The High Schooler Who Solved a Prime Number Theorem

[@QuantaScienceChannel]

Read more about Daniel Larsen in a feature by Jordana Cepelewicz at QuantaMagazine.org: www.quantamagazine.org/teenager-solves-stubborn-riddle-about-prime-number-look-alikes-20221013/ You can explore our other number theory coverage here: www.quantamagazine.org/tag/number-theory/

[@jan_phd]

Go White guy!

[@leif1075]

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

[@GEMSofGOD_com]

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

[@GEMSofGOD_com]

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

[@GEMSofGOD_com]

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

[@irisce2799]

Both his parents are Professors of Math at Indiana University and have PhDs in math from Princeton University. His father won a Gold Medal in the International Math Olympiad, tying for the highest score. Daniel's Uncle on his mother's side is a Fields Medal winner. High intelligence runs in families...

[@lemonstrangler]

and also high influence from a young age

[@hoixthegreat8359]

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.

[@eh1702]

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.

[@lemonstrangler]

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

[@dr.catcuddler194]

Or maybe their upbringing

[@doggosuki]

its always nice to see someone like this act so humble

[@InTrancedState]

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.

[@leif1075]

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

[@fabianr9394]

​@@leif1075 well, probably they are :)

[@WanderTheNomad]

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

[@대학원생-w4w]

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 :)

[@patrickjoyce244]

I went to high school with him. Dudes an actual genius

[@ssdgsci9400]

Can you explain how he was?

[@Seeker0fTruth]

What school??

[@ruinerblodsinn6648]

@@Seeker0fTruth Hogwarts

[@Seeker0fTruth]

@@ruinerblodsinn6648 cool cool cool same same

[@richierich8334]

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.

[@fabianomenezes5892]

You can clearly tell how talented he is based on how confortable he was explaining his finding, I mean anyone can learn the formula to the fourrier transform in a day from wikipedia, but being able to draw high level abstractions from it, and using them in practice in novel ways goes to show how different he is from the rest, and by a large margin, as Granville stated. I love it, thank you Quanta for the video, and congratulations to Larsen for his amazing discovery!

[@manamsetty2664]

This guy is a Magical genius

[@thinksie]

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.

[@zunriya]

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

[@leif1075]

@@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

[@leif1075]

@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..

[@bidoofus7921]

Man, I'm sitting here at my university as a graduate student working on a big assignment for my advanced numerical analysis class, been struggling all semester, stuff like that...When they showed some of Larsen's work here, which by the way is a lot more advanced than anything I'm doing right now, my jaw just dropped, haha. It both blows my mind and really puts into perspective just how amazing some people out there really are. Incredible stuff to see!

[@andreasxfjd4141]

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

[@user-oj7tf5vl9j]

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.

[@xyzct]

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

[@shatdharsanamuttamkumar775]

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.

[@sk8erJG95]

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.

[@raicyceprine8953]

Imagine being a pioneer of a mathematic theory at the age of 17. He's definitely exceptional even amongst the other prodigies. We've watched many stories of prodigies who just ends up doing what every other people already know. But contributing something new to the world is rare especially nowadays since most discoveries are done by big institutions and not by a sole man. Knowing a story like Daniel Larsen is refreshing. He has lot of years ahead of his life yet his name is already set to be remembered for generations to come. Truly an amazing kid

[@spoker2006]

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

[@johnvonleibniz]

@@spoker2006 That's quite sad

[@DarkUnicorn72]

well said

[@AdoptedPoo]

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

[@loop4569]

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

[@86sineadw]

This kid is so humble. He doesn’t even realise it when he said ‘don’t be afraid to write these big names they’ll write back’ that they probably don’t usually write back. But they wrote back to him, because he is working at a PHD level or higher! One day he will be one of those big names. What an amazing person he is

[@larryslemp9698]

Heck.....He already is!

[@severetiredamage6754]

He is definitely a catch. Intelligence is sexy.

[@Hi-xg9qr]

He gets no play

[@7XHARDER]

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

[@chefkoch5]

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

[@fletchercobb4398]

I think what makes him so cool is not how he make a mathematical breakthrough, but rather how the takeaway he gave to the viewers is that the great people can respond to you. That shows a humility that I find extraordinary.

[@nobytes2]

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.

[@exemanful]

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.

[@amrojjeh]

@@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.

[@fletchercobb4398]

@@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.

