Go White guy!

Who wrote the MUSIC in this video?? I love it.

... Except for these big names NEVER write back. Maybe because I'm Russian. Not even a Thank You from more than one in 500.

@Anne Woodward but only if you're not a vegan

@Anne Woodward What has 1+0=0 to do with it (and does it have it anything to do with anything really?)?

and also high influence from a young age

There's relatively good proof that intelligence is mostly hereditary, with a minor portion coming from upbringing and your own control. I don't doubt that he had both going for him. Either way, this is exceptional work from an exceptional person.

I think beyond a certain level of intelligence, what becomes the deciding factor is temperament. There are people of incredible intelligence who - literally - have dropped out at 15 and gone to work as a waiter. More whose adult life is low in intimacy / emotional support, and at work antagonism and friction with colleagues. They needed need more, rather than less than average attention to their social & interpersonal skills. Even for neurologically-standard kids, spending their childhood surrounded by adults who are focussed on the child - rather than learning to forge relationships among random peers whose priority is themselves - it can leave them floundering by early adulthood. Entering university full time at an age where they need an adult chaperone means, again, missing normal socialisation experiences. This lad had a great advantage in being the norm rather than a “special one” within his family. And he could get university level tuition while also attending high school, learning everything non-curricular that (for good or ill) high school teaches you. It shows. He comes across as a rounded human being, quite “sorted” for his age, already focussed on what he himself finds interesting but difficult (rather than easy) and ready to persist through the tough bits.

@@hoixthegreat8359 minor portion? upbringing and lifestyle is a huge factor and can pretty much dumb down someones intelligence

Or maybe their upbringing

I don't know. I kind of want to see a mathematical prodigy whos just flippant and unabashedly in your face. It would be kind of refreshing and they would be more marketable which would bring more public notice to their work.

For God's sake WHY shouldn't they eb humble..it's not like they are smarter than anyone else..

​@@leif1075 well, probably they are :)

Humility lends itself to intelligence. If you think you know everything, then you probably aren't trying to improve or learn more.

It is kind of natural for him to be humble, when his father is a great mathematician whose birthday conference (last June) was filled with people from 3 different areas of mathematics: group theory, number theory, and algebraic geometry :)

Can you explain how he was?

What school??

@@Seeker0fTruth Hogwarts

@@ruinerblodsinn6648 cool cool cool same same

He's not a genius, he's inherited the genetics of both parents who are both mathematicians. If both his parents were janitors and he had excellent math skills, then he'd be a genius.

Love seeing older ppl still invested in learning. Your comment is an inspiration for me, you got this!

@@schang_lh thanks! I really enjoy maths outside of a classroom. Studying at home and doing things in my own time let’s me explore things in detail I probably couldn’t in a class.

@@betaradish9968 I know a guy in my math class that is in his 50s, you're never to old to learn.

This is beautiful. Such an honest, humble and inspiring statement. May you have tons of fun on your maths journey!

keep it up man! keep us updated

This guy is a Magical genius

Nothing was random there, just hard work and educated guesses. So it makes sense for him to know everything about it so well. Very impressive.

that's how genius ways of thinking and problem solve hard things easily

@@manamsetty2664 why do youbsay thst .he had to work at least somewhat hard so don't see why most ppl couldn't do what he does

@Fabio why do youbsay that..anyone can get comfortable explaining once they studied jt..and he said it grtd interesting thst n is not prime and indont see why that makes it any more interesting..

Heck.....He already is!

He is definitely a catch. Intelligence is sexy.

He gets no play

@@Hi-xg9qr hard work doing what you love is the best kinda play

@@Hi-xg9qr hes lowkey cute af i think he gets play

still more impressed with a star high school quarterback. sorry!

@@spoker2006 That's quite sad

well said

@@spoker2006 yes a useless quaterback compared to a highschool math prodigy.

​​@@spoker2006rancid envy right here, that quarterback's not even got a quarter of his smarts for sure

My quote: people are like diamonds (very different, some diamonds are very precious and beautiful, others are out of the count)

Numerical analysis is by no means less advanced or less difficult than number theory, and the same can be said for other areas of mathematics. I did my PhD in numerical analysis, and trust me when it comes to research perseverance matters more than anything else.

You have to compare yourself to "yesterday you." As long as you are improving, that's all that matters.

I feel you bro...im like what i did not do in my childhood to become like persons like Larsen and I wonder if ever I could get into the big leagues even if I start from today.

