20 ms·
Teenager solves stubborn riddle about prime number look-alikes
- citizenpaul 4y ago
- jklinger410 4y agoYou are 100% correct. https://en.wikipedia.org/wiki/Michael_J._Larsen https://en.wikipedia.org/wiki/Michael_J._Larsen
- kevinventullo 4y agoHis mother is also a mathematician, and his uncle is a Fields Medalist. That said, I disagree with OP that this suggests his parents secretly did this work. Rather, it tells me that being surrounded by great mathematicians at a young age is going to foster success in those with raw talent much more effectively than, I dunno, attending some “gifted” program at a typical public school.
- zem 4y agoanyone who thinks a mathematician proved a result of this magnitude and decided to give credit to someone else does not know mathematicians very well!
- sbf501 4y agoWhy the concern of these people? Someone might get credit who doesn't deserve it? There are bigger problems in the world, and life is about getting fucked out of things you do deserve all the time. Meh.
- klyrs 4y agoThat's one of two parents. Ayelet Lindenstrauss, interviewed in the article, is also a mathematician, as was her father Joram, and her brother Elon got a Fields medal. To accept OC's comment as 100% correct is to accuse two mathematicians of academic fraud. And if we're going that route, are we going to insinuate Joram Lindenstrauss responsible for both Ayelet's and Elon's academic works?
- forgotpwd16 4y ago>Let me guess, this teenager has a parent that is an established mathematician. But wouldn't those teenagers have higher chance and assistance in studying higher math compared to peers? (Though being sole paper author is a bit strange.)
- deleted 4y ago[deleted]
- bawolff 4y agoPeople learn from mentors. Its not that surprising and doesn't neccesarily imply the parent did it. The parents probably did help by teaching them math.
- mlyle 4y agoThat's the thing. This is a spectacularly rare accomplishment for a kid that grew up in an academic family. But it's nearly nonexistent for kids who didn't have these advantages. So chalk most of it up to this kid, and some of it up to his rarified environment.
- strikelaserclaw 4y agoboth his parents are mathematicians and his uncle is a fields medal winner and his grandfather is a mathematician. I'm sure this kid is very intelligent, and i could even believe he solved most of the problem himself but in the end of the article stating "“He did all this without an undergraduate education,” Grantham said." made me roll my eyes.
- kevinventullo 4y agoI mean it sounds like he has already received the equivalent of an undergraduate education.
- strikelaserclaw 4y agothats exactly what i mean, they made it sound like this kid was some average guy who at the age of 15 went to the public library, read books and solved some hard math problem. I bet this kid had an advanced math education and math immersion since he was a toddler.
- kiba 4y agoI wish I was that enterprising at age 15.
- MikePlacid 4y agoDunno. 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+Perelman https://www.amazon.com/s?i=stripbooks&rh=p_27%3AYakov+Perelm... They are both challenging and entertaining and very simple - on the surface. Some were written in 1913 or so. Each American family can get such an “immersion” for their kids - total is less than $100 I guess. But you also should turn off TV and computers, so probably would not work. Also my daughter took major in mathematics - and I like my parents had no time to immerse her in anything - adults work, children play with fun but impractical problems. 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.
- tr33house 4y agovery impressive to have such fundamental contributions at such an early age. To even know it's applicability to modern day cryptography is also really impressive. All the best to Daniel Larsen!
- 4gotunameagain 4y agoGetting older, sometimes it can be so tough to accept the fact that people a fraction of your age achieve things you never will. Given the extreme connectivity of the present, we are also exposed to brilliant minds with incredible capabilities, making us (me at least) feel even more incapable.. I guess it is a lesson for humility. Good job Daniel, you show us !
- lo_zamoyski 4y agoWhy is it tough? This may be worth reflecting on [0]. [0] https://www.newadvent.org/summa/3036.htm https://www.newadvent.org/summa/3036.htm
- dylan604 4y agoYeah, I have no problem admitting that there are people much smarter, more talented, better looking, etc than I am. The day that I assume I'm the top of whatever category is a sad sad day, as I must be the only one left.
- bluGill 4y agoEither that or you have narrowed the field so much that you are the only one even doing what you do. (you might sometimes have a junior to help you, who then becomes the second best in the world)
- munk-a 4y agoPersonally, I can claim, without a doubt, to be the world champion at writing this comment.
- markus_zhang 4y agoI think what really bugs me is that for some hobby I chose, there is a always someone who already achieved everything I could dream to achieve in my life. Then I figured some hobbies are better suited for my use case. For example science is better suited for me. I somehow was never bothered by the fact that some geniuses in 19th century already knew enough math/physics that I could digest in my life. Science is infinite so however much knowledge someone gained, it's zero comparing to the total amount. I guess I need that kind of comfort to commit to something. Fossil collection is also a good one because every piece I collected is MINE and unique so I don't need to compare with someone else.
