The Riemann Hypothesis, Explained
5,060,613
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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Proving the Riemann Hypothesis is probably one of the hardest ways to make a million dollars.
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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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Thank you, Quanta Magazine. My understanding of the Riemann Hypothesis went from 0% to 15%. Great job (I mean it).
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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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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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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
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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 -
hold my beer, I got one A in math in high school, I got this
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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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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. -
Can I just appreciate how well the animation is? Literally, WOW.
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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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This is a truly fantastic video. The gradual exposition to the very casual person interested in maths is top notch
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I love this video! The explanation of the hypothesis itself is great, with all the right context and friendly explanations, but more importantly I've never seen such a concise yet captivating description of why the hypothesis matters