[@fletchercobb4398]

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

[@betaradish9968]

I am 40. I decided that I wanted to learn mathematics and now doing a degree. I love number theory. And seeing this guy I now want to study more. Normally you have older people been role models to younger people. This man is a role model to an older man.

[@schang_lh]

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

[@betaradish9968]

@@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.

[@AdoptedPoo]

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

[@antalkarolyi]

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

[@TheOfficialCasso]

keep it up man! keep us updated

[@homz83]

You read and see stories about high school "geniuses" often, and they're almost always blown out of proportion. But Larsen is the real deal. That's an amazing level of understanding and complexity that he has mastered at a young age. He is a true genius.

[@Mellowyellow8888]

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"

[@MrVaskor]

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!

[@MrVaskor]

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!

[@Chironex_Fleckeri]

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.

[@MrVaskor]

​@@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.

[@johannsebastianbach3411]

He seems like not just a genius but also genuinely a really nice caring person! Hope he gets a fields medal one day!

[@Shreksbigfattoeyo]

What are you doing here Bach?

[@ruchirjoshi8642]

They say Bach's music is very mathematical.

[@zwan1886]

hope he isnt jabbed

[@moisessoto5061]

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

[@JimSendre]

this is true

[@manny6479]

Apart from his maths genius, his complete humbleness & respect for others is incredibly refreshing to see in today’s world and an inspiring lesson to us all - whatever you do, keep working at it & give it your best, you never know where it will take you & stay true to good, honest values..

[@G5349]

I can see a Fields Medal in this young man's future. So brilliant and hard working.

[@aturitmo6819]

prizes and medals have turned against the original purpose of mathematics

[@AlxM96]

@@aturitmo6819 can you elaborate?

[@beerandmath]

@@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.

[@AlxM96]

@@beerandmath insightful, thanks!

[@minhquando100]

@@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.

[@chemistryphysics716]

This is a guy that moves the needle for humanity. We need to continue to encourage and support these individuals. Amazing.

[@user-lf4uk6ci5o]

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

[@Avicenna-ts5tk]

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-

[@Peno23]

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

[@sabbath275]

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

[@dtreezy]

well math is racist so

[@lagunamusic7686]

A truly intelligent person can explain something complex to people in a way that’s easy to understand. This kid is talented.

[@hugojj101]

What a legend. Clearly both creative and logical and also just nice, cares about the community and encouraging people to speak to top mathematicians due to the value it could have for both sides as well as maths and it's practical applications. Just wikid.

[@josueibarra4718]

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

[@eh1702]

He is a very good communicator. His analogies really help a person like me (literally innumerate) to get the broad gist of what it’s about. He seems to have a kind of mind that immediately sees possibilities in things beyond the context they appear in.

[@JMXZY]

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

[@darthasavage7213]

Dan seems like a very valuable addition to math theory he does a solid job of explaining how he tackled this problem which often is the most crucial job of teachers imo.

[@arrau08]

Well I'm just an old mediocre scientist always in a survival mode in my research area, and looking back I didn't know the names of big shots even when in college. His respect for top-tier scholars is another proof of his genius. Everythings's so impressive about this young man.

[@Itz_Ashley11]

What's your research in?

[@arrau08]

@@Itz_Ashley11 astrophysics

[@mors9757]

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

[@Whatismusic123]

@@mors9757?????

[@mors9757]

@@Whatismusic123 what

[@xyzct]

His last point that one shouldn't be afraid to email "big names" is a good one. I have humbly emailed people who I thought wouldn't give me the time of day, and I have always gotten wonderful responses.

[@jmg999]

I love how much he enjoys what he does. His work is immensely impressive, and it's all the better that he is contributing in a way that makes him feel good about what he's doing.

[@erinmcdonald7781]

What an amazing young person. Not only is he a math protegee, but he's unpretentious, and able to communicate his ideas in an understandable way. He is the type of person who I would hope considers doing some teaching and outreach. We definitely need more people of his caliber helping students connect with math here in the US. Hope to see much more of this guy in the coming years! 💜🌟

[@Hi-xg9qr]

He prob gets no play tho

[@justno984]

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.

[@oli2243]

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

[@oli2243]

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

[@gguchristine]

@@Hi-xg9qr wtf lol

[@vanderkarl3927]

His ability to explain the concepts covered in this 5 minute video with little in the way of external assistance is a striking testament to his exceptional understanding of said concepts.

