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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

#121

Post by TimTheTinker »

feoren wrote: post #105
misterprime wrote: post #83

Earlier quoted context omitted.

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 think society settled on a response of "yeah, but we shouldn't actively do anything about it as a group." I hope there comes a day when humanity is responsible enough to handle precise gene-tailoring of humans without it devolving into a cliche Sci-Fi dystopia. Until then, I'm glad that humanity has settled on "Eugenics could theoretically work but we know we're not responsible enough to do it right, so let's not…

> I hope there comes a day when humanity is responsible enough to handle precise gene-tailoring of humans without it devolving into a cliche Sci-Fi dystopia.

Power itself is a bit of a paradox - having some is essential to a free society, but too much ends up corrupting its holders and results in human suffering. The power you describe falls in the latter category, IMHO.

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

#122

Post by nicoburns »

svnt wrote: post #65
nicoburns wrote: post #21

Earlier quoted context omitted.

> 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 coll…

It's intended to push back more against "we won't hire anyone without a degree" type sentiments than "you shouldn't bother going to college" type sentiments.

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

#123

Post by jetbooster »

Avicebron wrote: post #111
Auracle wrote: post #92

Earlier quoted context omitted.

There should be some sort of university made for people like that - where they’re learning high level stuff but with people their age.

Bards college at Simon's Rock did something like this. My friend went when he was 15ish. I used to visit during the summers and while the education was relatively accelerated, there are a host of other issues that don't often get brought up with this model.

Added bonus is they come out of it being able to cast 4 first level and 2 second level spells each day

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

#124

Post by novosel »

swayvil wrote: post #107
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…

It's easy to be a genius. All you have to do is give 100% of your attention to your subject, indefinitely.

That is the definition of a genius-savant.

True genius is always happening at the crossroads of his interests. Not linear, not monosyllabic, but divergent-recomposing-thing.

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

#125

Post by MikePlacid »

BaseballPhysics wrote: post #96
MikePlacid wrote: post #25

Earlier quoted context omitted.

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…

There may be a language issue here, but to be clear: Elitist != rich. I've run across many poorer folks who harbour elitist attitudes (like, say, ascribing mental or moral failings to folks who choose to indulge in sex, drugs, or alcohol).

There easily can be a language issue here, but I believe the only negative word I used was “defect” and I’ve applied it to myself, not to my classmates who chose to indulge in these wonderful things you’ve listed. Sex is indeed wonderful. Alcohol also gives you some pleasant feelings. I do not get nicotine at all but people seem to enjoy it, who am I to disagree.

Note that indulging in all these pleasant activities does not prevent you from being successful. A lot of my heavily drinking classmates became rather accomplished. We have a head of a regional KGB office (our region is about 2 mln people, a dozen counties or so), a head of regional sanitary office (a medic who checks business medical safety compliance), doctors, engineers…

And if I was born say a hundred years earlier there would be no such a crazy demand for computer specialists, and I would have probably landed a job of math teacher at high school, or if I was lucky - at community college like my granddad.

Math teacher at high school - only some brain defect can lead you to give up pleasures of booze to get such a job, no?

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

#127

Post by ok_dad »

wingmanjd wrote: post #72
ok_dad wrote: post #71

Earlier quoted context omitted.

It was a while ago, and my memory sucks for those kind of things, so maybe it was you! Anyways, programming anything in the space of 5 minutes is hard enough for me, so I'm still amazed at that binomial expansion (which I had to look up, myself).

We're you in eastern PA in high school? Would be wild if we were in the same class!

I was in the opposite side of the country, but let’s pretend, haha.

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

#128

Post by acer4666 »

thaumasiotes wrote: post #115
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…

> This kid walked straight up to the board and explained how you can design a computer program to factor any polynomial equation string input to it, and in fact had implemented a polynomial equation factoring program while the teacher explained how to factor simple quadratic equations. I find this difficult to square with the well-known theorem that there is no closed-form solution to polynomials of degree five or mo…

And how does "no closed form solution" imply "no solution"?

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

#129

Post by vitus »

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.…

> It ain't as pretty as just between straight integer multiples, but the fact that it exists in some shape at all is cool!

Actually: the form that Larsen proved is stronger than "for sufficiently large X, there is at least one Carmichael number between X and 2X".

So with the more specific proof, he also proved the simpler statement that's easier to express.

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

#130

Post by MikePlacid »

bumby wrote: post #37
MikePlacid wrote: post #15

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 They may not be as mutually exclusive as you think. I remember reading some research years ago that investigated the positive correlation between alcohol abuse and IQ. Their theory was that high IQ personalities seek novelty and that can manifest in chasing novel mental states.

That may be true, but my “living experience” is causing me to doubt it, heavily. I’ve seen a lot of guys - most of them more gifted than me in math (I actually switched to computer science after 2 years in university cause I fell in love with computers but math seemed too abstract to me) - so I’ve seen both brains and lives of these bright guys completely destroyed by alcohol abuse, completely destroyed, not an easy thing to watch.
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