Numberphile - 2022-06-16
Extra footage at https://youtu.be/-r2agPNx0gA - Featuring Jared Duker Lichtman. More links & stuff in full description below ↓↓↓ A proof of the Erdős primitive set conjecture: https://arxiv.org/abs/2202.02384 More Prime Number videos: https://bit.ly/PrimePlaylist Jared Duker Lichtman: https://www.maths.ox.ac.uk/people/jared.lichtman Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/ And support from The Akamai Foundation - dedicated to encouraging the next generation of technology innovators and equitable access to STEM education - https://www.akamai.com/company/corporate-responsibility/akamai-foundation NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile Numberphile T-Shirts and Merch: https://teespring.com/stores/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9
When guys like Adam Savage talk about the magic of Numberphile, this is exactly the kind of video he's referring to. A young mathematician finding beauty in a famous conjecture, works in his spare time to prove it, and all throughout the video Brady is not only teasing out the points that help us laypeople understand it, but also highlighting the personality of the mathematician himself. Youtube at its best.
Unfortunately no nudity involved though
@aceman0000099 Yes..He's gorgeous
@philip thomey haha, stop it, you two! 🤣
Adam Savage likes numberphile? He just keeps getting cooler lol
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11:15 -- I can appreciate the modesty, but "Erdös-Lichtman" is a pretty boss name for a theorem.
The Erdös-Lichtman Primitive Set Theorem. Very cool.
Whether or not this catches on (and I certainly hope that it does) does this proof mean that Jared has now, effectively, an Erdös number of 1?
I like it
@Christopher Smith No
@Christopher Smith I thought of this while watching the video. I feel like he’s probably one of the only people to be able to legitimately make that claim since Erdös’s death
@Oliver Whiting To get an Erdös number of 1 you need to collaborate on a paper with Erdös. As cool as it is to prove an Erdös conjecture, it is not at all the same thing. There will never be another 1.
Perfect Numberphile content. Complex but beautiful problem - simply and clearly explained. Plus an Erdős connection. More from Jared Duker Lichtman please.
Make him darker and he looks like Srinivasa Ramanujan, maybe a reincarnation :-)
@Roy Roye bit of a stretch there but he's a genius
Not simple enough for me lol
I love how Brady asks smarter and smarter questions as the years go by, now being more and more knowledgeable in maths than when he started
And, don't forget, in gemstone trading.
Yeah he was asking some potent questions in this video
btw, Jared's supervisor is (I believe) James Maynard, who has been on the channel before! As a side note, I'm super bummed that Brady came to film in my department while I was there and I didn't see him - the reason I applied to do maths at uni was the twin prime conjecture video that Brady did with James Maynard (and then I got to take his course on analytic number theory, which was super cool).
Whoa I didn't knew James Maynard was supervisor of Jared.
So are you working on the twin prime conjecture?
What a fantastic communicator. He knew just the right tidbits to throw in to help people through his explanations. He was excited and charming. I hope to see him back here!
Z
absolutely agree!
false.
One can easily see how well this man understands this subject by the clarity of his explanations.
Absolutely. I was trying to express the same thought, but the words wouldn't come to me. I wish most professors could convey complex topics with anywhere near this clarity, studying STEM subjects would be that much easier!
Yeah he's been working on this problem for 4 years.
This guy is so humble and wholesome
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"When you discover something in math, out of humility you don't name it after yourself, you wait for your friends to do it for you, but sometimes your friends don't follow through."
-- (supposedly) Richard Hamilton, who discovered Ricci flow which was the technique used to prove the Poincare conjecture
I read an article about the discovery, about him and how he's working on it since his last year of bachelors; I read his paper and now I'm watching his numberphile video interview. His explanations are so clear and precise, just like his paper! Loved this video. I had a hard time understanding Erdos sums before. Especially his proof of the constant. No idea if this is useful but how interesting! So beautiful!