[@Richyw0278]

I like how passionate this guy is about maths. I am not an academic by any stretch but this motivates me just by seeing how this guy is with maths

[@pectenmaximus231]

I'm more impressed by how well-spoken he is at that age, especially given the depths of his mathematical ability. To express himself so clearly and plainly, that is a skill I think everyone should aspire to.

[@readdasein79]

It is quite incredible to hear a college freshman speaking about an area of advanced research in the manner of an engaged and competent university lecturer! It's easy to see he will be a great teacher when he gets there.

[@1missing]

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.

[@larryslemp9698]

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

[@chrisoneal2718]

Congrats Daniel! Number theory is such a fascinating field with so many unsolved problems and problems yet to be discovered!

[@bog6106]

what about unsolvable solvable problems? We never talk about those

[@eilysian_]

he’s really great at explaining and talking about concepts. I’m so excited for what he’ll do in the future and for the minds he will teach and inspire. even those exceptional in their professions, especially in complex fields, don’t always have the qualities it takes to teach.

[@y1.5]

This kid can say I solved that when I was in school.

[@maxfun6797]

This kid can say "I got schooled".

[@adaptercrash]

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

[@hurrayboy1995]

@@adaptercrash "not supposed" wat?

[@IntegerUnderflow]

@@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.)

[@ashleythekittymaster4907]

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

[@NikHem343]

Sadly this goes over my head, but it is very apparent that this guy is not only smart as heck, but also incredibly humble. Doesn't feel like he's bathing in the attention, just happy about sharing math ideas. Great guy.

[@lucasm4299]

And can socially interact too

[@richardwatts6802]

Gotta love a maths expert, special people I love listening to them. They always makes me smile, I never understand a word of what they are saying but they always make me feel warm and want to give them a hug :)

[@alexanderh9569]

I knew this kid for a little while in like 5th grade - just always seemed like one of those really genuinely happy and kind people who could understand everything

[@bermchasin]

ever meet his dad?

[@ReAgentMusic_]

The comments under this video make me sad. This kid is insanely intelligent, great at explaining hard to grasp ideas, and seems pretty down to earth and nice. Yet a whole bunch of comments still go, "yeah but he won't get laid" "get some pussy" "nerd" and calling him ugly and shit. Like damn, y'all are so superficial. I guarantee this kid will be 10x more successful than anyone here.

[@bevs9995]

He's actually very attractive by nerd standards.

[@joshuanandrie8859]

that doesn't make it any better

[@turbokaivuri8390]

WEEZER WEEZER WEEZER I LOVE WEEZER

[@turbokaivuri8390]

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

[@D402S]

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

[@aten1123]

I love this. Can't wait to see other mathematical conjectures he proves or creates in his career as a Mathematician. I thought I used to be good at math in high school until l saw this student. Having the brilliance of a PhD math student in high is incredible. Best of luck kid!

[@sk8erJG95]

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.

[@gustafa2170]

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

[@aten1123]

@@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

[@2hedz77]

It's true. Every great academic or engineer loves to hear that their work is appreciated.

[@Zen_Power]

He articulates himself like a professor would delivering a lecture. Get this guy some funding and a research group to solve some big challenges. No time to waste here.

[@williamterra574]

Much respect for this guy!

[@beamboy14526]

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

[@Sadnessiuseless]

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

[@ayo123]

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

[@reimu8454]

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

[@calvinjackson8110]

When I was his age I was struggling with algebra 1 in high school. All I can do is just watch someone like that who is already well on his way to the stars and admire him. I wish him nothing but the best!

[@shibity]

It takes a special mind to not only understand and be able to execute complex mathematical ideas, but then to go beyond that point and contextualize the subject completely and apply new ideas to it. I have a lot of respect for people with that gift, they drive a lot more progress in society than people give them credit for.

[@squirrelsunlight6510]

He's truly brilliant, and so humble.

[@VCT3333]

He says he used Fourier Analysis to get his results. If he'd used Fiveier Analysis, he could have done it faster.

[@idlesquadron7283]

nice!

[@sidenote1459]

I think it's super cool that they got an email from some random person and actually gave it the time to read through it and seriously consider its contents. That sorta humility can sometimes be missing from those well established in an industry. Nice to see.

[@Tommy_007]

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

[@alite0101]

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

[@sidenote1459]

@@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.

