Featuring Professor Edward Frenkel. Here is the biggest (?) unsolved problem in maths... The Riemann Hypothesis.
More links & stuff in full description below ↓↓↓
Prime Number Theorem: • Primes are like Weeds ...
Fermat's Last Theorem: • Fermat's Last Theorem ...
Prof Edward Frenkel's book Love and Math: amzn.to/1g6XP6j
Professor Frenkel is a mathematics professor at the University of California, Berkeley - edwardfrenkel.com
The Millennium Prize at the Clay Mathematics Institute: www.claymath.org
Number Line: • Number Line - Numberphile
CORRECTION: At 7:20 the zeta function of 2 should be (Pi^2)/6 as correctly stated earlier in the video (Basel Problem)
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Riemann: Makes a statement without any proof. Is widely regards in the mathematics world. Me: Makes a statement without any proof. Gets 0 in exam.
This is outrageous, it's unfair!
I, too, make statements that all the brightest minds in the world over hundreds of years cannot prove or disprove during my exam.
Fermat did it......
@@emeria9620 I guess you could make such statements tbh. You just need to know the topics where modern math is having a hard time solving. Any statement regarding the reimann zeta function, infinities, if a convergent sum is transcendental or not, tetration and beyond, what else? smth super abstract?
Adrian Nanad 😂😂🤣🤣😂😂
And the proof of the Riemann hypothesis is trivial and left to the reader as an exercise.
possibly it will appear 100 years later
Possibly i will do it
@@ravitaarya 5 bucks says u won't.
@@ethanhuyck4704 I have a proof by elliptic functions, and modern algebra but that won't fit here. ;)
420BootyWizard I honestly wish I could believe you
This is easily the most readable handwriting of any mathematician in the history of mathematics
Did you watch the same video I did? That ζ was nothing like how it should look like.
As a physics student I would like to enter our name into the ring. I think we might even be able to give doctors a run for their money.
OKAY?!!
@@pioneer_1148 you got nothing on advanced maths majors, even AI can't read their handwriting...
@@pioneer_1148as a fellow physics student, I agree
not quite true - Grigori was willing to accept the 1,000,00.00$USD prize however on condition that the award was co-awarded to another mathematician Richard S Hamilton the pioneer of the Ricci Flow whom Perelman credited with providing the basis for his own work - the committee declined to do this and instead simply withdrew the prize money denying both Perelman and his fellow mathematician Hamilton - I quote "Perelman refused to accept the Millennium prize in July 2010. He considered the decision of the Clay Institute unfair for not sharing the prize with Richard S. Hamilton and stated that "the main reason is my disagreement with the organised mathematical community. I don't like their decisions, I consider them unjust."
Thank you
Didn't know that, thanks for the clarification of this story
why wouldnt he just accept it then send half of it to Hamilton?
£~ _ €.
zsolt tildy Because that will be seen as a charity rather than a prize that he deserves.
Not sure why but his Russian accent makes me understand math better. My all time favorite Numberphile video.
eliran zach because you feel the vodka just by listening
I understood that he's Russian just when heard him. Russians know who's Russian and who's not.
It's actually a German accent
no
Me hear russian accent too. It's interesting because the man who named edward frenkel cannot be russian.
His way of explaining things is really amazing. He simplifies the things very nicely.
mathematician's brain at work
"If you can't explain it simply, you don't understand it well enough" - Albert Einstein
Simply explaining the very complicated is the mark of genius
Ok
Quanta Magazine have a wonderful video about Riemann Hypothesis. Frankly, I think it's an uncrackable problem, tbh. Physicists assume it's true and there are dozens of well established theories that are build upon it being true. It's fascinating, nonetheless.
"you can mark your favourite fractions" said like a true mathematician lol
This has been the simplest explanation of complex numbers, ever.
Really? I've been introduced to complex numbers in probably like 10 different classes at this point and it's always in a similar fashion to this. Saying that we simply cannot say sqrt of -1 doesn't exist so we assign it an imaginary value which then creates a complex plane.
@@TheVivi13 however, the main reason it's a cartesian plane (i.e., one with both basis "vectors" being orthogonal) is due to a slightly deeper property about i.
I have heard this explanation of complex numbers many times, but they often fail to explain the benefits of not discarding the i. That keeping the i in there opens up a whole new world of possible transformations and calculations. Continuing math beyond its borders. Like Rieman was extending the zeta function beyond its borders.
