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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
by ok_dad 4y ago
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 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.
Since then, I don't feel bad if someone achieves more than me, because clearly there are some people out there that are born to solve certain classes of problems (maybe their brain structure is better for those, or something, who knows).
- Vt71fcAqt7 4y agoAnd, 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.
- RC_ITR 4y ago>Throughout high school, Kaczynski was ahead of his classmates academically. Placed in a more advanced mathematics class, he soon mastered the material. He skipped the eleventh grade, and by attending summer school he graduated at age 15. Kaczynski was one of his school's five National Merit finalists and was encouraged to apply to Harvard.[17] While still at age 15, he was accepted to Harvard and entered the university on a scholarship in 1958 at age 16.[19] A classmate later said Kaczynski was emotionally unprepared: "They packed him up and sent him to Harvard before he was ready ... He didn't even have a driver's license."[9] But we also need to make sure that we respect the humans who possess those brains too...
- PakG1 4y agoAs discussed in Good Will Hunting: https://www.youtube.com/watch?v=-XCsE5NffMA https://www.youtube.com/watch?v=-XCsE5NffMA
- r00fus 4y agoFor those who, like me, were wondering - this excerpt is from the Wikipedia page [1] about the Ted Kaczynski, aka the Unabomber. [1] https://en.wikipedia.org/wiki/Ted_Kaczynski https://en.wikipedia.org/wiki/Ted_Kaczynski
- irrational 4y agoThank you. I couldn’t figure out who they were talking about.
- Auracle 4y agoThere should be some sort of university made for people like that - where they’re learning high level stuff but with people their age.
- Avicebron 4y agoBards 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.
- jetbooster 4y agoAdded bonus is they come out of it being able to cast 4 first level and 2 second level spells each day
- irrational 4y agoIt’s a Bard college. More likely they learned to play the lyre and sing ballads.
- lelanthran 4y agoBard is also a character class in many RPGs (nethack, Bards Tale); GPs comment makes sense in that context.
- tambourine_man 4y agoI 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.
- Manu40 4y agoYou 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...
- deleted 4y ago[deleted]
- lmm 4y agoLetting them get ahead is usually the best way to respect an intelligent student. I wouldn't put a lot of stock in one classmate's opinion about someone's emotional state, and a driving license is hardly the be all and end all (I didn't have one when I went to university, and never missed it). "Don't put students of any age through interrogation-style experiments that are designed to stress them" is probably a better lesson to take from Kaczynski's case.
- RC_ITR 4y agoSure if you want the student to never be around same aged peers and struggle to develop a social life so they instead focus on their work, I agree.
- lmm 4y agoStudents can tell who's smarter and who's not, and someone at the same level of learning will always be far more of a peer than someone who happens to be the same age. All the available evidence is that the best thing for children's social life is to let them interact with people at the same learning level rather than the same age. (To say nothing of the fact that segregating students by age is unnatural in the first place, and traditional cultures where kids grow up around people of a wide range of ages are far better for their social development than the western school model...).
- Huh1337 4y ago
- Zamicol 4y agoI don't hear this viewpoint acknowledged enough. Society wasting and discarding undiscovered talent is one of my deepest fears.
- doodledo32 4y ago
- Eisenstein 4y ago"I am, somehow, less interested in the weight and convolutions of Einstein's brain than in the near certainty that people of equal talent have lived and died in cotton fields and sweatshops." - Stephen Jay Gould
- EamonnMR 4y agoMismeasure Of Man? SJG is underrated.
- deleted 4y ago[deleted]
- wingmanjd 4y agoI 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.
- ok_dad 4y agoIt 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).
- saurik 4y agoI remember my teacher banned the use of software on calculators (not the calculators themselves) but left an exception for me because she knew I was writing all the software I was using and didn't want to discourage me using that to learn about both algorithms and the underlying math.
- noir_lord 4y agoI 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 they where curious. The UK has a very strange educational system, curiosity isn’t encouraged, you learn like a good little peg in a round hole. Left a very bad taste in my mouth but at least she did eventually apologise.
- JadeNB 4y ago> Since then, I don't feel bad if someone achieves more than me, because clearly there are some people out there that are born to solve certain classes of problems (maybe their brain structure is better for those, or something, who knows). As a math teacher, I very much like every part of your comment except for this. There are way too many people who decide never to try mathematics because they weren't born to it. I don't believe (and it seems rather insusceptible to proof) that math is something that you are born with a talent for, or not; instead, it's all about how much passion you have for it. Genius is any field is not born of effortless gift; it is born of tireless effort. The real difference is between the people who are willing to put in that tireless effort, and those who do not wish to do so (which is a reasonable choice for something you're not passionate about!).