In some sense, the interest and the beauty is the first priority in mathematics. Usefulness is not always knowable and often secondary.
Lol yeah me too I read about him on Quanta Magazine.
I look up these videos for inspiration.
I love this. I hope Jared will become a Numberphile regular...
I absolutely love these interviews with mathematicians talking about their work, especially the recent discoveries.
It makes a lot of sense to put his name on the Theorem! The Erdos-Lichtman's Primitive Set Theorem.
One name for the guy that proposed and for the guy that proved it.
Must have been a sensational theorem to make such a contribution to the math world.
As I understand it: Scientific etiquette is that you're not supposed to name a discovery after yourself, others have to be the first to name it after you.
Wow proving a number theory theorem in the 2020’s.. that’s quite an accomplishment. Gauss would be impressed!
I gauss he would!
I love Brady's constant need to name things after the subject he's filming. Good to see a humble young mathematician doing good work. And he's right - it's nice when there's things like this that confirm that primes are special.
Brady is such a great interviewer. He asks the questions that I dont think of, but when he does, I wonder why I didn't think to ask such an obvious question.
I really enjoyed hearing about how this was a bit of a "candelight theorem" for Lichtman. Amazing that he took the risk and followed his true passion to prove it. Thanks for sharing and teaching us!
More proof that you should follow your heart. Easier said than done though.
The best part of following Numberphile over the years is seeing how much math Brady has picked up. The questions he asks now are so clever and mathematical! I remember when Brady was afraid to even make conjectures!
Lovely clear explanation, Jared is a very nice addition to this channel. I hope he will be in more videos. Kudos to him for making the conjecture a theorem!
It makes sense that primes are the maxinal primitive set. If you were trying to generate the maxinal primitive set from scratch, what would you do? Start with 2, which rules out all multiples of 2. Pick 3, which rules out all multiples of 3. Skip 4, add 5, which rules out all multiples of 5. You're basically running the seive of Eristothenes!
11:14 he's so humble, heartwarming to see.
Probably my all time favorite Numberphile video, definitely my favorite recent video. The explanation, enthusiasm, and banter are wonderful. A modern mathematical discovery that can be simplified for the average viewer that still shares that magic that timeless proofs seem to have.
What I really appericiate about Brady are the questions he asks. He is unlike any ordinary interviewer, and always asks the questions which I would be thinking of at that moment. It really requires a certain amount of skill, so I thought I'd write a comment appreciating that.
Yes it should be the Erdos-Lichtman Theorem. What a beautiful idea, and another reason to love the Primes.
One who proposed the conjecture, one who proved it!
Hard to do a video on something this hard. But I appreciate how genuinely joyful Jared is about this topic. I appreciate him being quite humble, but good to know he knows how big this work is.
Erdős, a group of math students (including myself). A blackboard. Two hours. An Erdős conjecture. His first proof of same. (Notes lost.)
That man could see around mathematical corners. It was a privilege to meet him.
Indeed! Erdos was an amazing guy. He took simple concepts, saw the deeper meanings, and proposed conjectures about them. Many he proved himself, some are yet to be proven. All are interesting.
"Lichtman Primitive Set Theory"... has a nice ring to it.
This guy is so down-to-earth and great at explaining such a complex problem! Very fascinating, I hope he’ll have a fantastic career!
primo classic numberphile content. reminds me of old interviews with James Maynard before he went on to the big time leagues.
The set of primes is the greedy primitive set as well. As in, if you want to build a primitive set iteratively by always picking the smallest allowed number (but not 1), then the primes is what you will end up with.
Which corroborates the result from this video, that it is in some sense the primitive set with "the most small numbers".
That is actually super cool
This is however very obvious and therefor less interesting dont you think? :)
@Jonas Joko It's nothing more than the sieve of Eratosthenes, yes. Probably what lead Erdős to his conjecture in the first place.