@@ypey1 for most stuff, it's just a utility thing. You _could_ try to represent everything as a 2D vector, but complex numbers can be treated exactly like real numbers in most cases, so they're easier to work with, e.g., with exponentiation. For example, you could also represent negative numbers as a subtraction problem (and indeed there's a construction that does this), with a tuple of, e.g., (1, 3), but it's so much easier to just call -2 a number. Edit: The comparison isn't exactly the same, since vectors and complex numbers have different algebraic properties (whereas the tuple construction is a construction of the model of, say, integer arithmetic, so it has the same structure).
Ok
8:54 "да... uh, yes" I love this Russian guy.
Alex Hoffmann no comments? here have a comment
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Thank you, Jaime Lannister.
first thing came to my mind
HAHAHA that's the first thing i think
looooooooll!!!!!!!!!!!!!!
More like Gendry
He has some resemblance, but in any case, Russian Jaime Lannister
8:55 I love how he answered "Da" in response to Brady's question and then corrected it to yes 😆
When Jamie Lannister becomes a mathematician
Peter Griffin and Amy Adams?
I thought the same lols 😂
guy pearce
Bruuhh...
Ok
This should be a series. Like I would love to see a video on all the Millennium Problems. Especially the one that was solved.
Cold Ham on Rye an infinite series
You might’ve already seen it, but in case you haven’t, they’ve made a video about the poincare conjecture, which is the one that was solved. I’d also like to see videos about the other millenium problems.
The one of the solved one (Poincaré Conjecture) has already been uploaded. Check it out :)
Yes dey have made videos about 3 of Dem..p-np problem,reimann hypothesis and poincare conjecture. dey need to need make videos about remaining 4..I find especially hard to understand yang-mills problem
They also made one on Navier-Stokes
This guy is an awesome teacher.
am I the only one who thinks all math teachers should have that accent
Ah if only people like him would become teachers~ (and not just snobs who gain pleasure from making lives of kids around town worse)
for real! never had something so clearly explained
ILykToDoDuhDrifting I swear. If anyone solves this problem, it will be one of his students!
I love how Grady, who obviously really enjoys mathematics, can phrase a question to the guest like he's never seen an integral or a derivative in his life.
Fun fact: quantum computing algorithms have successfully managed to find prime numbers using a method that is only effective if the Riemann Hypothesis is correct. Of course, that's empirical evidence, not a mathematical proof, but maybe that just makes it even more interesting!
Riemann Hipothesis’ could well be one of the unprovable statements foreseen by Gödel’s incompleteness theorem - a true statement which cannot be proved within the given set of axioms!
Is Math becoming empirical?
Man in the world of Quantum Mechanics everything is possible. I wouldn't be surprised that in quantum mechanics may suggested that the universe is both finite and infinite at the same time.
@@rociot4690 even if it was unprovable, you can still prove something is false only if it's false. So you would just have to show that you can't prove the hypothesis as false. As far as I'm aware anyway
A Solution for the RIEMANN ZETA FUNCTION is extremely valuable because It also point to Solutions for enhancing the HAMILTON GEOMETRZATION Poincare conjecture, Hodge Invariance conjecture as it relates to PRIME NUMBERS and Doing Arithmetic past ZERO or Singularity as it is called in Analytic Geometry , and Algebraic Geometry, and it Directly points to the Prime factorization Algorithm , the Division algorithm, and the QUADRIATIC FORMULA This Solves many DIMENSIONS and RANK IN THE COMPLEX FUNCTION PLANE for MANIFOLD like The Kahler MANIFOLD ,CALIBU YAU MANIFOLD simeoustanesly and Points to Soulutions to the entire Millennium Prize Problems proposed by The Early 20th Century Philospher and Mathematician David HILBERT , Including the YANG-MILL Mass GAP , and the NP COMPUTATION time space COMPLEXITY problem also know as the Traveling Salesman problem
I love how passionate the speakers are in Numberphile videos.
Makes sense. Most of these guys will only ever communicate to a maximum of maybe to 500 people in a lecture at one time? They're getting an not so common opportunity interacting with a huge amount of people interested in the subject (numberphile fans subscribers)
Passion is sexy.
I have no idea whats going on, but i feel smart just watching
+CHARrrrrrrrr Welcome to math
+CHARrrrrrrrr what does it mean if I do understand it then??
