#### Опубликовано: 3 месяца назад

Длительность: 16:23

The Riemann hypothesis is the most notorious unsolved problem in all of mathematics. Ever since it was first proposed by Bernhard Riemann in 1859, the conjecture has maintained the status of the "Holy Grail" of mathematics. In fact, the person who solves it will win a $1 million prize from the Clay Institute of Mathematics. So, what is the Riemann hypothesis? Why is it so important? What can it tell us about the chaotic universe of prime numbers? And why is its proof so elusive? Alex Kontorovich, professor of mathematics at Rutgers University, breaks it all down in this comprehensive explainer.

Read more at Quanta Magazine: www.quantamagazine.org/how-i-learned-to-love-and-fear-the-riemann-hypothesis-20201214/

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## Комментарии

## Robert Schlesinger

Excellent video. Very interesting, informative and worthwhile video. A must see for every mathematics and science student.

4 часа назад## Galaxy

My great great great great lots of great grandpa made this hypopithis

8 часов назад## 1462-ADITYA KARODIWAL

If I solve this problem then can I get 1 million dollar?

10 часов назад## Sunil Gupta

this problem is only solve by person like Isaac Newton

День назад## Artificial Intelligence

Lie, truth, lie 010 010010 010 010 I AMA I BAPHOMETEMOHPAB

2 дня назад## Valentin Mihai

Explaining logarithms, at 3:32 you explain log[base2](8)=3. At 4:22 you explain '1/log(150)=1.995..' where correct would be log[base e](150), or ln(150), which gives 5.0106... Convention that I know is "lg" means 'logarithm in base 10', "ln" refers to 'logarithm in base e = Euler's constant' and for 'log' you should always indicate the base (2, or 3, whatever). That "e" (Euler's constant, 2.71828....) used in your demonstration is not explained, and it's a key factor.

2 дня назад## Jigsaw

Can someone link to a place where they show excactly how one of these non-trivial zeroes are calculated step for step because I don´t get how the outcome can be 0?????

2 дня назад## Sakura ShinRa

Wait a minute, let me see if I have this straight. Not only is the entirety of mathematics based on an unsolved equation that everyone assumes is correct, there's also imaginary numbers that, and I quote, "we just made them up." And people say artists are crazy... full disclosure, I am an artist and I am most definitely crazy but that's not the point because I don't make up imaginary numbers for lulz.

2 дня назад## sean arnone

Is running the hypothesis a trillion times not evidence enough that it's true??? I don't see how it is "unsolved" if it's proven true a trillion times

2 дня назад## sanket jaiswal

I don't have words to say, how beautifully explained. From 15:47 to some seconds after it, shows the power of mathematics...

2 дня назад## Devin Nall

Honestly I'm only here because I've been reading Scholar’s Advanced Technological System

2 дня назад## Millennial Sapiens

Pure Elegance !

3 дня назад## Varun Varin

Just hang in there,the updated version of the asians are soon coming to the market to proove it.

3 дня назад## Mohammad M

So we're 99% sure it's true, but the last 1% needs to be proven true to infinity...

4 дня назад## gate 13

Kudos

4 дня назад## PRO FF

Wut??

5 дней назад## Rocky Star

This could be solved if added to Jee mains in 🇮🇳INDIA

6 дней назад## vaibhavraj paneru

Thank you for making this video. My humble request to quanta magazine is can you tell what type of software is used for animation and how did you made this video.

6 дней назад## Jeet Singh

I am too stupid for this

7 дней назад## Ryan Ramnarain

8:20: It is wrong to say that the square of any real number is positive, because the square of zero which is a real number is zero which is not a positive number. It would be correct however to say that the square of any real number is non-negative. Great content btw!

8 дней назад## self similar

the graph of the zeta function reminds me of the mandelbrot/julia set, especially the spirals starting at 9:50

8 дней назад## Goat pepper herbal tea

I’m Alex an I’m a professor of bitchassery

8 дней назад## Gaurav Negi

One day some person would just randomly post the proof in an internet forum asked by someone jokingly.

8 дней назад## Jin Shun Lin

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9 дней назад## Chris Selvey

Brb, imma go take some ayahuasca and talk to the dmt fairies. They’re all made of geometric shapes so they’ll know.

9 дней назад## Dok Eddy Simanjuntak

Adding another one on my long list of 'How to make a million dollars' ! Probably easier to rob a bank and getting away with it. 😂

9 дней назад## Mohammed Alnamer

I think I can get it

10 дней назад## InterStellaFella -

What is the problem... It is not explained clearly ? Proving convergence when something > 1 ?

11 дней назад## Enjoying Self

What?? Only 1 million dollars? Make it 1 billion dollars and I'll stop sleeping and showering.

11 дней назад## qhk slz

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12 дней назад## Abd Aziz Abd Hamid

I find out proving any theorems is too hard for me to understand than solving problems.