- phaedrus 4y agoWhat's funny is I was that guy (not literally the same guy, but did similar things) as GP describes who could type in a program implementing the math lesson in the time it took the teacher to describe it. And. I. Struggled. So. Much. with math classes. Could never get homework done because I couldn't focus due to undiagnosed (and thus unmedicated) ADHD. On tests it'd take me the whole hour to do three problems out of twenty because I had to re-derive every equation and lemma from first principles before I convinced myself I was doing it right. And then (probably again due to the undiagnosed ADHD) I'd transpose symbols while working the problem or make other working-memory errors. The best math class experience I had (later in life) was with a professor at a community college who was a military veteran (mentioned because it influenced his attitude toward teaching). He said, "I'm going to spend hardly any time explaining things; we're just going to work the problems." And that's what we did; we just worked problems. You'd think I'd be bored with that, but it was the opposite. As I think about it now to try to explain why, I realize that other math classes I'd been in the expectation was lecture was for explaining the concepts, homework was for self-directed working the problems, and tests were for demonstrating that. But if you're bright and have ADHD you're quickly bored with the explanation and completely UNable to self-direct working the problems. So the class time was wasted and homework sessions were hell. So this professor using class time to work the problems was just what I needed.
- sudosysgen 4y agoI wrote a similar program in those years about when we were first learning of quadratics. It's not really that I'm very smart, my parents were just math teachers and they'd force me to go through more advanced math books where I learned stuff, and I'd get bored in math class. My algorithm was slow garbage though, so I'm sure your friend's was much better.
- jablongo 4y ago> 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.
- THENATHE 4y agoIf they’re talking about the quadratic equation, this is likely 8th grade to 10th grade in the US education system. Factoring would be y^2 = 3(ab)^2 + c^2, get y all alone so it’s y = _____
- casey2 4y agoYes, polynomial factorization does have a specific meaning. You should learn it. https://en.wikipedia.org/wiki/Factorization_of_polynomials https://en.wikipedia.org/wiki/Factorization_of_polynomials
- deleted 4y ago[deleted]
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- ctchocula 4y agoTo clarify, there do exist closed form solutions for quintic functions; they just cannot be expressed using rationals and a limited set of operations of additions, subtractions, multiplications, divisions, and root extractions. However, if you do not limit yourself to those operations, there do exist closed form solutions to quintics. See [1] for a few examples. [1] https://mathworld.wolfram.com/QuinticEquation.html https://mathworld.wolfram.com/QuinticEquation.html
- Waterluvian 4y agoSomeone 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.
- khazhoux 4y ago> Someone once told me, “comparison is the thief of joy.” I've seen it phrased better elsewhere, but otherwise yes.
- nuclearnice1 4y agoFeel free to share the better phrasing!
- cam_l 4y agoSartre perhaps? ..hell is other people.
- khazhoux 4y agoeh, I'll let my comment stand on its own ;-)
- Waterluvian 4y agoIt isn’t really standing then. ;)
- deleted 4y ago[deleted]
- vcxy 4y agoIt definitely does stand on its own, haha. I appreciated it anyway
- ducktective 4y ago>there are some people out there that are born to solve certain classes of problems exact same experience... there is literally a genetic factor but people are not willing to admit it
- swayvil 4y agoIt's easy to be a genius. All you have to do is give 100% of your attention to your subject, indefinitely.
- novosel 4y agoThat 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.
- swayvil 4y agoYa, true geniusses invariably add gratuitous multiple syllables to everything they say. It's one of the signs.
- strikelaserclaw 4y agoi mean achievement is at the intersection of luck, talent, and hard work. Knew several people with the raw iq to be great but these people would much rather spend their time doing mental puzzles.
- thaumasiotes 4y ago> 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 more. (Where a "solution" and a "factoring" are, for polynomials, the same thing.)
- TimTheTinker 4y agoMust have been for degree 4 or below.
- curt15 4y agoOr maybe it assumes rational roots.
- pedrosorio 4y agoWhich would be useless in context because even for quadratic polynomial problems in middle school, very often the solutions are irrational.
- TimTheTinker 4y agoIn which case it could say "no rational solutions found"
- pedrosorio 4y agoYeah, I could also write a program that checks if all solutions are 0 and output the factorization, otherwise say "there are non-zero solutions". That's far from "a program that factors polynomials". If you brag about how "you can design a computer program to factor any polynomial equation string input to it" in a class about quadratic equations and your code can't factor x^2 - 2, that's just not very impressive, regardless of your age.
- charlieyu1 4y agoI figure out the formula of the number of diagonals of n-sided polygon within 15 minutes when I was 10. I thought I would be the greatest mathematician ever. Gauss figured out the formula of 1+2+3+...+n at a similar age and the difficulty was similar, right? I have never been so wrong haha
- eyelidlessness 4y agoI 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.
- geebee 4y agoI'm going to be a little obnoxious here. Did he really implement a factoring program, or did he approximate the solution to a high precision numerically? Both would be impressive under the circumstances of course. But if he did it numerically, he still might want to pay attention to how to derive the quadratic equation using partial fractions. It's actually pretty clever.