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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

#181

Post by RHSeeger »

Waterluvian wrote: post #95
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…

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.

I like to use the phrase "I don't need to be better than someone else; just better today than I was yesterday".

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

#182

Post by rrrrrrrrrrrryan »

orangecat wrote: post #139
dekhn wrote: post #106

Earlier quoted context omitted.

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…

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 with higher IQ, or very nearly so. I would strongly expect the opposite. But I agree it would be beneficial to figure out which of us is right.

According to the latest studies, IQ is largely determined by early exposure to abstract thought. This is the main reason IQ is still rising in first-world nations where malnutrition hasn't been an issue for generations. If you rob a grade school kid of playground time and learning to share toys, and instead force them to grind out math lessons and computer science problems, their adult IQ will be significantly higher.

They might end up tremendously unhappy, of course. It just goes to show how raw IQ is a silly measure to value, let alone optimize for.

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

#183

Post by tylerhou »

NoImmatureAdHom wrote: post #173
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…

That's because intelligence is ~80% heritable! Or rather, ~80% of the variance in intelligence is explained by things you inherit.

(Note: "inheritable" here is not exclusive to inherited genetics; it also refers to upbringing.)

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

#184

Post by WanderPanda »

Waterluvian wrote: post #95
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…

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.

Consciously knowing that comparing yourself too much to others is one thing, actually stopping it is a whole different story at least for me. I didn‘t succeed yet. But I noticed that the idea of having 20% personal growth each year is really strong

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

#185

Post by suzumer »

thaumasiotes wrote: post #180
suzumer wrote: post #172

Earlier quoted context omitted.

No closed form solution means we can't write out the solution cleanly using standard algebraic operations. You can still write iterative algorithms that converge on the solution, such as by solving for the eigenvalues of a matrix.

Those won't tell you the solution; they'll tell you a number that is near the solution. When the solution is irrational, as is common for polynomials, it might be difficult to guess what it is based on knowing an approximation of it.

When using 64 bit floating point numbers with 54 bits of precision, (or likely in this case, complex values consisting of two 64 bit floats) and you use an algorithm which you can guarantee converges to within 55 bits of precision in X steps, you have found the closest representable solution. Yes, you don't know whether it's 1 + sqrt(17) or 0.9 + Sqrt[17.84...], but you know to a degree of precision that 95% of use cases need what the value is. I do understand what you are saying, but the parent comment was referring to a student factoring polynomials. You doubted what he did based on the fact that he couldn't exactly specify what the roots were. I just assumed that he likely found the roots to a reasonable accuracy and then factored with these approximated values. The parent never specified, but given doubting the authenticity of the comment or celebrating youthful ingenuity, I choose the latter. I understand what you are saying. Yes, you can not find the EXACT values of the roots, but within the context of this comment chain, I don't think that matters.

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

#186

Post by teachersaredumb »

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…

Among college-educated professionals, primary and secondary school teachers are near the bottom for intelligence, as measured by SAT scores. https://www.businessinsider.com/heres-the-average-sat-score-...

The pay is shit, so intelligent people decide to pursue other passions instead of teaching.

Also, the profession seems to attract the kind of people who like to exercise arbitrary authority over other people. Not a majority of teachers, but a substantial minority.

Once I realized these things, a lot of negative experiences I had with teachers made more sense. For what it's worth, I also had some great teachers along the way.

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

#187

Post by cam_l »

nuclearnice1 wrote: post #166
khazhoux wrote: post #146

Earlier quoted context omitted.

> Someone once told me, “comparison is the thief of joy.” I've seen it phrased better elsewhere, but otherwise yes.

Feel free to share the better phrasing!

Sartre perhaps? ..hell is other people.

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

#188

Post by Manu40 »

tambourine_man wrote: post #119
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.

I think you’d still have a problem mixing 7, 12 and 15 year old kids. Perhaps not as much as 15 with 20, but still. This growing up thing is hard.

You are so far from wrong, it hurts me to think about it.

Due to having a reading level 10 years ahead of my peers, and already having learned math concepts at least 4 years ahead of them... at age 8... I was put 3 years ahead of my peers in school until the teachers realized the other kids were having none of it.

They put me back in the 'proper' grade, because 'I' somehow wasn't going to develop social skills well enough in such an environment.

They might not have been wrong, but they would have been more correct to tune in the little buggers causing me grief. Or at least let me tune them in...

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

#189

Post by [deleted] »

Zamicol wrote: post #76
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.

I don't hear this viewpoint acknowledged enough. Society wasting and discarding undiscovered talent is one of my deepest fears.

[deleted]

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

#190

Post by ducttapecrown »

mkoryak wrote: post #160

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

https://artofproblemsolving.com/
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