Mathematicians: can't solve Riemann hypothesis Also mathematicians: *best we can do is to come up with infinitely many more unsolved Riemann hypotheses*
To explain why mathematicians do this: If you can engineer new Riemann hypotheses, you can study them as a whole. It's sort of like if we found life from beyond Earth, we would be able to study what "life" even is and how it can be. Now, if we can somehow solve one of these engineered ones, maybe we can use that solution to somehow solve the original one. At least we would have a framework for how it could be done. I do appreciate the joke though! I just thought it's valuable to understand exactly why this stuff is important. Mathematicians don't like to assume something is special, that too has to be proven :)
+David de Kloet Brady acts as the audience surrogate, probably very deliberately. I'm sure many of the questions he asks are things he himself is wondering, but I'm sure he also asks questions he already knows the answer to, because he knows the viewers will have the same question. He's very good at this role. :)
+boenrobot It helps us come a little closer to appreciating the vastness of infinity. You can have numbers spread so far apart and yet still have an infinite number of them. Example: Set each number to be the size of a power tower. So n1 = 10 n2 = 10^10 = 10 billion n3 = 10^10^10 = a number with 10 billion digits ... and we can fit in an infinite number of these n values...
+boenrobot Not really, if our universe is infinite, then life would still be rare and could aswell, be present on infinitly many planets. If throw a coin infinitly many times, I have infinitly many occasions of 1000 heads in a row, still they are rare.
+Baron ultra paw Observable universe is finite and contains a finite number of particles (somewhere on the order of 10^80 particles and 9 photons per particle). About 10 billion galaxies with 100 billion stars per galaxy. Infinity is really only something that exists in mathematics.
Brady - when I subscribed to Numberphile 4 years ago, I wished to learn more about concepts exactly such as this. And for 4 years I've been blown away. The service that you provide; your great contribution to spreading knowledge... it's absolutely awe-inspiring. Thank you SO MUCH for making these (seemingly) obscure and complicated topics accessible to such a wide audience. I've commented this before, but I'll say it again: you are a great asset to this world. Thank you, and please never stop!
This is probably the clearest video I’ve seen about the Riemann hypothesis. Most seem to focus on the setup and are kind of murky around the applications or the actual problem, but this one tackled the zeros very well.
+Seth M-T I have seen entire chapters of the lord of the rings posted in a single comment, though. :p So... maybe in 2 or 3 you would have enough space?
I mean, throw a dart on a dartboard. The probability that the dart lands at exactly 0.00000...... cm from the center (aka exactly the center) is zero. Kind of wacky, but makes sense. Discrete numbers are an infinitesimally small infinite subset of the continuous spectrum of real/complex numbers.
kinda like saying: there are infinitely many integers that are evenly divisible by the first 80 billion prime numbers. there's infinitely many because the integers never end, but they're rare because there are massive gaps of integers that don't satisfy this.
Yes! I'm always happy for more Riemann! I'm also very glad you're expanding to L-Functions. The thought of something that ties the Riemann Hypothesis to Fermat's Last Theorem is pretty crazy...
Awesome video! Numberphile has really come a long way! Just 4 years ago I wouldn't have even dreamed of anyone daring to bring an advanced graduate-level math topic such as this one to a broad audience while keeping the mathematics honest.
Thank you! A distinction mathematicians might, by the nature of their craft, be prone to miss. Darwin found a puzzle, sought a theorem, presented evidence, and stood prepared to be shown misguided. Maths developes by challenge-my-proof, and physical sciences develop by challenge-my-evidential-interpretation.
I believe all those connections between the Riemann-Zeta-Function, Ramanujan and Fermats last theorem are the main reason I love mathematics...however, amazing video as always.
one way to figure it out: make them puzzles in a game and put it on steam. players will definitely figure it out to the point where they take complete advantage of it
@@royhe3154 That seems abstract for some reason. Now put it on steam and offer LIFETIME FREE GAMES AND DOWNLOADS?!?!?! Trust me, the hypothesis would be solved in less than a month lol
"rare" has to do with their distribution. "infinite" means there is another of after each one you'd pick. the two are not mathematically, speaking, mutually exclusive.
If it was possible, I'll happily give my remaining life to resurrect Ramanujan. I'm almost 19 btw. He and many more Mathematicians and Scientists who died young deserve more lifespan(atleast the average lifespan) than a normal person like me :)
Don't forget Niels Abel. Only living to 26 because of tuberculosis, the mathematician Hermite said, " He's left us with more than 500 years worth of math to figure out."