***** Welcome to math class
+Smitty Werbenjagermanjensen This is much better than math class. Math class teaches the fundamentals whereas KZhead teaches the abstract and complicated topics.
I would give you a like for that comment but I don't want to encourage that way of being cool :)
I studied engineering, but listening to this magician talk about Maths really makes me feel like I should have gone into Maths. It's always such a pleasure to have a teacher or lecturer be patient about the work they're teaching. It inspires students far more than anything else.
"And at 1, that value will be, you guessed it, minus 1/12." The rest of the world:
S. Ramanujan blesses you from heaven
It's -1, not positive 1. Zeta(1) doesn't exist.
@@NateROCKS112 doesn't zeta(1) diverge?
@@skyiloh7460 that's just a specific way to say it doesn't exist. Edit: But to answer your question, yes, because Zeta(1) is just the harmonic series.
@@NateROCKS112 exactly!
my daily job is to sell fruits and vegetables, I was pretty bad at school in mathematics, and i'm here watching hours of mathemematical videos and i enjoy them so such because I can actually follow up. Thank you numberphile, deeply.
Gl my dude
This comment is so wholesome. Keep on learning
Wait, so you know what is an analytic function, the use of complex plane, and de moivre theorem?
@@howardlam6181 lol I'm guessing he knows about logarithmic branch cuts too
Keep on learning!
I watched Professor Frenkel in this video quite a while ago, and now he is my professor. Things work out wonderfully sometimes.
craftysunshine I wish he was my professor to, but I was rejected from Berkeley. Might apply for grad school though, I’d honestly go there just to talk to this guy in Russian, потому что я тоже русский
Damn
I could listen to this man talk about math forever. He makes the incredibly complex easy to understand for the laymen.
Me: I understood what has been said in this video My brain: it is a trap,it is a trap ,it is a trap.
we are no less I swear I'd watch a video and understand it, then read my textbook and I have no idea what is going on
@@workout9594 and in my case I then then read the textbook and eventually feel like I understand it, but repeat this pattern when I first read the exam. The problem is that I can't exactly afford to repeat that until I understand though lol
When you think you understand it, that is evidence that you don't understand it.
I have a truly marvelous proof for the Riemann hypothesis that this comment section is to small to contain.
That's terrible. Get out.
+MrJaco324 I have a marvelous proof for ALL the Millennium problems, which unfortunately my brain is too small to contain.
+MrJaco324 Fermat, is that you? :)
+Daniel Șuteu Didn't Fermat create more problems than he solved? :P
+MrJaco324 Fermat? haha
"There is more to this than meets the i."
This is the best introduction to complex numbers I have seen.
Actually a far better way is to think 'which representation, when squared, leads to -1. let's call it √-1. -1 is, also, a 1 oriented to 180°. if you multiply 1 by -1, it rotates it 180°. if you multiply 1 by √-1, it will rotate 90°. multiply again, it will rotate 180°. ' this has broad use, for instance, in electrical circuits and electrical engineering. moreover, one can easily see the relation with sines and cosines, Euler formula etc.
How wonderfully enjoyable to listen to a master speak about a field he is both brilliant in and passionate about.
"In this care there's more to it than meets the 'i"" Specifically 1/2 more than that part that meets the i.
ghlok
Time for pie, apple pie that is.
New Vsauce video, new Numberphile video... These are glorious days, I tell you.
Waiting for CGPGrey now.
Never learnt anything well from any of my past math teachers, first time I hear about most of the concepts in this video and this guy has made them crystal clear to me.
I love math, and respect to Prof Edward Frenkel for explaining Reimann zeta function, and conveying that mathematicians should be open to unconventionality to seek new answers.
yup. agreed...
The best explanation yet to a very complex problem. This man is an exemplary teacher.
It;s the brown paper isn't it, you need the brown paper
Ynse Schaap and a sharpie
And a dollar 40 cents annoying pen from Tesco
Ynse Schaap never seen ‘it’s’ spelled with a semicolon
i love the videos but the marker on the brown paper is so cringy.
@@peterparker-or2os wat?
I am gonna prove it. Believe me I am just 15 now, by the age of 30, I would prove it. It’s my contribution to the world’s best subject.
