The Riemann Hypothesis, Explained
5,126,451
Published 2021-01-04
00:00 A glimpse into the mystery of the Riemann Hypothesis
01:42 The world of prime numbers
02:30 Carl Friedrich Gauss looks for primes, Prime Counting Function
03:30 Logarithm Function and Gauss's Conjecture
04:39 Leonard Euler and infinite series
06:30 Euler and the Zeta Function
07:30 Bernhard Riemann enters the prime number picture
08:18 Imaginary and complex numbers
09:40 Complex Analysis and the Zeta Function
10:25 Analytic Continuation: two functions at work at once
11:14 Zeta Zeros and the critical strip
12:20 The critical line
12:51 Why the Riemann's Hypothesis has a profound consequence to number theory
13:04 Riemann's Hypothesis shows the distribution of prime numbers can be predicted
14:59 The search for a proof of the Riemann Hypothesis
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All Comments (21)
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My math professor once said, “I’ve know the existence of these math problems for many years. And I assure you, there are a lot easier ways to make a million dollars”
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I have discovered a truly marvellous proof of this, but it's much too large for this youtube comment to contain. Therefore it is left as an exercise to the reader.
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I really appreciate that you explain the more “basic” things (e.g. what a log function is). It makes the video feel welcoming to people who aren’t necessary very good at math (like me, lol)
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This is like becoming an astronaut, discovering a previously unknown planet, finding a river on that planet, and at the bottom of the river is the perfectly fitting other half to a broken rock you found in a river on Earth as a kid. The Universe sees the look on your face and laughs silently.
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Thank you, Quanta Magazine. My understanding of the Riemann Hypothesis went from 0% to 15%. Great job (I mean it).
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Whoever does these animations, massive props to you. These are literally the best math illustrations I've ever seen.
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For the first time in my 46 years, I have truly understood what the Riemann Hypothesis actually is. Thank you!
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I'm amazed by Riemann, Euler, Gauss and other mathematicians/physicists how their brain and curiousity for math and science managed to find these sort of algorithm and new fundamentals that we even use today. Amazing vid, love your animations!
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Literally if my math teacher had just said “logarithms are to exponents what division is to multiplication,” I would have had much less trouble with them. Thanks dude
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Reimann, gauss, euler and all other guys did all this stuff without matplotlib😳 I can't even imagine the extent of their hardwork and dedication
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When pure mathematics comes with lucid explanations, and the two are complemented by a perfect vanilla icing of aesthetic graphics. A million thanks for this amazing presentation.
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Hats off to Kontorovich sir. He explained such a complicated topic in a very simple manner. I just want to develop this skill.
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Proving the Riemann Hypothesis is probably one of the hardest ways to make a million dollars.
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hold my beer, I got one A in math in high school, I got this
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I can't believe I understood this. I've heard about this for years, but this is the first explanation I've seen that makes sense. Great video.
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Just discovering the Quanta math videos. These are my new favorite math explainer videos because — they take on difficult mathematics that I actually want to know about, explain it thoroughly and artfully, with stunning animation that is both entertaining and very well thought out, and makes it all seem easy and inevitable. And having a narrator who has a great voice AND is a personable mathematician seals the deal.
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If there was a video like this for every math concept, I would never take my eyes off the computer screen.
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There's a janitor in Boston who I think could take a crack at it.
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This video goes so well with the 3blue1brown one. It explains the Riemann zeta function in more detail and helps you get an actual feel of the 0's, especially the trivial ones. But like all other Riemann zeta function videos I've seen before, they say 'it's important for primes' and refuse to elaborate. NOW I understand, thank you! At least, I understand enough to appreciate it. I've wanted this for so long. Thanks, once again! Also I never appreciated how much of the Riemann hypothesis was actually done by Riemann himself. What a juggernaut! I thought he laid the foundation and it stopped with 'I think the zeroes are on 0.5' and that someone later realised the connection with primes.
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Watched this a few months back. A few months of studying maths rigorously later, and I can finally start to appreciate how magnificent this is