Something Strange Happens When You Take This To Its Logical Conclusion

A massive thank you to Prof. Steven Strogatz for his expertise and enthusiasm.

A huge thank you to Prof. Haithem Taha, Prof. Anthony Bloch, Dr. Carl-Fredrik Nyberg Brodda, Dr. Sarah Millholland, and Dr. Andrew Mitchell for all their help with finding the story and getting it right.

A special thanks to Dr. Aurèle Adam, Ron Haaksman, Marc Serra Peralta, and everyone at the Delft Makerspace for their help with preparing and performing experiments.

00:00 One rule that replaces all of physics
00:51 The problem of fastest descent
05:09 Fermat's principle
07:17 Bernoulli's solution
10:38 Maupertuis' principle
12:28 Maupertuis attacked and ridiculed
14:01 Euler & Lagrange to the rescue
17:22 The general approach to solving these problems
19:32 Writing the principle into its modern form
23:17 Why the principle works
27:08 Another way to do mechanics
30:19 A “spooky” breakthrough

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Patrons: Adam Foreman, Anton Ragin, Balkrishna Heroor, Bertrand Serlet, Bill Linder, Blake Byers, Burt Humburg, Chris Harper, Dave Kircher, David Johnston, Evgeny Skvortsov, Garrett Mueller, Gnare, gpoly, I. H., John H. Austin, Jr., john kiehl, Josh Hibschman, Juan Benet, KeyWestr, Kyi, Lee Redden, Marinus Kuivenhoven, Martin, Matthias Wrobel, Max Paladino, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Stephen Wilcox, Tj Steyn, Toni , TTST, Ubiquity Ventures, wolfee

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Key references:

A fantastic book on the history of the Principle of Least Action: Rojo, A. and Bloch, A. The

Images & Video:

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Directed by Casper Mebius
Written by Casper Mebius and Derek Muller
Edited by Trenton Oliver
Animated by Fabio Albertelli, Ivy Tello, Mike Radjabov, Gregor Čavlović, Emma Wright, James Finnemore and David Szakaly
Illustrated by Jakub Misiek, Emma Wright, and Maria Gusakovich
Filmed by Derek Muller and Casper Mebius
Additional research by Gabe Bean, Gregor Čavlović, and Geeta Thakur
Produced by Casper Mebius, Derek Muller, Rob Beasley Spence, Gabe Bean, Gregor Čavlović, and Tori Brittain
Thumbnail contributions by Jakub Misiek, Ren Hurley and Peter Sheppard
Additional video/photos supplied by Getty Images, Storyblocks, and NASA SVS
Music from Epidemic Sound

[bluebrown]

This was so beautiful. I was thinking of revisiting the old video I made with Strogatz about the Brachistochrone and Johann Bernoulli's solution, but this honestly does most of what I could have dreamed and so much more. Bravo!

[artbryanmoldon]

Man! Euler is that superhero backup that arrives just in time when all hope is lost!

[DataIsBeautifulOfficial]

Physics is just old guys arguing over who invented the best shortcut.

[ahwe]

veritasium changed my life, from almost quitting school to mechanical engineering

[RENO_K]

"I recognize the lion by his claws" is such an epic quote

Imagine being so legendary you don't have to sign off your letters/papers and people instantly know who wrote it

[nolanthedude]

One thing I adore about these videos is that they bring attention to history's forgotten heroes. Nakamura wasn't given the credit he deserved for the blue LED, and that video brought his contributions into the spotlight for millions. Now, Maupertuis has been given the spotlight and he can be recognized for his efforts alongside some of history's greatest mathematicians. If only he lived long enough to see this.

[ctoid]

It's truly an Eureka moment when all the things just came out to be F=ma

[fernandoizaurieta]

I'm a theoretical physicist, and I'm astonished by how precise and well-presented the video is. It reminded me of the wonder I felt as an undergraduate attending beautiful lectures on classical mechanics. Thank you for creating such wonderful material for everyone on YouTube.

[raktimaryabiswas]

Waiting eagerly for the next part.
Please take the least possible time !

[SochWrld]

Watching this from Nigeria, and it's incredible how i can have access to this quality of information for basically free. I really love the internet sometimes.

[Beryllahawk]

My son sent me to watch this. I'm already subscribed but so frequently when it's physics I get a bit wary, I'm very much not a maths person. You start throwing equations across the screen and my mind often just quits right there, lol. But this was fascinating. When he told me the name of the principle I blinked at him and said "You mean conservation of energy?" and he started hopping up and down going "NO! That's just the thing! Augh, go watch it Mom!"
SO here I am! And I see what y'all are saying. Interesting to think about and I look forward to the next one!

[arthurcuesta]

I just saw another brazilian watching this video on the supermarket while waiting for his Uber. It was a somewhat old dude with his daughter. You've become massive, man. Great to see it.

[StarFury]

16.5M subscribers, and still not afraid to show entire formula deriving process using calculus! Bravo!

[MrNpr]

I generally dont leave comments. But I felt I had to write this down. 24 years ago when I took my physics class as a first year under grad student, I was quickly introduced to the Lagrangian and Hamiltonian in a physics class with just the equations thrown around. There were books in the library which provided tons of equations but never the intuition behind them. It was assumed that the reader knew why this had to be the case. I never got back to digging this deeper as my primary area of focus had shifted to other subjects. But after so many years I am finally happy to see the beautiful thought process behind them. Really appreciate you for making such valuable and interesting content.

[notenoughmonkeys]

They should make a movie about this, Least Action Hero.

[xxvimilia]

I love these math videos because its so weirdly satisfying when you introduce another famous mathematician, and I'm like, "My man Euler was in this???". Its the same kind of excitement as the portal scene in Avengers endgame.

[harananand]

As a Mechanical Engineer I certainly knew the principles of Lagrangian and the Eulerian. I also knew Newton and Bernoulli's story. It touched my heart to learn about Euler's kindness and Maupertuis contribution. I never knew that. The human element was the most special. Thank you for sharing.

[SalilShahane]

15:34 the smile on Derek's face when he was compared to Euler made my day.

[Lukav]

This is such a great transition:

Mapertui is bullied - depressing music playing
Euler mentioned - Boss battle music starts playing 🔥🔥🔥

[strysphere]

Veritasium has now surpassed the quality of netflix docementaries. Really one of the best videos on math i have ever seen. Well done Ve. Cant wait for part 2