All the best for that big guy
@@jellyj1696 thank you sir. All the best for your future ventures too
@@athuldevraj3948 thankyou. Well how's your progress
@@athuldevraj3948 Perhaps look at what Terrance Tao said about becoming obsessed with a big problem first. You must have a solid understanding of everything else and a varied toolkit. These haven't been solved for a reason. They require entirely new math which needs to be made from scratch. All the best luck.
@@willywonka1962 sure sir! Thank you for the support and advice
8:24 Nice
Nice
"We can ban root of minus 1" "This is a bad point" I laughed too hard 😂
Me too
"Then you can mark your favorite fractions" on the line. After all, who doesn't have a favorite fraction or two? :-)
I have one half favorite fraction
There's nothing more satisfying than watching a mathematician enjoy his craft.
When Edward used analytical continuation and out popped -1/12 where infinity was supposed to be, it felt like magic. I remember watching Numberphile’s -1/12 video and thinking that Ramanujan’s proof was not meaningful. This was super beautiful and Edward made the explanation entertaining!
I didnt' get how zeta(-1)=infinity at the start of the video, and became zeta(-1)=-1/12 at the end.
@@davip116 There are two ways to right the riemann formula. Either by saying (1/n) + (1/n^2) + ... OR by plugging it into a sigma sum. The sigma sum is what gives -1/12, while just writing the infinite sequence does not.
This guy is a great teacher. I wish he had have been my maths teacher, he distills the basics down so a maths dope like me can understand it perfectly :-)
This is my favorite Numberphile video. And it does NOT back up the false assertions made in the "-1/12" videos. (Which are my least favourite of all Numberphile videos.)
richo61 have you ranked them all?
Im an engineer so I am no expert on theoretical mathematic. I understand it blows up but why does the process they used to end up with -1/12 incorrect. substitution is a valid procedure in math
Numberphile "have you ranked them all?" Not yet! Of the ones I have so far viewed, this is my favorite. 8-)
Goyathlay Amedeo thank you makes sense
Yes but that is a direct contradiction. This video is based on the riemann zeta function which says that zeta(-1)=-1/12. They showed it to you via "floozy" math but it's a serious result in math. I don't claim to understand what it means, but it is what it is.
This is definitely the best Numberphile video. Mathematics is beautiful but the way in which maths is taught in classrooms around the world makes it boring and disinteresting. Thanks to videos like these , channels like Numberphile and applications like Mathematicia, Wolfram Alpha and Matlab, learning maths becomes exciting.
I will solve the Riemann Hypothesis
Yo bro I want $1 from the million dollars
Belive in u
In dreams
this is my professor at berkeley next semester. Im am so friking ecstatic
ssimarsawhney have you finished your education?)
@@user-go7sr1zf6dAll the math broke his brain, he's long gone lol
This is the stuff I want to do for a living...I love wrapping my head around things like this, even if I make no progress on them. I've loved numbers for as long as I can remember. The way everything in math connects and intersects is beautiful to me. It's mind blowing to think that we, humans, some random species on some random hunk of rock in this absolutely massive universe, have developed a universal language to define everything we observe, everything we can't observe, and everything in between. I really hope I'm still around when some of these brain stumping math problems and equations are finally figured out. To see what advances could be made once we have some of the answers. It'd be even more interesting to know what the people that originally thought them up would have done with them if they had figured them out.
+Justin Siehl Well for now you have to deal with whips and nae nae's. Yes I do realise im 2 years to late.
Justin Siehl we have developed a universal language or we discovered a universal language? Math isnt a human creation, according to some people. Its much more than that
This is the best guy on Numberphile. When others explain the RZ function, it seems to go over my head. When he explains it, it seems so simple that elementary school me could have grasped it.
I'm not a math whiz, but I find the explanations of Prof. Frenkel to be clear and easy to follow. I imagine he is a rather popular teacher?
That was the best explanation of imaginary numbers I ever heard.
I've come to learn that everything with Riemann's name on it is a massive headache inducer
Not quite everything, Riemann Integral is pretty simple and straightforward, You cut an area into many rectangles and sum up their respective size. Everyone knows what rectangles are and how you can calculate their area, so it's really easy to visualise.
I love Riemann. All the cool stuff in maths is named after him! :D
1 Million Riemann Dollar !
How about a "Riemann" paracetamol pills? Will they also give you a headache?