[@frankG335]

His work is that of a top mathematician, not just a PhD student. He's a superstar.

[@gameacc6079]

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

[@lex6709]

He really explains complex theme into super simple terms. Thats so cool

[@dpie4859]

Goosebumps! This young boy is one in a billion. Extremely rare to be so talented an also able to think out of the box. 😮

[@BennettAustin7]

I’ve been studying Carmichael numbers for a couple years, so great to see this young legend prove this

[@KrunKid]

I’ve been binging most of your videos now. They are very well edited and I love the information you show. Keep up the great work!

[@t81629]

When a mathematician calls your work "a little technical" haha What struck me the most is how humble and kind he is.

[@jonnieinbangkok]

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

[@t81629]

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

[@jonnieinbangkok]

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

[@t81629]

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

[@jonnieinbangkok]

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

[@MrLloydLockett]

This video is further proof of how vastly different humans can be. He obsesses over Math the same way an artist would obsess over a painting or a philosopher obsessing over the meaning of existence. Very peculiar how this human literally fits into every stereotype of a "Math prodigy"...it is almost by design that this is his destiny.

[@1mol831]

How about you? What kind of prodigy are you? I think most of us are "Failure prodigies"

[@spoker2006]

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

[@Kyree6703]

​@@spoker2006why's that if you don't mind me asking?

[@spoker2006]

@@Kyree6703 it's sexy....this is not

[@T33-q9c]

@@spoker2006 He's gonna be earning a hell of a lot of money after he graduates. Which i'm guessing is sexy to vapid people like you?

[@onecommunistboi]

"... don't be afraid to write these big names, they will write back!" What I really like about this sentiment of his, is that in a few years he might very well be one of those names. And you betcha he'll write back:)

[@sk8erJG95]

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.

[@lonestarr1490]

@@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".

[@vendetadesign]

@@lonestarr1490 An objective and fair response.

[@stxnw]

@@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.

[@sk8erJG95]

@@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.

[@Will-thon]

so refreshing to see someone so smart seemingly such a nice guy. Well done Dan, awesome work. never stop being you!

[@beamboy14526]

virgin

[@Will-thon]

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

[@brianorozco8506]

@@Will-thon ☠️

[@jd-zr3vk]

What I like about this kid is he knows why this work is important. It is not just for the sake of solving a problem for the sake of solving the problem.

[@Excalibur32]

Great to see smart kids like this following their passions and not wasting their talent

[@DeaconOfTheDank]

Incredible stuff from such a bright, young mind. I love how he talks about the direct application of prime numbers in the field of cryptography - it really helps one understand the importance of these concepts!

[@HouseTre007]

All knowledge is important, seemingly insignificant discoveries could be the missing piece to a technological advancement that hasn’t even been imagined yet.

[@Young-ep8ik]

There are many math problems that seem to have no practical relevance at first glance. But as history proves, the elegant theorems/conjectures usually find their way into practice decades or centuries later. This kid proved something conceived to be true before cryptography existed. That's just how fascinating math is, truly the language of the universe.

[@idragyz5994]

What an awe inspiring bad ass. It’s people like Daniel that are working to push humanity forward.

[@caspermadlener4191]

For me, this is really inspiring. The fact that a 17-year old university freshman really makes me think I can do the same myself!

[@blinded6502]

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

[@akaakaakaak5779]

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

[@Tondadrd]

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.

[@drmonkeys852]

@@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

[@Skyl3t0n]

@@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

[@mikemotorsport]

To think about this kind of thing your brain just has to be different. It is amazing how someone can take a problem and get to a solution that no one has seen before. Fair play to this guy he clearly has a bright future

[@elmerparedes1098]

Dude, I don’t know how I got here, I don’t know anything about Carmichael Numbers, I understood nothing about the video but I’m 100% amazed at this man’s genius.

[@joeaverage8329]

Amazing kid. He has so much potential!

[@Zjoway]

We need more people like this in our society, I wish I could have at least 10% of his passion for math.

[@Ts-mf8wx]

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 )

[@Ts-mf8wx]

With full heart no disrespect

[@wyboo2019]

a lot of people saying he inherited this from his parents and that feels very bioessentialist. another equally valid explanation without getting too far into it is that he was raised on mathematics given both his parents were mathematicians, not that it was genetic. in reality it's a combination of genetics and nurturing, but i think that most people have the capability of 'genius' even if it doesn't 'run in their family'

[@k4piii]

This shows that society is great and allow these geniuses carry humanity and make us better. Great win for humanity and I am so happy to heard about the math community was open to his ideas and those were appreciated. The guy is a genius and I hope society can provide him all he needs to keep developing more proofs.

