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Teenager solves stubborn riddle about prime number look-alikes

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

#21

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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.

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

#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. Bertrand postulated (Chebyshev proved) that for any n>1, there is a prime p between n and 2n. That's cool!

4. Is it true that there is such a bound for these pretend-primes? Well, we have an interesting fact that there are x^(1/3) of them below any x, once we pass a certain point (i.e. there exists an X such that there are x^(1/3) of them below any x > X) so that makes us think it could be true! Worth seeing!

5. But what about this common-ness measure like the B-C result for primes? Well, it turns out that it exists. It ain't as pretty as just between straight integer multiples, but the fact that it exists in some shape at all is cool! That's what this kid proved. Absolutely rollicking fact. https://arxiv.org/abs/2111.06963

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

#23

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 !

I wonder how many more Srinivasa Ramanujan‘s died in poverty in a rural village?

Maybe there’s a path now for these kids.

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

#24

Earlier quoted context omitted.

Dunno. My granddad was a mathematician and my mother was a mathematician (and my father was a mathematician and a computer scientist, but they divorced). Still the only “math immersion” I got was Perelman books, scattered around our apartment, like Physics for Entertainment and Algebra for Fun: https://www.amazon.com/s?i=stripbooks&rh=p_27%3AYakov+Perelm... They are both challenging and entertaining and very simple -…

> 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…

Yep and Einstein got laaaaaaaid.

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

#25

Earlier quoted context omitted.

Dunno. My granddad was a mathematician and my mother was a mathematician (and my father was a mathematician and a computer scientist, but they divorced). Still the only “math immersion” I got was Perelman books, scattered around our apartment, like Physics for Entertainment and Algebra for Fun: https://www.amazon.com/s?i=stripbooks&rh=p_27%3AYakov+Perelm... They are both challenging and entertaining and very simple -…

> 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 rationed.

In elementary school - while my mother was on the field trips gathering data for her PhD thesis on methan gas distribution in coal mines of Donbass region I was living with my mathematician granddad. It was a small house shared by three families, no running water and amenities inside. My grandparents grew their own vegetables since you can’t buy vegetables on the market (since there were no market), and even bread was rationed - it was Khrushchev time. Elitist family, indeed.

Btw my ancestors were slaves, freed about the same time American slaves were freed. And then communists killed a brother of granddad, and a father of my stepfather, and then national-socialists killed the only brother of my mother, my uncle. My stepfather was never allowed to college, as a son of the “enemy of the people”.

If you want to see “elitist” - look at any American house.

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

#26

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 !

Why is it tough?

This may be worth reflecting on [0].

[0] https://www.newadvent.org/summa/3036.htm

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

#27

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 !

[deleted]

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

#28

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 !

Why is it tough? This may be worth reflecting on [0]. [0] https://www.newadvent.org/summa/3036.htm

Yeah, I have no problem admitting that there are people much smarter, more talented, better looking, etc than I am. The day that I assume I'm the top of whatever category is a sad sad day, as I must be the only one left.

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

#29

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."

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

#30

Earlier quoted context omitted.

Why is it tough? This may be worth reflecting on [0]. [0] https://www.newadvent.org/summa/3036.htm

Yeah, I have no problem admitting that there are people much smarter, more talented, better looking, etc than I am. The day that I assume I'm the top of whatever category is a sad sad day, as I must be the only one left.

Either that or you have narrowed the field so much that you are the only one even doing what you do. (you might sometimes have a junior to help you, who then becomes the second best in the world)
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