This bloke exudes intellect and charm. I can watch this clip repeatedly as I can the Graham's number clip and the Collatz conjecture one. These narrators of themes of such complexity are both humble and like flashlights illustrating a window into darkness for those of us grasping at these fascinating concepts. Special mention to Holly Krieger for being a fractal femme extraordinaire.
Ten damn years later and this is still one of the best explanations I've ever seen of the Riemann zeta function and hypothesis.
I love it the video says "keep watching" when our old friend from -1/12 videos appears
This is probably the most coherent and enthusiastic explanation of a math mind-bender that I have ever seen. Talk about breathing life and importance into an otherwise dull concept! Well done sirs.
the Riemann haircut looks like the integral symbol
hahahahahahhahahahaha.....
He walked the walk.
😂😂😂😂😂
7:19 that calculator of yours is faulty
yep; there was a typo; should have said pi^2/6 but instead said pi/6
Him: "It's an answer you can find online." Me: "I am online man."
I want to really thank Numberphile for teaching me about Riemann Hypothesis clearly because I had struggled very much to understand this problem since when i learnt about the Milllennium problems. Thank you so much for describing briefly about Riemann Hypothesis
Incredible explanation. Pure gold. Videos like this keep me from uninstalling KZhead.
This was so well explained. Very well done. Great video! So insightful.
Extremely interesting. I've heard of the Riemann Hypothesis but never knew what it was until now.
What an easy explanation! I love his Russian accent.
Я тоже сразу заметил: русский человек.
+či šo suka či šo Он даже один раз где-то "да" сказал, оговорился )
да да, вместо three три говорит :)
Rare seeing another korean around on an english video!
님 한국인임? 근데 이름이 왜 이렇게 독일스러움?
Love Edward Frenkel's accent. And I respect him even more than before, after listening to his episode on The Numberphile Podcast.
Thanks sir, for explaining so beautifully about zeta function. Simple and eloquent.
At 7:20 the video shows the calculator returning a value of pi/6 for when 2 is the input of the function, but it says earlier in the video that the value is pi squared over 6
sorry
pi^2 / 6 is correct. The special effects are cool, but take them with a grain of salt!
Numberphile it's ok
Description dude
He wrote that 2 years ago, the description was updated after numberphile read the comment
The answer is 42. Thank you, I'll take my million dollars now.
lol
That's not between 0 and 1 ;)
Eddy Proca what about .42 then? :D
after 1+2+3+4... being -1/12 I can belive 42 is between 0 and 1
Error: Implicit convertion from integer to boolean failed!
Dr Eswaran from India has proved it!
No
I only just came across this video by recommendation thinking Im only gonna watch a few min to get the idea and move on. But I ended up watching the full video because the Theorem and the way professor explains it are so fascinating!
The real unsolved problem is if this guy will ever blink
4:17
Not a blink actually, he simply roll his eyes downside creating the illusion of blinking. He never blinks until disproven.
15:17
Zolth fake news
We don't blink in Russia. No blink, no smile. Only while testing nuclear weapons.
Could we possibly get a video explaining how the non-trivial zeros relate to prime number distribution?
Get a master's degree in number theory
Andrew Christensen Too busy doing PhD in telecom
Yeah, this is kind of the elephant in the room after this video. I have no idea how the two are related and I´d really like to know. Maybe we´ll get an "Extra Stuff" of this video.
Jeremy J. I am aware of how the behaviour of the Riemann Zeta Function relates to Prime Numbers, because it is equivalent to an infinite product function of all Prime Numbers. Also, the Riemann Hypothesis is equivalent to another conjecture that states the error of the Prime Counting Function has a definite limit. However, I'm not sure how the non-trivial zeros are related to it.
love how tidy and clear his annotations on the paper are. I can't understand my own writing after i write more than 3 letters.
I wish I was smart enough to even attempt to solve something like this.
Comments like these assure me that I'm not alone :P
If you were that smart, you wouldn't care about money, so you wouldn't attempt it, or just for fun, just like this russian guy who refused the 1M $ prize on one of this problem . ;) no hate.
***** i never saw that, but come on ... that is too obvious. Even if your comment is pretty well placed.
Oh Yeahh Really i domt think u can call "too obvious" he didnt mention anything about that, i mean could be but i dont know where did you get it from his comment
sufficientlyoldskool you are smart enough, it doesn't hurt to try.
I loved the explanation of real, imaginary, and complex numbers in this video (~ 4:40-7:10). If it was taught to me this way in school I would have actually understood it!