[@vonneumann3571]

His dad already did provide lol

[@PatricioHondagneuRoig]

Mad respect for the guy, I can see he has a bright future ahead

[@ccwoodlands1565]

The addictive part of math and the application of math, e.g. any of the engineering disciplines, is that you can solve an equation and get THE answer. There is tremendous comfort in THE answer. With so much uncertainty around us, we need the comfort of certainty every now and then.

[@quantum_encrypt]

Amazing! Really happy for him! By the way everyone, both his parents are Math Professors :) It goes to show that you can't expect to get far by yourself. You need guidance and mentoring from others above you in the field. You need to have the humility to listen to them and be willing to traverse the path they traversed to reach where they reached and perhaps surpass them. Don't feel too bad. Its likely for many of us that if we had the mentorship and guidance that he had (and the intelligence) we may have reached as far. (Not taking anything away from him, he's brilliant and resilient! Just contextualising). :)

[@SkeletalMisunderstanding]

IQ is passed on in the genetics. A good environment also helps. To be this good, you need both nature & nurture.

[@winterkeptuswarm]

I think you're right. There's a lot of people that are saying genetics, but having the right influences, environment, and privileges in society are super important for a child's development, all of which good parents bring to their kids. Good job to this man's parents!

[@bjrnlsriedelriedel7500]

It astonishes me how knowledgeable and confident he is when he is explaining his proof of Carmichaels Numbers by using a new technique that he wrote about in James Maynard’ paper “Small gap’s between primes” and how he used Fourier-transforms to abstract his findings and made a proof out of that. He seems so outstanding because math seems so innate to him that he knows where to search for abstract mathematical items and how he could abstract techniques and use them for his own proof. Amazing.

[@neilwani1178]

So nice we have a math genius so young. Knowledge only accumulates and people like this are really needed.

[@crweewrc1388]

I wish him the best of luck ❤️❤️❤️ He is very talented and seems nice as well.

[@johnwayne2103]

I envy the people out there with such wonderful minds. I wish him all the luck and success in solving the great mysteries in mathematics.

[@eirdonne_]

me too, i envy them and at the same time respect them. its a fine line and i support him with everything! wish i could meet him or people like him once

[@VarunGupta3009]

Thinking about early day inventions and breakthrough discoveries, so many people, (earlier myself included), dismissed them as elementary and plain obvious. But most of these required either very critical levels of thinking, questioning the stated facts, or challenging previous postulates. Most of them may seem obvious *after* you understand the theory behind them, but they actually required significant out-of-the-box thinking for their generational circumstances, and also faced a lot of backlash and critisism. It's lovely to see something similar in action, but in a world where you can not only prove it in real time but also understand, interact, and share this with billions of people, especially kids, and pique their interest in STEM :D The fact that research also garners more attention and interest than critisism shows how much we've evolved as a species.

[@servv3167]

he is a legit maths prodigy - he clearly understands the concept and application of his work, which is a wormhole of complicated concepts but yet he put it as simple as an apple on a tree - the true level of high abstract understanding is "if a person can explain the concept to a kid and the kid understands" - and he is at that level. I'm proud to be human because of this kind of ppl - also ashamed because im writing this, wasting my time, while he is making breakthroughs to push mankind to the next level -

[@sk8erJG95]

If it makes you feel better, his dad is Michael Larsen, a Princeton/Harvard educated mathematician who is a number theorist at Bloomington. He has probably been raised his whole life being taught number theory. His paper acknowledgements thank a letter from Maynard and "a number of useful conversations with Michael Larsen", aka thanks dad! Not to say he didn't still take recent theorems and apply them to prove new, cool things (i.e. he is obviously still a great mathematician). But he clearly has had quite the advantage having a number-theorist dad. Like most "prodigies". With some exceptions, of course, Ramanujan probably the most well-known.

[@cosmicwakes6443]

What an amazing mind and truly gifted person.

[@matttzzz2]

He's way too skinny tho he needs to eat and lift

[@crazyraptor2907]

@@matttzzz2 manliness isn't just lifting and gaining weight it's also about being the smartest and most knowledgeable you can be but i belive you failed at the second half.

