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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

#151

Post by eyelidlessness »

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 was by no means this kid. But I remember many times I’d passively listened to the lesson of the day, then get called on because I seemed (was) distracted, and offered a simpler solution. Usually got a “we’ll cover that in future chapters” with very little attempt to hide the frustration.

I’m sorry if I ruined anyone else’s math classes! If it’s any consolation, I ruined them for me too. I lost interest in the whole subject when I recognized the pattern.

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

#152

Post by thaumasiotes »

acer4666 wrote: post #128
thaumasiotes wrote: post #115

Earlier quoted context omitted.

> 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"?

No closed form solution means you cannot write a program that will, given an arbitrary polynomial, tell you the solution. Which is what was claimed above. Obviously the solution exists, but there is no single algorithm that can tell you what it is.

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

#153

Post by WanderPanda »

sho_hn wrote: post #101
Waterluvian wrote: post #95

Earlier quoted context omitted.

Someone once told me, “comparison is the thief of joy.” I’m confident this is a famous quote. But once I heard it, it kept resonating. Then years later I watched Bluey with my kids and mom says, “just run your own race” and it all clicked. I’m so thankful that it clicked because I feel liberated from this self-imposed sense that I need to absolutely maximize my time here, which is an impossible task.

Learning a new and at the time somewhat obscure (in my setting) foreign language when I was around 30 taught me this lesson at the time. I did well in the small class I attended with others, but not as well as some of the far younger students with both more free time and perhaps better age-given baseline performance at language acquisition (though this is not entirely clear-cut scientifically). I realized it didn't m…

Thank you! I feel like this step-by-step mentality is a good replacement for the naivety of the youth when it comes to attacking complex problems.

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

#154

Post by thaumasiotes »

dekhn wrote: post #106
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.

This isn't eugenics. People are allowed to choose their mates for their phenotypes, and we don't sterilize (except in very rare, extreme circumstances, with legal approvals) people who don't have specific phenotypes. It's a gedanken experiment, but I would expect that people who measure low on IQ tests but are raised immersed in an technical or artistic environment have as much potential to become masters as people w…

> This isn't eugenics. People are allowed to choose their mates for their phenotypes

The fact that something is allowed doesn't make it not eugenics. Choosing your mate for their phenotype is eugenics.

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

#155

Post by hi41 »

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…

Couple of years back there was an article that talked about higher incidences of autism in kids with such parents.

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

#156

Post by paulpauper »

Vt71fcAqt7 wrote: post #55
paulpauper wrote: post #35

Earlier quoted context omitted.

we're talking even greater than Terrance Tao level of IQ. No amount of parent's help can instill that kind of talent.

>greater than Terrance Tao level of IQ Can you describe how you arrived at this conclusion? >No amount of parent's help can instill that kind of talent. Totally agree here, but the use of tallent can be shaped by parenting. I think it's fair to say that his upbringing allowed him to develop an interest in mathematics at an earlier age. Not to mention being able to discuss it all the time (making some assumptions here…

Can you describe how you arrived at this conclusion?

Even Terrance Tao didn't publish anything original of such noteworthiness until his 20s. This guy knows as much as he did without even going to college. mind-blowing x10.

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

#157

Post by FeepingCreature »

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…

IMO, the reason it feels enlightened is that we don't clearly perceive the negative consequences of not doing it. If societal IQ was as pervasively tracked as global temperature, "let's not" might feel as enlightened as "let's not mess with climate engineering."

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

#158

Post by [deleted] »

casey2 wrote: post #143
jablongo wrote: post #94

Earlier quoted context omitted.

> A computer program to factor any polynomial equation string input to it: Do you mean a program to solve for f(x) = 0 using numerical approximation? Factorization has a specific meaning and is not necessarily possible for quintic and higher-degree polynomials / there is no closed form solution like the quadratic formula for n>=5.

Yes, polynomial factorization does have a specific meaning. You should learn it. https://en.wikipedia.org/wiki/Factorization_of_polynomials

[deleted]

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

#159

Post by markdown »

noir_lord wrote: post #97
wingmanjd wrote: post #62

Earlier quoted context omitted.

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.

I had a maths teacher who accused me of cheating because we had coursework to solve a particular problem, I solved the problem for that case and then the general case using math she hadn’t taught me even had a pascal program that you could enter parameters and it’d give you the answer. She literally couldn’t get her head around a student going to the library, taking out a book on maths and teaching themselves because…

Not unique to the UK. This is common all over the world. It's the most efficient way to educate the masses cheaply.

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

#160

Post by mkoryak »

My daughter is in 3rd grade and is bored with her math lessons, so I started to do my own nightly math lessons. Long division was a big hit, but what I really want is to find some accessable number theory material, preferably about interesting patterns. Any recommendations?

Probably something in the 10-15 age range, or 8-10 and originally in Russian

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