This guy is great, his presentation is amazingly easy to follow.
This video is such a treat to watch. I see it time and again.
Very interesting. I'm currently studying Complex Analysis right now. Since I found it so similar to Vector Calculus, I'm constantly going back to it to find the corresponding arithmetic operations between the two. I'm excited to find out that my current studies are approaching the Riemann Zeta function, and that it plays an important role in the distribution of prime numbers. Thank you for your video!
Fantastic accent and delivery. Bravo!!
His enthusiasm is contagious. A great teacher and a great video! As a side note, the -1/12 result for s=-1 (it's also one the Ramanujan equations) still baffles me although I've watched excellent videos about it. I get it that we should say it's a super-summation and not a regular sum (the series is still divergent with a regular summation). But the fact that that very result explains the Casimir effect in real world physics is akin to magic.
I like that he explains sqrt(-1) is called "i" because "we imagined it." There's still plenty of debate about whether "real" numbers are any less just a product of our imaginations!
Not among smart people :)
They are
He has beautiful writing.
I opt for Walter Lewin in that matter. I've developed my 'mathematical' writing style by mimicking what i saw at his famous physics course.
love the passion Prof Ed Frenkel shows for his math :D
Wow, you can feel this guy's passion for math
It all sounds esoteric. A bit later: So we connect it to distribution of primes... I know he wanted to point out the significance, because we all somehow care about the primes (computer security...). But it made me smile :)
Million Dollar Math Problem - Numberphile
Numberphile The roots are S=0+(pi +,-2pik)i/lnp^n , n=1,2,4,16,...
Numberphile Well my brain hurts ill come back after college and try
Numberphile Did you not say that zeta function is valid for values more than 1, so why do you include negative integer line in your video?
Sid Sharma The series representation for the zeta function is indeed valid only for those values of s whose real part is greater than 1, but there is a fancy technique called analytic continuation that allows us to define the values at, say, negative integers. This analytic continuation is perfectly well defined at the negative integers, but more importantly is equal to the summation for values bigger than 1, so we sort of abuse the equals sign and just say that the zeta is in fact the series.
RandomEnsign but i only see that with negative zeta function, the series will be divergent. how can e.g - zeta(-4) which is equal to 1^4 +2^4 + 3^4 ........... be convergent?
IF i have had seen this video 12 years ago I would probably fall in love with math. Great stuff
I came from Veritasium's video about his deeper and richer love for turbulent flow and bias towards laminar flow. It was a nice video.
Magnificent explanation, it is the first time in my short life that I understand something clearly
I love the random "keep watching!" message. Do they think we are going to say something like: "nope, this video is longer than 4 minutes... that is too much interesting information for me today!! I have to stop watching RIGHT NOW!!" xD
I think it was to quell all of the youtube math experts starting a shitshow about how that particular sum is -1/12 because they watched Numberphiles other video
Did you notice what was being discussed right when the annotation appeared?
It's because he says 1+2+3+... doesn't equal any number and they have a video about it equaling -1/12.
I think it is more to prevent pointless questions/rants in the comments that could be avoided if they just watch the next few seconds.
It's because otherwise people would all immediately pause the video in utter outrage because they KNOW 1+2+3+4... = -1/12
This guy has explained it so well. Bravo and thank you sir!
Here after the Indian Mathematician proved the hypothesis. Absolutely mind blowing.
What a lovely explanation! Thank you!
I'm only seven minutes in and this guy just explained imaginary numbers in such a comprehensive way that... I think I finally get it It's beautiful I think I might cry
When I saw 3:30 I started to scream. That -1/12 videos still haunts me.
Great video, excellent "teacher", clear and clean explanation. 👍❤️
Came here to see this great video after watching the recent podcast with Lex Fridman. So much passion in his eyes!
You can feel the passion for math when this professor speaks. Makes me wish I had time to learn complex math.
A beautiful lesson. The better explanation of riemann zeta function that expose perfectly and clearly how simply and beautiful is to arrive on the wall of the 1 million dollar question. I am beginner in math, but this take me exactly at the base of the wall. Excellent.
I love it when a Non Native English Speaker explains Math, it's direct to the point and concise
I'm in love with his accent!
Russian, pal.
Thank you Brady for doing a piece on Riemann hypothesis. I have been waiting for this for a while.