@Lone Starr I agree. When building "optimal" sets of integers like this (depending on what restrictions you have and what metric you use to measure) going greedy is almost always a decent first attempt. It doesn't work every time, but it is usually worth trying. In this case, it did work, and I thought that was worthwhile to point out.
@MasterHigure Worthwhile it definitely was, for without your comment I wouldn't have spotted the connection to the sieve of Eratosthenes. Erdős's conjecture feels a lot more natural to me now than it did before. So thank you ;)
So glad that conjectures like these can be found proof for! Congratulations :D
0:31 "We have the Queen here in England, I guess"
Brilliant
I did Chemistry as an undergraduate, sometimes I wish I had studied Mathematics. And then I listen to someone talking about number theory topics and I realise that maths at degree level would have been way beyond me. Fascinating, but far too demanding in rigour of abstract thought. Numberphile is a pleasant way, fifty years on from then, of musing on the beauty of mathematics. Thanks Numberphile!
Exactly the kind of content I love from this channel. Thank you!
Re: the "fingerprint" number dropping as k increases until k=6 - that's reminiscent of how n-dimensional ball volumes turn out. If r=1, a 5-ball has the largest 5-dimensional measure of all the n-balls. When n=6 the n-dimensional measure tapers off and tends to 1.
Actually I think it tends to 0
Most of us mathematicians are extremely timid when it comes to our work and progress. We know that we're standing on the shoulders of giants. But we also know that we're helping to advance understanding and theories that, eventually, will provide somebody else an opportunity to stand on our shoulders and become the next important name in the direction we've gone.
But I doubt I'll ever stand as tall as Jared. Congrats, mate!
for sure colonel dookie
It's almost romantic how Jared discusses this, beautiful mathematics that I do not understand in the slightest. Lovely and wholesome video :)
Amazing result! I’m always interested in results that suggest the primes are some kind of optimal subset of integers. Like he said, we all have this intuition that primes are special, and these results confirm that
I like how embarrassed he seemed to be when Brady pushed him, inadvertently, into a position of implicitly comparing himself to Erdos.
What a wonderful clear and precise definition and speaker - Numberphille we want more from this expert!!
This guy is amazing. It's so obvious that his mind is full of genius.
Erdős-Lichtman Theorum, sounds about right 🙂
This guy is great. I hope he can come back and explain more math for us.
Hey Brady, I like how you are getting better and better all the time in the mathematical way of thinking. It shows in the questions you ask :)
6:30 and I was looking for that comment
amazing work, and really good content. Don't know what I enjoyed more, the brilliant maths, or the charming conversation and rapport between these lovely people.
This was an excellent and very entertaining video. Congratulations on this great result!
I am impressed with your ability to see it, its is just beautiful and it continues forever and wraps on to itself in a new theroy and new sets that combines into millions of of sets. Congratulations 143.41
Brady, you've done it again! Presented a topic that is, by definition, at the very cutting edge of mathematics, in a way that a layman can follow, but not feel patronised. Well done to Jared too, for his proof, and for his clear explanations.
This is great.
Also, loving to hear more of Erdős, not much people know of him inspite him being great scientist and a great man.
@Seth_M-T - 2022-06-16
It makes me smile thinking that, if Jared was born 300 years ago, his name would appear in textbooks and we'd probably have nothing but a single painting of him to know what he looked like. And yet here we are, watching a YouTube video of him explaining his theorem for free.
@StefanReich - 2022-06-16
We'd probably have seen him in a nice wig though
@davidbarnes6672 - 2022-06-16
My thoughts exactly, what a privilege
@blairkilszombies - 2022-06-16
This reminds me of the fact that the only picture we have of Legendre is that one caricature.
@yashrawat9409 - 2022-06-16
Numberphile is also like an archive of such discoveries ( like the videos with J Maynard)
@heaslyben - 2022-06-16
If not a wig, maybe a hastily folded dish towel {:-)