The Simplest Unsolved Problem in Math

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A huge thank you to Steven Strogatz, Alex Kontorovich, Harald Helfgott, Senia Sheydvasser, Jared Duker Lichtman, Roger Heath-Brown, Kevin Ford, Carl-Fredrik Nyberg Brodda, Kaneenika Sinha & Shehzad Hathi for their invaluable expertise and contributions to this video.

Look out for the upcoming @fern-tv video on the tragic life of Srinivasa Ramanujan! A huge thank you to Ruben Katschko, Mathias Hawk, Chris Varga, Elmer and David from fern for working with us!

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0:00 What is Goldbach’s Conjecture?
4:33 Goldbach and Euler
7:03 The Prime Number Theorem
11:16 The Genius of Ramanujan
14:57 The Circle Method
27:31 Proving the Weak Goldbach Conjecture
32:40 Math vs Mao
36:06 Back to Chen Jingrun
37:15 How you can prove the Strong Goldbach Conjecture

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References:

Images & Video:

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Special thanks to our Patreon supporters:
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Writers: Casper Mebius & Derek Muller
Additional Writers: Darius Garewal, Callum Cuttle & Aakasha Bagga
Producer & Director: Casper Mebius
Editors: Jack Saxon & Peter Nelson
Camera Operators: Casper Mebius & Derek Muller
Animators: Fabio Albertelli, Emma Wright, Ivy Tello, Allama Nandii, Emma Foster, Mike Radjabov & Andrew Neet
Illustrators: Maria Gusakovich, Jakub Misiek & Caine Esperanza
Assistant Editor: James Stuart
Researchers: Darius Garewal, Geeta Thakur & Gabe Strong
Thumbnail Designers: Ren Hurley & Ben Powell
Production Team: Rob Beasley Spence, Tori Brittain, Casper Mebius & Gregor Čavlović
Advice & Feedback: Gregor Čavlović
Executive Producers: Derek Muller & Casper Mebius

Additional video/photos supplied by Getty Images, Pond5.
Music from Epidemic Sound

[fern-tv]

Thank you for the opportunity to collab 😊
Fantastic video!

[stevenstrogatz]

Thanks for having me on again :-) And hey Veritasium fans: Sorry I messed up the numbers while getting emotional about Ramanujan. Here's the right version of the story, quoted from Robert Kanigel's book on Ramanujan: " [Hardy] would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.”
― Robert Kanigel, The Man Who Knew Infinity: A Life of the Genius Ramanujan

[arshil]

I remember when I was a kid, probably in 8th grade. I was obsessed with the Goldbach Conjecture because I thought I found a solution to it. Then I wrote an email to Eddie Woo Sir. And to my surprise, he wrote back. pointing out a stupid error in my calculations. That was the most magical moment of my childhood

[bonitasweeneyy]

I still have the book "The Goldbach Conjecture" by Xu Chi, which I received as the winner of a high school mathematics competition in China in 1978. The book contains several articles, one of which is titled "The Goldbach Conjecture" and tells the story of Chen Jingrun. It described mathematics as the most elegant and beautiful thing in the world, the most deserving of study, and Chen as a hero and almost saint. It had the greatest impact on me, and probably on my entire generation. I became a mathematician and even proposed my own conjecture (about Stokes equations). It was a pleasure to watch this video. Thank you very much! It's incredible that there are already over a million views.

[VEE]

"write the formula on his tongue" is like a proverb in India meaning the goddess spoke through him - not to be taken literally.

[tst_]

You know you’re looking at the next mathematician of the century when you see a guy reading a math textbook during an air raid

[kruksog]

For anyone who isnt already a math nerd, the part where Derek guesses Leonhard Euler (said "oil-er") is a little funny moment, because Euler shows up nearly everywhere in math. There is a joke that many things in math are named after the first person to discover them after Euler. There is a shockingly long wikipedia article entitled "List of topics named after Leonhard Euler."

Hopefully at least one person reading this wasn't already aware of this "maths inside joke."

[AcheOcho]

14:08 Hardy casually gives mathematicians power levels like anime characters.

[dmadalengoitia]

29:31 I'm from Peru and I remember when they announced he proofed the weak conjecture, he was like a rockstar amongst scholars here

[МихаилСовин-хш]

I’ve spent years chasing answers in documentaries, podcasts, even ancient texts—and none of it hit me the way The Obscured Principles book did. It’s like it was written for the few who are ready to break the illusion and remember who they really are.

[Glorious_Potato]

14:23 in the footnote, Hardy rates him a 100 factorial. Well, Ramanujan deserves it.

[KrishB]

Everytime I learn about the Ramanujan's theorems be it the asymptote theorem of partitions or the tau function, it's the stories behind them that give me the chills !.

[Xingchen_Yan]

I am a Chinese and grew up in China's education system. To most students, Chen's story was sometimes used as a counter example as how one can be so into math so he became delusional. One commonly referred story is that he bought a truck load of cup noodle to eat everyday just to solve this. But I was lucky enough to have a highschool math teacher that is very passionate about such topics and he lightened us with this story like 15 years ago. I feel really grateful for that. This video just reminds me of all those things and yeah, it is such a great video. Thank you Veritasium.

[winstonxie]

I still have the book “The Goldbach Conjecture” by Xu Chi, awarded to me in 1978 as a winner of high school mathematics competition in China. The book contains several articles, one of which is “The Goldbach Conjecture”, which told the story of Chen Jingrun. It described mathematics as the most elegant and beautiful thing in the world, the most worthy of pursuit, and described Chen as a hero and almost a saint. It made the deepest impression on me and probably on my whole generation. I became a mathematician, and even proposed my own conjecture (on the Stokes equations). It was a delight to see this video. Thank you so much! It’s amazing that there are already over a million views.

[umountable]

for me, a stronger argument for solving "difficult and irrelevant" problems is that they often yield to completely novel methods of prooving (like the circle method) that in turn can be applied to other problems. basically tackeling a extremely hard problem brings tools to live that are helpful also for other problems.

[Shadow]

When a guy is chill enough to read a math textbook during a raid, he is prolly the next messi of mathematics

[jamaluddin]

The circle method that Hardy and Ramanujan developed is so intriguing to me. I couldn't imagine ever thinking along that direction. It shows the intellectual prowess of both of them.

[prehistorictool]

The explanation of the circle method was really insightful! It's amazing how Hardy, Littlewood, and Ramanujan's work led to the eventual proof of the weak conjecture. And Harold Helfgott's contribution, combining theory with massive computation, is truly impressive.

[Aurianbuyss]

"Dont work on what you think is important, but work on what you love. because you will work with passion and that will lead you to do great things." what a quote

[akosv]

Story if Chen Jingrun breaks my heart. Thinking how much he had to suffer, and then seeing how much the whole world held him up as a hero for his struggles, memorating him really made me tear up. I just imagined how much his struggles were thanked by the whole world, like a huge "Sorry" that humanity expressed. Wow.