Is your parent a Princeton/Harvard educated mathematician who has worked with some of the largest names in Number Theory? No? Then don't beat yourself up. Daniel Larsen's dad is Michael Larsen. I'm sure he's had some help with his research goals and ideas.

he's was not really a highschooler in my opinion.. first of all he's not a high schooler anymore (misleading title).. plus when he was probably in high school.. he's already doing graduate level math which I assume no high school is teaching him graduate level math.. the title should probably should have been.. "teenager solves prime number theorem"

When I was in the final year of 'high school' (actually, the Upper Sixth Form, in the UK), I was in an advanced mathematics class with others, in addition to being in an even more advanced class with just three of us, looking to get into the University of Cambridge to study mathematics. I eventually didn't get in, and ended up in my second choice university, which was still world class in mathematics. The other person in my year got in. The third person was actually two years junior to us, and really exceptionally bright. I except he probably achieved and/or is still achieving really great things, but since this was before mobile phones and the internet, and it was the last year of school for me, I didn't find out. (Maybe I'll search for his name now, 28 years later, to find out!) Anyway, I realised just before one of our sessions that we would need some background knowledge to attempt one of the very advanced problems during one of our sessions, and he wouldn't have that knowledge, being two years behind us. So while waiting for the teacher, I very hastily taught him how to solve second order ordinary differential equations in about five minutes. He soaked in my teaching all immediately (and with full understanding, based on his subsequent work), which from my perspective, was also a helpful exercise in consolidating my own understanding of the knowledge. The interesting consequence of this was that he somehow got the idea that I was super brilliant, which he politely and respectfully told me so at the time, even though I had only taught him what we had been taught in a larger class ourselves over a few hours, albeit in the advanced classes!

OK, I think I have found him, and not at all surprisingly, he is now a university lecturer in mathematics! I intend to e-mail him in order to reconnect after almost three decades!

I don't actually doubt that most schools have a genius. This kid in the video is above and beyond just having a very high IQ. He has achieved academic maturity at such a young age. That shows he will continue to be at or above that level as he continues his education. Congratulations to the kid, but the word genius is tricky because it depends where you set your markers. I usually hear top 0.1%. Well maybe this guy is at the top 0.00001% or something as a math student and future mathematician. I guess he already is a mathematician with some level of publication! Statistically, an average HS of 1,000 should have a genius. Let's say top 0.1% of traditional measures like IQ. This is tested for essentially by all the standardized college admissions tests. Graduate and professional school entrance exams count as well. For law school you take the LSAT, and the top scorers will be the only ones considered at some institutions. That's genius. They aren't all Hawkings or Einstein and that's fine. You get into a weird area where you've got multiple students who score a 35 or 36 on their ACT (36 is perfect), and that is just a different version but same principles as an IQ test. If you are scoring a 35 or 36, you're testing at what is considered genius levels. You'll be the smartest in almost every room. Someone who scores a 32 is scoring better than 98% of test takers. Top 2%. Gets you into a lot of great undergrad programs with a merit scholarship. That top 2% person, in theory, should be one of the smarter people in a room of 100, but if you make that room of 100 a bunch of engineers or mathematicians - you get someone who is maybe in the top 25 of 100 if they're lucky. They aren't geniuses but they'll go on to become doctors, engineers, lawyers, Ph.D students, etc if they work for it. They tested the world's top chess player for IQ and he was pretty near average. That surprised a lot of people, but the guy told people he wasn't some genius, just a genius at chess. He doesn't process the game itself the way other top players do. Maybe this kid's brain is built like that. He's genius and then some.

​@@Chironex_Fleckeri I normally consider the definition of a genius to be someone who leaves a particular field in a different state, rather than just high academic achievers or people scoring high on IQ tests. By that definition, Daniel Larsen could probably qualify.

What I find extraordinary besides his modesty, is that he used a technique from another field which shows great thinking outside the box. Shows how PhDs get locked in their own world. This gentleman has an extraordinary mind without a doubt.

It's not humility, more like the opposite. Of course they'll respond if you're a once-in-a-generation prodigy who's just solved (or is about to solve) an interesting open problem. Most of us aren't.

@@exemanful He didn't know who he was but he still looked at his paper. That's to say that they'll look at your work regardless of who you are, and the fact that that's the advice the Larsen is sharing talks greatly about how much he admires them.

@@exemanful As Amr Ojjeh said, they had no idea who he was and they still gave him the time to look over it. But even if they only looked at his paper because it had a big claim, he has the humility for the final takeaway to be that they will write back (4:43), so even if he is wrong, he is humble.

