How Simple Math Led Einstein to Relativity

Einstein turned the world on its head in November of 1919, when data collected during a solar eclipse matched the predictions of his Theory of General Relativity. But Einstein’s path to discovering his theory traces back much further, to when he was 12 years old and he first learned about an ancient mathematical method…

Special thank you to Professor @AlexKontorovichMath of Rutgers University and Museum of Mathematics (MoMath) for his help and participation.

Additional credits:

Giacomo Belletti - camera
Brandt Adams - newscaster voice
Kolja Gjoni - drum roll
Valentin Cazako - help with creating the “Pringle chip” model and 3D animations

Music from Epidemic Sound and Envato Elements.

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To learn more about Special Relativity and Minkowski space-time:

To learn more about General Relativity:

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**A Note about how I use AI generated images in my videos**

The emerging ability of artificial intelligence to generate compelling images from text prompts opens new possibilities for compelling storytelling. However, when mixed with real historical imagery, as is in my video, it has the potential to create confusion, or worse, if not handled properly.

I have set a few guidelines for my use of AI generated images in this video so that a viewer can easily understand which images are real photographs and which are synthetically generated:

ALL images that have been placed in a “frame” (eg a border that resembles an old photo print, etc) are REAL historical images.

ALL images that include Einstein's full face, as well as all World War I related images, are REAL historical images.

I have used Midjourney AI to create “stock” image elements including backgrounds, illustrations, and objects.

I have used Midjourney AI to create some images that are implied to be of Einstein. In these, Einstein’s face is FULLY OR PARTIALLY OBSCURED.

Please send me a message or drop a comment and I'll be happy to clarify any specific images.
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Items that Appear in the Video:

•“Notes for an Autobiography” by Albert Einstein - originally published in the Saturday Review of Literature, November 26, 1949
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Additional Sources:

Photos:

Note: Amazon links are affiliate links which help support the channel at no additional cost to you.

[bensyversen]

Thank you for watching! I hope you enjoyed this one as much as I enjoyed making it. I'm thinking about what story from the history of mathematics to tell in my next video, so please drop a comment if you have a suggestion!

[Mahesh_Shenoy]

Whether gravity is fictitious (just an artefact of accelerated frames) or real (contains tidal forces that cannot be co-ordinate transformed) is the same as asking whether geometry is flat or curved was Einstein's key insight! Riemann probably never thought in his wildest dreams that his math would be useful to model curved spacetime. That's incredibly insane. Thanks for this wonderful video, Ben. I loved how the video slowly put all the pieces together. Wow!

Also, thanks for the shoutout. Cheers!

[logankoster]

"This was when Einstein came upon what he later called the happiest thought of his life. He imagined a painter falling from the side of a building-"
This made me laugh

[Begeru]

I really appreciate you bringing up Einstein’s contemporaries that aren’t household names but we’re an integral part of Einstein’s work.

[TheNewLooter]

30:07 bro went "my pain is greater than yours" 💀

[CreateSmarter]

Wow Ben! This must've been a huge undertaking. Amazing video, full of wonderful visual explanations and put together extremely well. Great music choices, great story. Love the addition of the interview with Professor Alex K! You should be very proud of this.

[mavgr]

Besides Minkowski and Grossman, Einstein also received help from Constantine Caratheodory, a Greek Mathematician considered one of the best of the 20th century. Caratheodory researched and wrote his PhD under the supervision of Minkowski at the University of Gottingen.

[Dr.Nguyen-Bakersfield]

One of the greatest achievements of this short video is it allows me to see all these great historical figures in the overall context. We all know Riemann hypothesis, the Hilbert list of problems etc. But now I can directly connect all these geniuses and see them in the great spacetime of the cosmos.

[mnazaryan]

I‘m so glad Youtube recommended this incredible quality video after two months

[rickwilliams]

I remember reading about the history of mathematics and Archimedes use of infinitesimals. It gave me a much better understanding of calculus.

[lauriefaber]

I remember a moment during a tutoring session nearly a decade ago when you gave me the best explanation of the number "e" - and years later, when teaching logs and "e", I still attempt to replicate your demonstration of a random accountant trying to continually compound interest with an obsolete gear/lever machine until his arm nearly fell off (of course, I add my own dramatic flair)! Anyway, fast forward to this week, when one of my more curious students came to me asking me a LOT about "e" and its discovery and significance and oh so much more. Naturally - pun intended - I thought of your work, and that this might be an interesting topic for a future undertaking of yours!

[nadionmediagroup]

This is awesome. Your visuals compliments the concept and you explain it well. Not too easy, but not too dense either.

[priyanshuindra]

One of the best video I ever watched on this weird website... Great work guys!!! Thanks for making such a great video...

[EmdrGreg]

I'm not a scientist. I have only a layman's grasp of the basics of all of this. But I too was baffled by the mysterious merging of Einstein's theory and the miraculous math that supports it. How on earth did this 'just happen'? This video really sheds light on the whole thing. Thanks Ben and Alex.

[TheNewPhysics]

Ben Syversen,
I would like you to accept a challenge in which I prove (using Occam's Razor) that Einstein was wrong about everything he said about Relativity, Time, and time Dilation.
You can count on me to provide an alternative representation (not using geodesics) that can reproduce all Einsteins' successes and succeed where he failed.
The Occam's Razor support comes from me providing a simpler model that doesn't require geodesics, metric, inflation, false vacuum decay, Higgs Mechanism for Inertial Mass Creation, Quantum Field Theory, Dark Matter, Dark Energy, Space Stretching.
You seem knowledgeable about Einstein's work and might still be capable of learning new tricks...:)

Marco Pereira

[montyhall]

Levi-Civita gave Einstein the tools he needed to flesh out general relativity with tensor calculus.

[carlosdario]

I wouldn’t call tensor calculus “simple math”. Anything else that tries to explain GR without tensor calculus is an offensive oversimplification, and sadly YouTube is full of this kind of quacks.

[MrNeada]

I would really have enjoyed your video if it weren't for the volume of the music, i had to leave halfway I couldn't put up with it any longer.

If you do an update without the crappy music I'll subscribe.

Cheers

[TMTER]

Stunning video! Always fun to learn about the history of physics. Especially with a production value like this. Impressive work

[binbots]

Now the next step is figuring out how general relativity and quantum mechanics fits together and once again time is the key. General relativity and quantum mechanics will never be combined until we realize that each individual observer is observing them both at different moments in time. Because causality has a speed limit (c) every point in space where one observes it from will be the closest to the present moment. When one looks out into the universe they see the past which is made of particles (GR). When one tries to measure the position of a particle they are observing smaller distances and getting closer to the present moment (QM). The wave property of particles appears when we start trying to predict the future of that particle. A particle that has not had an interaction exists in a future state. It is a probability wave because the future is probabilistic. Wave function collapse is what we perceive as the present moment and is what divides the past from the future. GR is making measurements in the observed past and therefore, predictable. It can predict the future but only from information collected from the past. QM is attempting to make measurements of the unobserved future and therefore, unpredictable. Only once a particle interacts with the present moment does it become predictable. This is an observational interpretation of the mathematics we currently use based on the limited perspective we have with the experiments we choose to observe the universe with.