The High Schooler Who Solved a Prime Number Theorem
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- Опубліковано 12 жов 2022
- In his senior year of high school, Daniel Larsen proved a key theorem about Carmichael numbers - strange entities that mimic the primes. “It would be a paper that any mathematician would be really proud to have written,” said one mathematician.
Read more at Quanta Magazine: www.quantamagazine.org/teenag...
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Quanta Magazine is an editorially independent publication supported by the Simons Foundation www.simonsfoundation.org/ - Наука та технологія
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/
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?)?
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...
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
its always nice to see someone like this act so humble
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 :)
I went to high school with him. Dudes an actual genius
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.
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.
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
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!
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..
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
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
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
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
A truly intelligent person can explain something complex to people in a way that’s easy to understand.
This kid is talented.
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!
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.
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.
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.
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..
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!
I can see a Fields Medal in this young man's future. So brilliant and hard working.
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.
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.
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.
Congrats Daniel! Number theory is such a fascinating field with so many unsolved problems and problems yet to be discovered!
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
He seems like not just a genius but also genuinely a really nice caring person! Hope he gets a fields medal one day!
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
This kid can say I solved that when I was in school.
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
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.
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.
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.
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
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.
Yea + he's able to communicate his work and why it's important in simple terms. Really a rare and valuable alloy
Damn, Daniel Larson really everywhere nowadays 😂
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!
This is a guy that moves the needle for humanity. We need to continue to encourage and support these individuals. Amazing.
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
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.
Literally innumerate, nice phrase. Better than being numerally illiterate.
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...
Thank goodness for people in our society that are truly exceptional. We all benefit from their contributions.
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.
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.
What an awe inspiring bad ass. It’s people like Daniel that are working to push humanity forward.
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.
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.
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..!!
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.
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.
I hadn't really thought about "almost-prime" numbers before, but now that I see this video, the concept seems fascinating. Also, that dude is amazing!
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! 💜🌟
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
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.
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.
So nice we have a math genius so young. Knowledge only accumulates and people like this are really needed.
When a mathematician calls your work "a little technical" haha
What struck me the most is how humble and kind he is.
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.
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 :)
Seems like such a genuine person! What a gem
I like how he broke down a very complicated math problem in visual layman's terms. Describing the set of all real numbers as a tree and the apples are the special Carmichael numbers he is looking for.
What a legend, so exceptional and yet so humble.
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.
Nice going. Good job. When I was studying math and physics, I occasionally had what I thought was a brilliant insight, only to find out that my "insight" has been known for hundreds of years. In this case, the insight was genuine.
Congratulations on passionately succeeding at something you clearly enjoy and are talented at.
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
ever meet his dad?
"... 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:)
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.
It's encouraging to know that genius continues.
His work is that of a top mathematician, not just a PhD student.
He's a superstar.
dude literally said top level GRADUATE student. he is far from the likes of terence tao
He gave the key to success in life: being curious about something and working at it.
Massive dose of inspiration, Thank you Daniel. Even though I might not have the best parents educated in mathematics, I will become the best maths parents for my kids. You are my inspiration daniel.
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.
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.
He's truly brilliant, and so humble.
I'm really glad we have people like this to think about our world problems and make the world a better place. thanks dude 👊
The kind of passion that is enviable.
Goosebumps! This young boy is one in a billion. Extremely rare to be so talented an also able to think out of the box. 😮
It's true. Every great academic or engineer loves to hear that their work is appreciated.
Bravo young man! wish you much success in your future studies.
I discovered some theories when I was younger describing a new aspect of 3D space that most people cant really see. But when you see it, it changes the way you look at space and what it means to move in a vector with inertia and what it means to have a black hole with a radius which is much much larger than its circumference.
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!
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
Congratulations, Daniel, both for your mathematical gifts and your kind and generous heart.
It's so hard to grasp what amount of knowledge is required to even understand the problem. And the methods he used for proof are really advanced. Incredible.
I still have a hard time grasping what a log is. This guy seems crazy smart, humble too. Kudos.
Much respect for this guy!
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 🤣
I’ve been studying Carmichael numbers for a couple years, so great to see this young legend prove this
Interesting. This feeds my curiosity and drive to learn more about Math. Math is really hard for me yet so fun at the same time. It's like that feeling you get playing a very hard videogame level but you just LOVE to keep playing to try and solve it and progress forward to reach desired levels to fain and earn new items and stats and play with the new stuff you've learned, acquired, and mastered along the way. Sooner or later, high skill isn't that impossible bar for you to reach but a fun little scene you love pulling off and I find great pleasure in doing that and that applies to Math and many real life stuff as well.
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.
Mad respect for the guy, I can see he has a bright future ahead
I cant wrap my head how his parent or himself can have such a passion for math, its incredible.., i can understand if its for physics, chemical or biology.. but for math, the beginning level is boring, the intermediate level is hard and the advance level is fascinating even for a non academic person like myself.. i really wish i can guide my children to have such passion for knowledge too
Really Amazed by his works
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
so refreshing to see someone so smart seemingly such a nice guy. Well done Dan, awesome work. never stop being you!
virgin
@@beamboy14526 im sorry to hear that Beamy. Hopefully you get laid soon
@@Will-thon ☠️
I actually just learned about Zhang and Maynard's work the other day! I love when you learn about something and then it is referenced again just a week or two later.
I wonder what type of teacher could foster that kind of talent enough so that he knew a lot not only about the theorems he studies but also knew a lot of the specialists, and how many genious level kids that simply didn't had that kind of access
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.
Great to see smart kids like this following their passions and not wasting their talent
Amazing!! Hope you have fun and happy in your career Larsen!
Man, *I* thought I made an incredible achievement in high school when I used an eraser and colored inside the lines.
Very impressive for this young man!!
Amazing kid. He has so much potential!
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.
I figured this problem out years ago but just didn’t feel like submitting it. It’s good to know everything checks out.
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.
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.
Great story. Bravo. And I guess, bravo to his professors in highschool and to his parents. Being able to follow your passion is still not understood at so many levels.
absolutely impressive, hope to hear more from this kid :).
I like this yougin, I love watching brilliant young people take to flight
I LOVE this. I have such great respect for the curiosity and work ethic of this young man (cool brains but he was born with those). At the same time, I rejoice with him that there are still communities of science where the joy of discovery and working together supercedes pride. The truly great work to support the work of others. You're leading by example Andrew Granville!
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.
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.
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.
really appreciated the relevance of finding these large primes for cryptography. that was a really nice touch. I never really understood why you'd want to find these large numbers.
I wish him the best of luck ❤️❤️❤️
He is very talented and seems nice as well.
Thumbs up! My dude looks EXACTLY like someone who I'd expect to solve a prime number theorem. You go, boy!
man.. I have no idea what he is talking about but could listen all day
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!
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
WOW! Very impressive! And kudos to the "big names" who helped!
I am a complete dummy when it comes to most math. And an absolute ignoramus when it comes to higher math
And yet
I’m always drawn to it. Utterly lost in what is being postulated but simultaneously enthralled.
I likened it yo listening to music sung in a language I don’t understand. It’s still beautifully alluring and can listen to it for hours
One more thing I observe about this young man is his language skills. He has a facility of language to express his thoughts and accesses it effortlessly well. He’s twice blessed. Congrats 🎉