12 дней назад## Gilly Erdbayr

0:02 all i see is an onion forming

13 дней назад## Bill Tai

Stupid question : if we already able to check and verify 10 trillion samples, can't we just treat this as proven for practical purpose? Do we have any precedence in mathematic history that that trillions of validated sample ended up proven wrong?

13 дней назад## Jah Read

So is this how our brains resolve higher dimensional information from the hologram into say 3D visual field or into the flow of time or into gravity (of course assuming that Kant was correct and space/time is a “mere mode of perception “ which I think he was as the infinite regress objection ignores the possibility that such a regress could take the shape of a feedback loop...or Reimans hypothesis)

14 дней назад## Algerian Culture and Traditions

I can write prime numbers from 01 to 30,000 even more and in order without using the primal test

14 дней назад## Akshay

This was an amazing video!!! The moment you said " Logarithm function undoes exponentiation , the same way division undoes multiplication" was the moment I actually understood what Logarithms were. It was like a Aha moment. Thank you for making such a beautiful video. It was like listening to a folk lore.

15 дней назад## L Lawliet

Honestly I understood nothing but I'll try to

15 дней назад## Robert Telarket

You seem to forget the mainly federal taxes alone deducted would leave you with say perhaps a paltry $200,000!

15 дней назад## Robert Telarket

It is worth far far far far far more than a nonsense small $1,000,000. The reward for proving or disproving the Riemann Hypothesis should be 2 or 3 billion dollars a small pittance for Western Europeans countries or U.S. etc.

15 дней назад## Max Bolton

Alex, thank you!!

15 дней назад## Martin atkinson-weller

Any chance of links to (or info about) the music in this video? Especially the last piece. Thx

16 дней назад## Special Android

I think i followed the first micro second of this

16 дней назад## Balbina Santana

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16 дней назад## Costinga

Someone with no university degree solved it and has proofs. Again not everyone is created equally. Education is super important but some are simply on another level

17 дней назад## Costinga

Oh I would but this is not me we’re talking about and I take no credit. Hopefully the person in question will submit his findings and get this over with. I still don’t understand what this really is.

7 дней назад## Artur Renato B.B

I suppose you're patting yourself on the back here

7 дней назад## Costinga

Solved soon to be announced

17 дней назад## Felix IV Lavilles

If you were my professor in math at college, I wouldn't have flunked that subject thrice

17 дней назад## Jeff

wish you would have showed some math about the fundamental and it's harmonics.

18 дней назад## marvin makwarimba

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18 дней назад## amin nima

Why is it blue though?? Please answer before you do

18 дней назад## Mistah J

"You don't need an advanced degree in mathematic to go on this journey with me" Ok, yay I'll understand some math. "So there's no negative square numbers" Ok got it. " So we made some up" O... k... "Imaginary numbers have cousins" ... "Combinations of real numbers and imaginary numbers are complex numbers" oh Lord... "They might look like two numbers but they're actually one number." Aaaigh, Imma head out and watch some cartoons...

18 дней назад## A Grand

Just remember that we define what numbers are. Complex numbers are just an extension that we decided to add because it's useful to us. It's like adding negative numbers to the set of natural numbers.

17 дней назад## AG''''killer

LOL

18 дней назад## A Alagao

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18 дней назад## gloria sanders

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18 дней назад## Edward Donato

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18 дней назад## gloria sanders

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19 дней назад## Manish Saini

Best video to getting sleep😴😴

19 дней назад## Shubham Vishwakarma

I will do it.

19 дней назад## rishab basera

some problems are not meant to be solved .........? maybe not

19 дней назад## Nietzsche Bloch

We can solve this by professor method

19 дней назад## Christian Ehrnsperger

Quick reminder: "Jesus said to him, “I am the way, the truth, and the life. No one comes to the Father except through Me". John 14:6

19 дней назад## John Gottuso

The obtainable january therapeutically plant because minister finally risk until a periodic pamphlet. obedient, serious pocket

19 дней назад## NoName

So what is the importance?

19 дней назад## John Rogan

The critical line!

19 дней назад## John Rogan

The DNA of math!

19 дней назад## John Rogan

Waves...ocean waves...sound waves...math waves

19 дней назад## John Rogan

Earliest petroglyphs show this pattern!

19 дней назад## John Rogan

Biden knows the answer..so do Harris and Obama...and Trump!

19 дней назад## John Rogan

Gravity.. Not even real.

19 дней назад## John Rogan

The universe

19 дней назад## russo thuga

The magical loaf preferentially need because sphynx mainly guess in a calculating pocket. creepy, cautious gliding

20 дней назад## Tammy Davis

Can someone please tell me what the piano piece at the end of this video is?

