests/ quizzes after I demoed it.

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

#63

Post by quickthrower2 »

paulpauper wrote: post #45
363849473754 wrote: post #36

Earlier quoted context omitted.

Not to downplay any of Daniel’s accomplishment but sometimes it isn’t a “fair” comparison when others started younger with more resources. His father is a distinguished professor of mathematics and his mother is a professor of mathematics. When you have that sort of resources available at a young age and advanced training you’ll probably accomplish more sooner than someone of similar IQ without those resources who st…

There are thousands of mathematicians in the US. I am sure many have kids. How many of those kids do even a fraction of what Daniel did even when having every possible advantage? Today, young people have assess to more resources than ever, yet talent is one of those things that resists this trend of egalitarianism seem elsewhere. More resources means that the super-talented will pull way ahead of the untalented or on…

Resources also include parental encouragement, not being bullied, not having to do stuff to get by that isn’t delving into deep work, not trying to fight boring school lessons and exams in subjects not of interest, no pressure to shape your studies to get a job. These are not universal.

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

#64

Post by jll29 »

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.…

By the way, if you don't like reading bulky proprietary PDFs, there is a trick: substitute the x in arxiv.org by the digit 5, and you will see the paper rendered in HTML5, e.g.:

https://ar5iv.labs.arxiv.org/html/1910.06709

(great work by FAU Erlangen's Michael Kohlhase and team).

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

#65

Post by svnt »

nicoburns wrote: post #21
strikelaserclaw wrote: post #7

Earlier quoted context omitted.

both his parents are mathematicians and his uncle is a fields medal winner and his grandfather is a mathematician. I'm sure this kid is very intelligent, and i could even believe he solved most of the problem himself but in the end of the article stating "“He did all this without an undergraduate education,” Grantham said." made me roll my eyes.

> He did all this without an undergraduate education I take your point, but I think it serves us to be reminded that formal education isn't the only place that one can learn things.

Is this some strange attempt to align this article with the “college education isn’t necessary” mantra?

Like college education isn’t necessary as long as you have college professors for parents?

The absurdist continuation is something like: “I’d like to think if I was motivated enough I could retroactively convert my parents from city bus drivers to tenured professors in a lucrative field, then I wouldn’t need a college education”?

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

#66

Post by BaseballPhysics »

c1ccccc1 wrote: post #48
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…

Is that really true about Feynman? I thought he wrote in "Surely You're Joking" that he didn't take psychoactive drugs because he loved thinking and he "didn't want to mess up the machine".

My understanding is he was reluctant in his earlier days but did indeed experiment later in life.

From: https://gizmodo.com/10-scientific-and-technological-visionar...

> Nevertheless, Feynman's curiosity got the best of him when he became acquainted with none other than John C. Lilly and his sensory deprivation tanks. Feynman experimented briefly with LSD, ketamine, and marijuana, which he used to bring on isolation-induced hallucinations more quickly than he could when sober.

As an aside, that page has a list of other notable scientists who also experimented with psychoactive drugs.

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

#67

Post by kevinventullo »

paulpauper wrote: post #34
strikelaserclaw wrote: post #10

Earlier quoted context omitted.

thats exactly what i mean, they made it sound like this kid was some average guy who at the age of 15 went to the public library, read books and solved some hard math problem. I bet this kid had an advanced math education and math immersion since he was a toddler.

Think of all the millions of dollars spent on immersion and tutoring by rich parents. How many of their kids produce anything of noteworthiness at any age, let alone so young as he did? This is 99% the product of IQ/talent. It's a huuuge leap to go from merely having an advanced math education to actually solving or proving important stuff. This is mathematician-caliber work, not just someone who took advanced course…

Eh, the kind of immersion and tutoring that rich parents can buy doesn’t remotely compare to having two professional mathematicians as parents.

The tutors for rich kids are likely to be local grad students who meet with the kids at most a few hours a week; you can’t exactly hire a fields medalist for tutoring. Perhaps more importantly, those rich kids are not getting singular training in math, they’re getting tutored in a gazillion things so they can be “well-rounded”. Also, those kids are not likely to develop the intrinsic motivation to do this stuff because their parents are still the ones instilling values in them. Those values are going to be “go to law school” or “start a business” or “pursue the arts” or some other avatar of “make as much money/social capital as possible”. Those values are likely not going to be “study math and prove theorems because it’s interesting”.

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

#68

Post by dekhn »

svat wrote: post #29
4gotunameagain wrote: post #19

Getting older, sometimes it can be so tough to accept the fact that people a fraction of your age achieve things you never will. Given the extreme connectivity of the present, we are also exposed to brilliant minds with incredible capabilities, making us (me at least) feel even more incapable.. I guess it is a lesson for humility. Good job Daniel, you show us !

Tom Lehrer once said: "It is a sobering thought that when Mozart was my age, he had been dead for two years."

More Lehrerisms here: https://en.wikipedia.org/wiki/That_Was_the_Year_That_Was

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

#69

Post by [deleted] »

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…

[deleted]

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

#70

Post by renewiltord »

jll29 wrote: post #64
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.…

By the way, if you don't like reading bulky proprietary PDFs, there is a trick: substitute the x in arxiv.org by the digit 5, and you will see the paper rendered in HTML5, e.g.: https://ar5iv.labs.arxiv.org/html/1910.06709 (great work by FAU Erlangen's Michael Kohlhase and team).

Good tip. I should have just linked the arxiv.org page for the article and not the PDF directly https://arxiv.org/abs/2111.06963
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