Riemann Hypothesis - Numberphile



Here is the biggest (?) unsolved problem in maths... The Riemann Hypothesis. Prime Number Theorem: http://youtu.be/l8ezziaEeNE Fermat's Last Theorem: http://youtu.be/qiNcEguuFSA Prof Edward Frenkel's book Love and Math: http://amzn.to/1g6XP6j Professor Frenkel is a mathematics professor at the University of California, Berkeley - http://edwardfrenkel.com The Millennium Prize at the Clay Mathematics Institute: http://www.claymath.org Number Line: http://youtu.be/JmyLeESQWGw Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Google Plus: http://bit.ly/numberGplus Tumblr: http://numberphile.tumblr.com Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran A run-down of Brady's channels: http://bit.ly/bradychannels CORRECTION: At 7:20 the zeta function of 2 should be (Pi^2)/6 as correctly stated earlier in the video (Basel Problem)

Comments

  1. But why the function is undefined with 1? Why it is a divergent series?
  2. 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!
  3. i hate my schooling system -for not telling me these stuffs, like this ...
  4. "There is more to this than meets the i."
  5. 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
  6. lol.. the mad hatter, this is how i see it, the inverse or divergent as he puts it, is the lames term that, if a whole series of itself is infinite, and the mind views it as a size of large, which numbers them self actually hold no size, and no distance... so.. the decimal itself, is infinite... and could come into a pattern but its infinite to a point that doesn't exist. Such as, just invert the equation and it tells a story... which is the same as the divergent.. Seems like calculating infinite or putting al limit to system in which has is al language based on without limit then it doesn't make a lot of sense. It would be like in Grammar to make a rule in which endless loops a person to adding and removing the same letters to a word based on so form of rules. Funny though, but meh.

    Imaginary number isa way of doing negative roots... but what is the signs of the number origin is adding and subtracting. So all rules apply. The math of language goes into madness when the rules of symbols used to represent an a argument of adding or subtraction that contradicts itself. 2/1 is itself, but zero itself is infinity. 2/0. where as 0/2 is nothing. meh.
  7. The most fascinating hypothesis is summation from n=1 to infinity of n = -1/12 which makes no sense to me even if i am taking multi variable calculus.
  8. The Humans brought me here.
  9. Others said a counterexample does not worth 1mil.
  10. Thank you very much sir
  11. Fermats last theorem "It was solved In the miss 90's"
    Brady: "But it wasn't a millennium problem?"
  12. how about 1/2 + pi * i
  13. s = 1.83364 (I guess)
  14. and you can not derivate the zeta function?
  15. So he's brilliant at maths, in his second language.
    And I'm brilliant at....................... nothing
  16. I wish I was intellectually gifted ☹️☹️
  17. If we plot a 4d graph of real numbers, imaginary numbers, and the zeta function, wouldn't we be able to find patterns in the graph to show us if there are nontrivial zeroes in the critical strip?
  18. t 4:30, he says the series is divergent to infinity. That one is actually equal to negative 1/12. See other video.
  19. very clear and nice explanation..thanks


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Visibility: 1562540

Duration: 17m 4s

Rating: 21742