[@beamboy14526]

@@matttzzz2 also virgin for life

[@Pankeekii]

@@crazyraptor2907 while I agree with what you said about manliness, I wouldn't jump to say that the person you replied to was necessarily talking about being manly. For his overall well-being, the young man could definitely gain some heatlhy weight

[@MasterQuestMaster]

@@crazyraptor2907 Believe me, you don't want your muscles to deteriorate from sitting and doing math all day. A healthy amount of workout can prevent serious health issues in the future. Speaking from experience here.

[@viccywiccyy]

When I was in college I struggle with calculus and I barely made it to graduate with a civil engineering degree. This guy blows my mind, I mean, the math related to do this kind of work is just so freaking difficult, people that took calculus 1, 2, and 3 in college know what I'm talking about.

[@alexjbriiones]

Daniel is truly an inspiration to everyone who wants to understand the nature of numbers.

[@dababy7178]

he’s not even the smartest daniel larson

[@hellobro9280]

totally useless. All his life will be inside one room looking at the paper and counting.

[@billbatson6165]

Good god no Alex. Daniel is at the top, I doubt you can be inspired by one of the peons on the proverbial Mathematical Olympus. Nah, for inspiration we'll have to wait for some autodidatic country yokel.

[@RadThings]

Very interesting. When I was in school way back in the late 90’s I was studying cryptography and was analyzing prime numbers for RSA encryption and came across this exact same question was how do you know if you have a strong pseudoprime number in my head but never explored what this person talked about. I saw it as an interesting problem to find ways to strengthen cryptography and now 20 some years later came across this video. So cool!

[@revpgesqredux]

Something tells me he'll be working on NSA encryption if he isn't already

[@youtube1stViewer]

For RSA, if a prime number generator generates a number that is not prime but escapes the primality test(cause there is no 100% primality check) to be used as the private/ public key. The encryption/ decryption checks will fail and the program goes back and regenerates two more prime numbers until the encryption/decryption works. The program doesn’t just use one non prime and make the encryption weak. Do I have this wrong, because RSA equations still work with non prime numbers?

[@Michael-bt6ht]

@@revpgesqredux The NSA will definitely contact the guy so another country doesn't do it first.

[@amazinggrace5692]

He gave the key to success in life: being curious about something and working at it.

[@galefray]

So much respect for this dude, seems like the genuine article. I wish him great success; I'd wish him luck but clearly he doesn't need it lol.

[@gustafa2170]

What a legend.

[@joelerickson3065]

Thank goodness for people in our society that are truly exceptional. We all benefit from their contributions.

[@n8wrl]

WOW! Very impressive! And kudos to the "big names" who helped!

[@Tletna]

Very impressive and interesting to me personally too. I will have to look into this later on. I wish this young man all the best.

[@annihilationHaven]

Even though I only have an undergrad in physics, it's enough to appreciate the work of the mathematicians well above the appreciation of anybody else out there. I just wish they could apply their logical minds to social problems because that's why I never continued developing my talents!

[@asliceofcheese9989]

"only" have an undergrad in physics

[@DeJay7]

Number theory is easily the most interesting thing I personally know about. I hope I can get to a level where I can work on it. Massive congratulations to Daniel Larsen, also motivated me a little bit :D

[@ryanjbuchanan]

Wow, very cool! I truly look forward to seeing Larson succeed. What a bright mind; smart kid!

[@trucypher1040]

We need people like him so bad, they are a dying breed, he will change the world in some way

[@serviusmadsen8173]

This guy is vey inspiring and he seems very nice. I m very proud of his work

[@HawthorneHillNaturePreserve]

Wow! This young man is a genius. What’s interesting is he has a great ability to communicate, which is not always the case with prodigies especially number geniuses. It’s no wonder MIT scooped him up. Definitely want to know more about this kid and will follow his career.

[@drumcdoo9050]

What a lovely modest and humble young man he is who will no doubt go far in life and likely do great things for mankind. He is so right when saying ‘don’t be afraid to write these big names they’ll write back’. Had the same experience once when writing to a renowned Professor in engineering. He wrote back and we talked about a new invention. He was very modest and gave his time to give valuable advice. The difference compared to Daniel is I left school without qualifications and just had enthusiasm and ideas. Due to his inspiration and encouragement the product became successful. And all because of not being scared to write to a man you never dreamed would bother to reply...