Does anyone think there are 3D functions like this, with symmetric fields and planar zeros? Maybe finding these could help understand the 2D functions.
Fun fact: Darwin didn't go to the Galapagos Islands to find evidence for evolution. He was a geologist as well and wanted to study the unique geology. He noticed that there were very similar finches etc... he came back with a theory, which he then started to study. (This may not be entirely correct, I seem to have forgotten some details. e.g. he may not have been a geologist, I just remember that it had something to do with the soil or lava or something like that)
I see Wiles quietly and secretly working on the Riemann Hypothesis in his study ever since he finally fixed his FLT proof. Twenty years and counting. Wake up. sit at desk. Go for walks. Talk to the wife/kids. Go to bed and dream about it. Wake up and do the same FOREVER! I'd like to think the average joe with a bit of math expertise might be able to crack it...but I don't think so. This is going to take a TRUE Mathematician with world-class skill.
I've been toying with it for about 5 years now, I got hooked on it after I bumped into the viral 1+2+3+4+... = -1/12 video. I'm a professional software engineer and a recreational mathematician. It's been a fun ride, mostly my "blow off" problem when I'm not dreaming up new ways to reinvent all of computer science with Homotopy Type Theory, Quantitative Type Theory, and a little something special I call Full Duality. I've tricked myself into thinking I've proved it about once a year. Usually a bit of exploration or redoing the algebra demonstrates my error. I've been stuck on a few lemmas this year, some nasty limits that really look like they should work but just refuse to behave when actually doing the algebra. Maybe I'll nail it down one of these days. Don't count us amateur mathematicians out, the crucial insight might come from not being exposed to the current methodologies.
+Shiny Rayquazza Its a world away from school. I wish I had the capacity to understand more. I don't know what schools are like these days but if I were a teacher I would incorporate these YT videos into my class.
+Riotlight EZ use a computer to do it for you x - 24 x^2 + 252 x^3 - 1472 x^4 + 4830 x^5 - 6048 x^6 - 16744 x^7 + 84480 x^8 - 113643 x^9 - 115920 x^10 + 534612 x^11 - 370944 x^12 - 577738 x^13 + 401856 x^14 + 1217160 x^15 + 987136 x^16 - 6905934 x^17 + 2727432 x^18 + 10661420 x^19 - 7109760 x^20 etc (You need a lot of terms to get it to work though)
Em how are you going to expand that stuff to the 24th power? Especially when its infinite... that'll take a while lol unless theres something im not aware of
If you take enough factors after some amount the coefficcients you get after expanding don't change anymore. For example, let's look at the product: x(1-x)(1-x^2)(1-x^3)... In every (1-x^n) the 1 basically states "Copy everything", and the x^n produces terms between x^(n+1) and x^(n+n-1), therefore if I would cut off the product at (1-x^3), I can be certain that all coefficients from terms upto x^3 in the final expansion are correct. The same goes for (1-x^n)^24, except that (1-x^n)^24 would produce terms between x^(n+1) and x^(24n+n-1). It takes like 10s to expand the first 200 factors, guaranteeing everything up to x^200 to be correct. (It yields a polynomial of 482 401 terms of which only 200 have the correct coefficients though Lol)
Could you please do videos about all the Millennium problems? You have videos about Poincare and Riemann, and there's a video on Computerphile that talks a bit about P vs. NP, but I think that's all you have.
Like most "popular" expositions about the Riemann zeta function, this one has a HUGE gap almost from the very start: He begins with the definition of zeta(s) as the sum of a series, which converges only when the real part x of s = x + i y is greater than 1. Next, he states the property of symmetry across the line Real(s) = 1/2; but that makes utterly no sense unless and until one has defined what zeta(s) means when x < 0, and he has not done that.
I guess you just were not telling the truth. That's pretty sad just because you don't like me and you don't even know me I am not worthy of credit or the prize how does that work? You should of said that before but I still would of solved it. I just wouldn't be bitter about it. But honestly I expect nothing less.
What I will do is try and solve them all. Then try and strip or deny me of that you think you Feel awkward now just wait until I solve another. Lol I bet I can do it. It won't take years either I am sure. The last one took a couple hours lol
Dipshit, this channel has no power to give you an award. You also definitely didn’t solve it but if you feel so confident post your “proof” here or on stackexchange. Ranting isn’t going to change anything.
OMFG!!!! Why do I insist upon watching these videos when I HATE math...and I have absolutely NO idea about which they are speaking. Not even close!!!! Yet, I can't stay away..
