In this video, we will understand what the Riemann Hypothesis is - one of the seven mathematical problems of the millennium!
Someone was waiting for a new video with higher mathematics, someone with an entertaining one, someone craving for a more complicated material, someone more easily. I am sure that this video will be useful and interesting to everyone: from elementary mathematics we will reach the open problem of the millennium - Riemann's hypotheses!
Level 1. Prime numbers - 0:05
Level 2. PNT - 1:30
Level 3. 1859 - 3:09
Level 4. Riemann's hypothesis - 4:32
Level 5. Riemann Zeta Function - 5:17
Level 6. Thoughtful friend -6: 51
Level 7. Analytical continuation - 7:39
UPD. At 2:23 the hypothesis of Gauss and Legendre, of course, immediately consisted in the asymptotic behavior of the function π (x) ~ x / lnx (x → oo). The fact that the equality is not fulfilled is obvious for the same example from the video for x = 100.
The phrase at 3:37 should also be corrected. Of course, we are talking about the fact that n runs through natural numbers, and sigma sums all the inverse numbers to n ^ s.