- renewiltord 4y agoSummary: 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. Bertrand postulated (Chebyshev proved) that for any n>1, there is a prime p between n and 2n. That's cool! 4. Is it true that there is such a bound for these pretend-primes? Well, we have an interesting fact that there are x^(1/3) of them below any x, once we pass a certain point (i.e. there exists an X such that there are x^(1/3) of them below any x > X) so that makes us think it could be true! Worth seeing! 5. But what about this common-ness measure like the B-C result for primes? Well, it turns out that it exists. It ain't as pretty as just between straight integer multiples, but the fact that it exists in some shape at all is cool! That's what this kid proved. Absolutely rollicking fact. https://arxiv.org/abs/2111.06963 https://arxiv.org/abs/2111.06963
- vorticalbox 4y agoThanks for this. I find articles like this super hard to read due to the mixing of the topic and all the "back ground". It does sometimes feel like it's only there to bulk out the article.
- renewiltord 4y agoOne can hope that future AI autosummarizers can be aware of our personal level of knowledge!
- jbverschoor 4y agoLazy writers and/or who get paid per word. The writer can fix the article, or let every reader fix it in his mind.
- Ar-Curunir 4y agoMaybe just consider that the audience of the article is not you?
- ok_dad 4y agoI 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
- dgs_sgd 4y agoCongratulations to him! That's an amazing accomplishment. There's a lesson in this line > For more than a year and a half, Larsen couldn’t stop thinking about a certain math problem. It's rare to be able to focus on something for that long without giving up.
- skyhvr 4y agoTo your point, one of the more fascinating details about John Nash from Nassar’s book ‘A Beautiful Mind’ was that this very trait set him apart from a number of his contemporaries. He was capable of focusing on problems for what appeared to be quite a bit longer than most, systematically breaking down the barriers that would’ve turned another person toward some other pursuit.
- dekhn 4y agoI'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 thing in the children of world-class athletes.
- misterprime 4y agoAgreed, 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.
- nominusllc 4y agoI wish this could be discussed more openly. I feel the same way.
- feoren 4y ago> 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". It feels like a very enlightened stance: better than pretending selective breeding would literally not work, and certainly better than doing it badly. Why could we come to such a sensible consensus on this topic but fail to do so on so many others? All that being said, I still want to see what would happen if Michael Phelps and Katie Ledecky had a child together. You know. For science.
- TimTheTinker 4y ago> 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.
- goy 4y agoNobody is talking about the proof, but about the fact that the person who produced it was younger than them and they are trying to explain the achievement by innate abilities or parent influence. The fact is just that most of people don't want to do something like that. They just want to be someone who do things like that.
- YeBanKo 4y agoThe article talks about the proof and how he came up with it as much as it talks about his age.
- polynomial 4y agoOf course that's just the first (coarse) filter. Once you've selected for those who actually want to solve the problem (and not just "be" the one who solves it) there is still the the incredibly fine filter of who actually has the ability- that confluence of nature/nurture that is itself such a subject of debate.
- 120bits 4y agoCongratulations! This is a great achievement at his age. Maybe a Fields medal next?
- deleted 4y ago[deleted]
- mkoryak 4y agoMy 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
- kotlin2 4y agoI 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-pdf.pdf https://corbettmaths.com/wp-content/uploads/2018/12/nth-term...
- ducttapecrown 4y agohttps://artofproblemsolving.com/ https://artofproblemsolving.com/
- quacked 4y agoMy best friend was a child prodigy at math and his parents started him on "The Number Devil" which I believe is number theory
- pfdietz 4y agoThis guy has Sitzfleisch, a very useful thing for a mathematician to have.
- Der_Einzige 4y agoDo Germans really say that people with grit have a lot of "butt" because that's what its looking like here!
- pfdietz 4y agoYes, that's the other meaning of the word. :) Here, it means the mental stamina to sit down and focus on a single problem for a long time. Disclaimer: I'm not German (although some ancestors in the 1800s were.)
- cod1r 4y agoWeird how this came out on the day I bomb my probability test. T_T
- kristopolous 4y agoQuanta is doing really solid science journalism these days. They have a number of fantastic podcasts as well. It's bankrolled 100% by this generous billionaire https://en.wikipedia.org/wiki/Jim_Simons_(mathematician) https://en.wikipedia.org/wiki/Jim_Simons_(mathematician) and I hope he continues to fund it