I love mathematics, every day i could time for it. i and i was economist. but i have been training with this subject since 2017. i have bachalor and masters degrre at the moment. i have 50 research works, two paper has been published in math journal. it is belong to probablity theory and number theory. i proofed Ferma`s theorem. it is very simple. half page is enough for it. I have a completely different conclusion about the Riemann Hypothesis. I will announce in the coming months. however, in s> 1 natural numbers, I collected the sums of the zeta functions. my name is Khodjaev Yorqin, this accaunt is belong to my friend. I can say for sure that only when the essence of all the theorems is studied, it is possible to feel their simplicity. in the future all sciences will unite again
That just sounds a bit too communist. But there is an i in community. Also in society. Also in sociology. Hmm. And according to my TI89 graphing calculator √-1 ≠ i. (Well unless you first do the variable assignment of *_i_* --> i.) Actually, it is a funny italics looking version of *_i_* but it is actually a different character than i. So it would be √-1 = *_i_* .
At the mark 8:39, Ramanujan's sum of powers of x, is there a formula for this summation series? The bloke say's just multiply this thing out, but I am not a gifted by aliens dude like Ramanujan lol
I've spent years trying to wrap my head around what a proof of the Riemann Hypothesis would even look like, or how long it would have to be. One day...
I feel that this video is either going to be something already understood or beyond the current understanding of the viewers. I'd appreciate the host stepping in and explaining a little more.
I solved Riemann's hypothesis that every zero does end up on the line and I have proof to show you in a way for you to check and see if every zero ends up on a critical line
A proof by Andreas Speiser states that the Riemann Hypothesis is equivalent to the absence of non-trivial zeros of the derivative of the ζ(s) function in the strip 0 < Re(s) < ½ That reduces the RH to half the critical strip. It means if one can find only one zero of the derivative of ζ(s) in the strip 0 < Re(s) < ½ , then this will be a contradiction if assuming the RH is true.
3:28 - It's interesting that it's known "at least 40%" of the zeros are on the symmetry line. How can we be so sure at least close to half of them are on the symmetry line? Is it because, though 10^36 is still well short of infinity, there is far less frequency of prime numbers at such large magnitudes?
+DAK4Blizzard Yes, I did not understand this part. Did he misspeak? Or is the emphasis in the wrong place? The animation does not clear up this mystery either.
+DAK4Blizzard It's possible that there has been a proof that at least 40% of them lie on the line - proving the Riemann hypothesis would be showing that 100% of them lie on the line, I guess.
+DAK4Blizzard I don't think that this has anything to do with the numbers already checked. What I guess is that you can estimate an integral which gives the ratio of numbers on the line to be at least 0.4. But I don't know.
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
This is a pleasure to watch. Professor Keating's introduction is clear and informal. The graphics are also helpful, as are the series of questions and historical background.
"There are infinetly many?! I thought you said they were rare?!"You just want to reach out and say "What's 1/4 of infinity? What's 1/10000 of infinity? Still infinity Brady, you silly bugger."
"...that a non-mathematician could find this pattern..." ...I kinda feel like once you prove the Riemann hypothesis, you lose the right to call yourself a "non-mathematician."
I think the meaning there is "someone that isn't paid to do math and think about these things all the time." 150 years should have been plenty of time to find the answer if it was going to come from the standard process of iterating combinations of older theorems. As it has not produced an answer, I suspect we need some fresh insight, untainted by the standard mathematical mindset/worldview. That's what he was getting at, I think.
Hello I'm from Brazil the formula for non-primes automatically you discover the primes add 3+3+3... to infinity and the 7+7+7+7 to infinity and the perfect squares odd minus with final 5 .
At 4:08 I think he means von Neumann and not allen turing. The turing machine was an abstraction, while the von Neumann machine was the actual implementation of it. As a computer guy, I had to correct this
Turing helped build some of the first general purpose computers after using machines to help break the Engima encryption, as well as coming up with the hypothetical machine used in proofs. Von Neumann designed the basic components of the modern CPU architecture, yes, but Turing was also building real computers around the same time.
Numberphile evolves in the way it has to, I'm glad of this. Nice seeing some math being done and not only explanations, and nice seeing modern math (not only Fibonacci or stupid debates about pi vs tau)
Randomness chaos and predictably exist in all systems. It is the level of understanding of the system and in turn available information that determines how the system is perceived.
I have developed a new theory, I have called Partitions Trigonometric and I have discovered something amazing. I can do X Rays with these equations applied to Z Riemann.
For me, the z function looks a lot like an sphere surface projected to a plane. What if we put a second imaginary axis there and see what comes out of it?