@@amrojjeh Heckin' thank you for introducing me to reverse polish notation when I clicked on your channel. That is fascinating.

prizes and medals have turned against the original purpose of mathematics

@@aturitmo6819 can you elaborate?

@@AlxM96 I think the sentiment is that the "pure math" fields (for example, number theory, which the result in this video inhabits) have historically been studied for the simple joy and wonder they offer, and that prizes give an alternate motive for the study and development of these fields. I don't agree with the sentiment - I've met a few fields medalists, and none of them gave the impression that they set out to win one. But I get what A Tu Ritmo is saying.

@@beerandmath insightful, thanks!

@@beerandmath that’s a stupid sentiment if people actually believe that. Even if there are people who are doing it for the sake of winning a field’s medal, I don’t see anything wrong with that. Imagine telling Olympians they should only compete for the joy of it instead of winning gold. 🙄 The way I see it, I don’t really care why people are trying to tackle these difficult mathematical problems. As long as they’re willing to put in the work to solve these problems, then that benefits everyone because we need more innovation in mathematics, not less.

This kid can say "I got schooled".

I'm not supposed to know how to do quadratic functions and I figured that out with no references in high school

@@adaptercrash "not supposed" wat?

@@hurrayboy1995 I think he means that it wasn't in the curriculum for his school. (How the hell does a high school not teach quadratics? Also, I don't like the mentality that whatever is outside the curriculum is somehow "forbidden", as if it's non-beneficial to learn ahead.)

I can totally see that some kids doodle and he was just making advanced mathematical proofs

What are you doing here Bach?

They say Bach's music is very mathematical.

hope he isnt jabbed

Honestly, what a cool guy, I already like math, but this was a source for even more inspiration

this is true

As long as we put our knowledge to good use, I agree

Could you please explain, in Which way The humanity benefits? Do you have an example for me- in this specific case/ All credits to this Young Humble Man-

@@Avicenna-ts5tk he said finding these carmichael numbers that are not primes can lead to better encryption.

@@Avicenna-ts5tk so you one of those people huh??? You have to have others thing for you 🤣👍

well math is racist so

What's your research in?

@@Itz_Ashley11 astrophysics

@@arrau08 theres always gonna be someone better than you, don't downplay your accomplishments my man. You are doing great

@@mors9757?????

@@Whatismusic123 what

Yea + he's able to communicate his work and why it's important in simple terms. Really a rare and valuable alloy

Literally innumerate, nice phrase. Better than being numerally illiterate.

He prob gets no play tho

I don't know why people have this idea that scientists are pretentious. most scientists I've seen in my life are actually quite humble people cuz that's what the world of science does to you, it truly humbles you.

if he gets to teach, i hope he doesnt end up in elementaryschool - highschool, would be a waste of his understanding

@@user-vw3vp8iw1d the fuck are you talking about?

@@Hi-xg9qr wtf lol

I always make the analogy, teaching for professors is like refilling the ketchup bottles as a server. Yeah it's a responsibility, but it's hardly the focus of your job.

@@1missing Man, I think that yours, is an excellent comment, and probably exactly right..!!

What gave you the impression he's kind...did he say anything about helping the homeless or feeding stray cats?

@@jonnieinbangkok please tell me you're not too stupid to discern someone's demeanor.

@@t81629 So you're saying nothing or that you're clairvoyant.

@@jonnieinbangkokOh I'm saying a lot about you, but again, you're too slow to discern.

@@t81629 Again no answer to my question...only the ad hominem attack.

He's actually very attractive by nerd standards.

that doesn't make it any better

WEEZER WEEZER WEEZER I LOVE WEEZER

Not only Weezer but OZMA ???!??!?!? SOOOO BASEDDD

Because it's always the donkeys who usually make more noise than those who are intellectually superior to them.

ever meet his dad?

He's literally the son of an incredibly well-known mathematician Michael Larsen. He probably emailed them because his dad suggested it and they probably answered because his dad is who he is. His paper also thanks his dad for help, so it's not like there's a 2nd Ramanujan here. This kid was probably bred to be a mathematician and probably was pushed in a very specific direction by his dad very early on, which is how almost all of these "prodigies" are.