[@chipsafan1]

WOW. This is one of the most profoundly incredible contributions to the world that I have seen recently. The implications on the future of cryptography, and therefore global security cannot be overstated. Bravo.

[@emmanueloluga9770]

Yes, this!

[@toadmathematics]

His dad is one of the leading algebraists in the world. His uncle is the leading dynamicist in the world and a Fields medalist. His grandpa was one of the leading functional analysts in the second half of the 20th century. But yeah he lived up to his pedigree. P.S. Problem with this video is that they don't bring up his background.

[@revpgesqredux]

Better out this family on the shroud and Sudarium theorem

[@Tommy_007]

A teacher can only open the door for you. You have to be able to walk through it yourself...

[@Shabudana]

Belive it or not this high-schooler is much cooler than those trying hard to be cool guys, he really used his teenage time in some worth stuff

[@rope321]

Can someone explain to me how these Carmichael numbers can register as primes? That just doesn't seem true to me, unless there's some approximate algorithm used for finding large primes? But even if that's the case, I sincerely doubt that any well-known encryption method relies on 'approximate' primes

[@japanada11]

Cryptography relies on primes with hundreds of digits; to prove with 100% certainty that such a large number is prime takes an unreasonably long time even with the fastest computers. The Fermat primality test is much much faster, and works very close to 100% of the time, so in practice it's much more useful then a perfect test. But it fails for Carmichael numbers. So the question is whether you're willing to put up with a small chance of failure, or whether you want to dedicate several months of computing time to give you a 100% correct answer.

[@japanada11]

And actually yes, in practice, real world cryptographic applications like RSA *do* use pseudoprimes!

[@znull3356]

@@japanada11 So then to rope's point, yes, there's an approximate probabilistic algorithm used for testing the primality of primes rather than the typical brute force of just checking every number up to the square root of the number itself. Very interesting, I hadn't heard of the Fermat primality test. Thank you for the insight. 😀

[@rope321]

@@japanada11 Very interesting! Thanks for the insight indeed

[@zanti4132]

Fermat's Little Theorem (FLT) states, given n is a prime number and a is an integer such that 2 ≤ a ≤ n - 1, then aⁿ⁻¹ - 1 is divisible by n. The reason FLT doesn't work as a test of primality is because sometimes n can be composite and still divide aⁿ⁻¹ - 1 for some values of a; for example, 2³⁴⁰ - 1 is divisible by 341, but 341 is composite. And the real fly in the ointment is, some composite numbers fail the test for ALL values of a. These are the Carmichael numbers. A Carmichael number C has the characteristic that, when C is broken into its prime factors, i.e. C = p₁p₂p₃...pₙ, then C - 1 is divisible by lcd{p₁ - 1, p₂ - 1, p₃ - 1, ..., pₙ - 1} where lcd denotes the least common denominator. For example 561 is a Carmichael number: 561 = 3 × 11 × 17, lcd{2, 10, 16} = 80, and 80 divides 560.

[@NoNTr1v1aL]

I think it's better to change the word "solved" to "proved" in the title.

[@InTrancedState]

Depends on how you view reality I suppose

[@broannoying8765]

These types of geniuses are what society relies on yet we treat them so poorly. Fuck those haters bro.

[@moyeonkim]

I always thought I was smart when it came to math because high school math came so easily. I realize it doesnt take a genius to solve school problems easily. This kind of dude has made mathematics his life much like how icons devote themselves to their passions. I’m no genius, I was just a teacher’s pet. This man is a proper genius.

[@himanshi7896]

idk what I was doing in highschool. I was very lazy in my highschool and I regret it a lot. loved it seeing a lot of young ppl going beyond their limit.

[@GreenvillesAnonymous]

Congratulations on passionately succeeding at something you clearly enjoy and are talented at.

[@Calikid331]

This guy’s already making a name for himself at 17, wow. Not to get ahead but if he keeps this up he could be the next person to greatly push physics forward if he applies this insane level of critical thinking. Props to him!

[@taopaille-paille4992]

he pushes maths in case you haven't understood

[@akapilka]

@@taopaille-paille4992 but math helps physics too!

[@gameacc6079]

@@taopaille-paille4992 IAMVERYSMART

[@rebajason1460]

There are a few Carmichael numbers on my tape measure, and I’ve been trying to find them for 50 years. I’m glad this kid is working on it.