20 дней назад## XxX AlPhA eVeRyThInG XxX

1 million for such a tough problem is a shame. Kylie Jenner makes 2 million on instagram every time she shows her ass

20 дней назад## Robert Cad dock

The animated pail radiographically interest because city uniquely expand through a absent slipper. wakeful, aboard rat

20 дней назад## Gewitterhund

42? Maybe?

20 дней назад## Y A

MIND BLOWING!

21 день назад## Spare Cat

i? I think you mean j (this post was made by EE gang)

21 день назад## Yashwanth P

Half way through the video and already scrolling through the comments :)

21 день назад## Dorothy Miles

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21 день назад## Jack Tinney

Is this connected to the Mandelbrot set?

21 день назад## Steven Corley

So what’s the problem? Disproving the theory by counting to infinity????

21 день назад## Samanta Saita

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22 дня назад## Piotr G

P = N - {forEach(p in P): forEach(n in N): return n*p} does it make sense ? P - prime num., N - natural num., {} - set

22 дня назад## alpha1beta1gamma

Boys, I solved it. I need you to send me $1000 admin fees to complete my paper but then I'll win the prize and give you a fat cut of 100000 smackeroonies

22 дня назад## Flightcoach

Watched with great interest, good buildup and explanation. Being a non math genius myself I did find the video to end unexpectedly with that statement that mathematical proof is needed. So why exactly is that a problem then? What hurdles need to be crossed to get there? And are things in science not like "it is true until proven false?" If you have a trillion points on the critical line and no aberrations... that's proof right?

22 дня назад## Flightcoach

@A Grand thanks for taking the time to explain this. Learnt something new! I always thought it was like with many laws of nature: a hypothesis is true until someone disproves it. But i now see this is different. Good stuff.

18 дней назад## A Grand

I forgot to mention that proving Mertens conjecture would prove the Riemann hypothesis lol. Too bad it was disproven.

20 дней назад## A Grand

The problems/hurdles is that it's really really hard to prove. There's not much else to say. Unfortunately in math, you can't just assume that the pattern is true just because it holds for unreasonably large computations. It's a subtle fallacy that people subscribe to because they haven't asked the question: How do you know with 100% certainty that it won't break at some point? The only way you can know is through a rigorous mathematical proof. Besides... There are plenty of counter-examples. Look up: Mertens conjecture Euler's conjecture on the sum of like powers The first one is particularly interesting because you need a computer the size of the universe to calculate it but we know with 100% certainty that the pattern must break somewhere... All thanks to proofs

20 дней назад## asn65001

Such an excellent video. Thank you!

22 дня назад## Blue Angel

Great video! Well done.

22 дня назад## Dylan Kizer

Somehow I'm less intelligent coming out of this youtube experience

22 дня назад## David Jordan

The unknown variable equals A singular beginning, that's both infinite and limited in possibilities? A philosophical paradox, A conundrum of 8' s laying horizontal, like a pair of specectals pure and simple. Omen, 8 is great, right? I can draw it starting wherever I want, but when I'm done, no one knows where I begun? Riddle me this, Does science require Faith? 🙄 Who knows, why Jesus spoke in parables?

23 дня назад## David Jordan

2 Negatives × 2 Wrongs = A negative, Right?

23 дня назад## David Jordan

Q C, WHWW HWW x 50 bpm × 6 - 6 x - 6 = Hallelujah Math is _ ____

23 дня назад## comedyshorts gamer

"so logs are just the opposite of exponent functions. damn why the teacher never say that?" *Pauses the video to drop another log into the toilet*

23 дня назад## Tony Richard

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23 дня назад## Randy Zeitman

Man is this a great video ... even for a layman as myself.

24 дня назад## 123TeeMee

Maybe instead someone can prove that we can't prove it, or prove that we can't prove that we can't prove it

24 дня назад## shadowatom

You may be joking, but funnily enough, those actually are valid options. You can either prove it correct, disprove it (prove that we can't prove it), or prove that it's not possible to prove either way (in which case, you've proven that it's true, because it can't be proven false). Look up Goedel's Incompleteness Theorem if you're curious about that last option.

17 дней назад## Alexander Grube

"Riemann was able to rigorously proof that if you add up all the harmonix of the zeta zeros, you get a perfect match to gauss's modified prime counting function" yes of course, i knew that

24 дня назад## VOZAMARAK TV - ART

Mathematics is so beautiful !!!

24 дня назад## CJ Hicks

Every right minded person knows that the square root of -1 is j, not i. And I think Euler deserved more credit for complex number theory in this video.

24 дня назад## Flounderhouse

I'm probably missing something, but it sounds like the reiman hypothesis has already been solved and the real problem is that yall have a problem with infinity.

24 дня назад## Amour Learning

If a computer proves this with a chatbot, who gets the million dollars? Computers can't prove theorems by example, but they can certainly prove theorems. Proof of concept: 4-color theorem* (not hypothesis)

24 дня назад## kukul roukul

i saw a FRACTAL right there ! 11:07

24 дня назад