@@sk8erJG95 About the emailing back because of who his father is: maybe there are some mathematicians out there who are like that (looking at you, Harald Helfgott), but most of them are not. If you're polite, they'll usually find the time to look at what you send them (given it doesn't claim to solve the Riemann hypothesis, of course). About being bred to be a mathematician and pushed in a specific direction: well, there's hardly another way to be a prodigy otherwise. Humans are at peak learning capacity somewhere between 18 and 25. And most concepts in modern mathematics are so advanced that you've virtually no chance at arriving there within that time frame without that kind of specialized tutoring. Ramanujan was a one in a billion exception even in his time. You cannot expect something like him to occur every ten years or so. Furthermore, the results are valid and new regardless of when their tutoring started. It's still new math; being the son of whoever doesn't take away from that. Thus, there's absolutely no justification for those quotes around "prodigies".

@@lonestarr1490 An objective and fair response.

@@lonestarr1490 How many of these "prodigies" actually just have parents with a PhD? Anyone can become a prodigy, but you first need to be at the doorstep.

@@lonestarr1490 I agree most Mathematicians would respond to a mathematically-valid email with at least some kind of response. I've known a few to collect the crank emails they get, in fact! So perhaps that was unwarranted. And for the second part, I agree, that's all I was saying as well. It just makes me sad seeing people who are like "I'm 17 and could never do that" or "I'm a graduate student and have no hope compared to someone like this!". My point is that he's not just some random genius - he was probably raised on discussions of number theory and having a number theorist in the house with you makes it very easy to (1) find resources and results, (2) even get the ideas of certain things/connections/conjectures given to you, and (3) make connections to established mathematicians doing research in what you're interested in. Indeed, this isn't taking away any validity of his work and ability. It's just acknowledging that he got a world more of help than most of us could ever dream of having available.

Don't compare yourself to people like this. You can absolutely still be great at math without being at the level Daniel is. Ramanujan is a story of inspiration for us all. But Daniel Larsen's dad is Michael Larsen, a well-established mathematician and number theorist who probably taught Daniel number theory since before he was a teenager. In this paper they're discussing in the video, he thanks James Maynard for an email and then thanks Michael Larsen "for a number of useful conversations". A.k.a. Daniel proved the result but was probably heavily led by his dad. A shit ton of students at top math schools (undergrad/grad) have math professors as their parents. It's easier to be successful in math when you're raised by people intimately familiar with research mathematics who want to make you look like a prodigy when you're a teenager.

He has two mathematician parents, so consider that before proclaiming he is organic genius.

@@sk8erJG95 Reminds me of Edward Witten and Physics who went to Grad school with a PolSci undergrad degree. His Dad famously said that his son was his greatest contribution to the field of Physics

It probably didn't take them more than two minutes to realize that the sender wasn't a random person.

I'm sure 3 obscure professors of prime numbers are flooded with emails lol. Probably the first email he had gotten in 10 years

@@alite0101 These are professors, they get TONS of emails, I promise, regardless of if they're in a teaching role. Also, primes are a fairly hot topic; there's multiple huge open source projects involving 1000s of contributors. It's super important for computers and cryptography is why. It's also part of how one of the greatest mathematicians alive, Terence Tao, got his name. Which really goes to show how insane this kids breakthrough was.

then you are respecting a virgin. he gotta lift some weights.

@@beamboy14526 Ok and? You're definitely a gymrat.

@@beamboy14526 why you being jealous. Just appreciate what he did and move on

@@beamboy14526 imagine typing that comment out you absolute caveman 🤣

dude literally said top level GRADUATE student. he is far from the likes of terence tao

Sure, if you've been dedicating all of your being to it for many years

unfortunately you almost certainly can't unless you're in the top 0.0001% of the population genetically and have devoted years to it

You are right! There are so many unexplored alleys in mathematics. You could prove something new with few years of study. Or if you were enthusiastic about maths in highschool, just find the right problem! It doesn't have to be ridiculously hard like the problem presented here... Is my response to the other comments.

@@Tondadrd Yes exactly, you don't need to solve the any of the millennium problems. There's a strong chance you can find the solution to something just because it's been overlooked cause it was only really considered by a handful a people who never really had the time for it. And with maths it's impossible to know how groundbreaking something will be in the future. All of cryptography is based on what was considered curiosities back in the old days

@@akaakaakaak5779 Nah, finding a progidy genetically probably isn't that hard. I think it's more that most people don't show any interest in that field or never try it even though they would excell at it. I mean exposure is the biggest problem

virgin

@@beamboy14526 im sorry to hear that Beamy. Hopefully you get laid soon

@@Will-thon ☠️

You can if you actually strive for it put out the games put the drugs just go for it (none of what I said I assumed just the statistics of why most people struggle through stuff is these two )

With full heart no disrespect