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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

#171

Post by kotlin2 »

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

I remember something a math teacher gave me in middle school as extra work. It was a packet of patterns and it gave you the first few items in the sequence and you needed to write a formula that expresses the value for the nth term. Something like this: https://corbettmaths.com/wp-content/uploads/2018/12/nth-term...

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

#172

Post by suzumer »

thaumasiotes wrote: post #152
acer4666 wrote: post #128

Earlier quoted context omitted.

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.

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.

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

#173

Post by NoImmatureAdHom »

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.

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

#174

Post by collin128 »

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.

Reminds me of Seneca:

"However much you possess there's someone else who has more, and you'll be fancying yourself to be short of things you need to exact extent to which you lag behind him."

Lucius Annaeus Seneca, Letters from a Stoic

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

#175

Post by Nursie »

idunno246 wrote: post #142
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 wrote programs too. Even had them print out the work. Checked with the teacher at the beginning of the year and she said no problem. After rampant cheating, mostly people just writing notes in the programs section, she instituted a policy of deleting everyone’s calculator before any test. but let me keep mine too, I had asked to not delete it and I’d take a class calculator if she insisted.

Waaaay back at school in the 90s, that was the policy in our public exams, we were allowed the calculator but it would be wiped on the way in to the hall.

So I memorised my quadratic-solver-with-intermediate-steps and tapped it back in while we were waiting for the test to start :)

The calculation was not hard, but it was still faster just to run my program and scribble down the steps it spat out than to do the solving manually each time it came up. IIRC I had one for simultaneous equations too.

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

#176

Post by steve_adams_86 »

collin128 wrote: post #174
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.

Reminds me of Seneca: "However much you possess there's someone else who has more, and you'll be fancying yourself to be short of things you need to exact extent to which you lag behind him." Lucius Annaeus Seneca, Letters from a Stoic

Though this tends to be true, once you become aware of it and begin to recalibrate your perception of what it means to have ability, possessions, fortune, any of it – it stops mattering nearly as much, and can often even go the other way.

There are many people who are fortunate in material or circumstantial ways, but you see ways in which they’re enslaved by it or it somehow dictates their life. The classic “owned by what your own” paradigm which is eerily common in western culture.

This can have the effect of making you feel fortunate for having less, rather than envious.

I love Seneca. What I haven’t got a good grip on is time. On the Shortness of Life is a bit of a gut punch for me.

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

#177

Post by ziddoap »

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…

>(do you know what sewing machine is for? It’s to repair your old clothing)

Do you find these condescending tactics work well when you're trying to change someone's view?

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

#179

Post by rrrrrrrrrrrryan »

thaumasiotes wrote: post #154
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…

> 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.

No - eugenics is by definition arranged. If a government nudged you to pair up with someone, that would be eugenics, but if you choose a mate of your own free will, it's not.

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

#180

Post by thaumasiotes »

suzumer wrote: post #172
thaumasiotes wrote: post #152

Earlier quoted context omitted.

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.

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.

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