The Revolutionary Genius Of Joseph Fourier 

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What impressed me most is the use of FFT algorithm, popularized by Cooley and Tukey in 1965, was first invented by Gauss 1.5 centuries prior to that(which he didn't publish because he thought it was useless) and he even predated fourier on representations of functions as infinite harmonic series. He had a lot of "This theorem was discovered by [insert name], but it turned out to have been proven by Gauss 10 years prior" moments, hence the phrase "you're smart but you're no Gauss". He really just needs a better PR team, akin to those of Newton's

Whenever my university taught me the Fourier (and the Taylor) series, it genuinely felt like I was witnessing something incredible and fundamental about math. Generalization is king, and this series is the king of generalization.

I'm french and study in Fourier Institut at Grenoble, France. Cool to see the story of the brilliant man who gave his name to my institut !

I never realised how old Fourier actually is! Great video!!!

Wonderful, I'm french and the auto generated subtitles keep my focus. Fourier is a true genius, one of the first geniuses that Normale Sup and X created

Dear Will, thank you. You have answered a question, I have been pondering for the past 42 years. As I watched your video, I was teleported back, "through space and time" to the summer of 1982. I was studying Fourier analysis and I had an epiphany, the first time my "wave function collapsed". I simply realized,"If you give me any function, any function f(x), I can express it in terms of a simple combination of sines and cosines." - Pure mathematics at its best, QED. Or as Sidney Coleman said it, "The career of a young Theoretical Physicist consists of treating the harmonic oscillator in ever increasing levels of abstraction."

way too underrated, you explained it well

Amazing quote for Fourier in the beginning ! Thank you!

What a gem of a video, I really enjoyed the animations and explanation. Very well made!!

Thanks! I was looking for this from a long time!!

Thank you so much for your videos!.

just finished studying everything I think I need from the heat equation to FFT and this is a nice dessert to wrap things all up...

Thank you Dr. Will! You're providing a precious resource by providing an insight into the intellectual maneuvers and methods of the minds which shaped our world, Awesome Video :D

Very nice video, I like that you were more holistic in your exposition and this was a succinct and well motivated video. As an idea, a similar video on Galois would go down well, you could do him justice.

Hi Dr. Wood! Great teaching!

awesome video you have represented the beauty of doing Physics and for the first time I saw the derivation of heat equation

One of the best explanations!

great work!

Excellent! Thank you very much.

Well done vid on a person people should know a lot more about. 😀👍

Hey, man! Amazing video! Loved the background story!!! I would like to know if you can do the same for the Laplace Transform. I did a lot of digging through the years and I actually figured that it just came to be what it is from trial and error. However, I am aware that there is a way to derive it from Fourier Transform. Anyway, would be awesome to see you covering these topics as well!

thank you DR.

Great video! It would have been really nice to see the actual approximation as a 3D function (the values over the x-y plane), not only the section at x=0.

Nice video! One nit, around 6:00, dT is a pretty bad choice of notation as you do not mean an increment in temperature but an increment in the _derivative_ of temperature.

Epic video as usual; never fails to disappoint. You upload too little and too late 😔

Wow. just wow. I am using FFT since like 25 years ago and I never realized what a breakthrough was at the time. We are lucky he was not killed during the french revolution

I don't understand at 6:04 why it's the second derivative. Isn't that used to determine the inflection points? Did I miss something in maths class?

That which is like to itself in differentiation and exponentiation must be directly related to the exponential function, and Gamma(z) is equal to it for certain values, and seems to oscillate between cosine and sine at multiples of 1/2. In fact, it seems to act like a generalization of exp(z), and Gamma does after all show up in the partial sum of exp(z) itself which would also seem to imply a way to possibly generalize factorial given a means to compute the nth digit of e in some base? So far, my guess is there's probably a sum of four independent terms involving the exponential which I hypothesize from the likeness and alternative representation of the simple sum of complexes z + w as z+w=\left(\sqrt{z}+i\sqrt{w} ight)\left(\sqrt{z}-i\sqrt{w} ight)=\frac{1}{2}\left(e^{-i\arccos\sqrt{z}}+e^{i\arccos\sqrt{z}}+i\left(e^{-i\arccos\sqrt{w}}+e^{i\arccos\sqrt{w}} ight) ight)\cdot\frac{1}{2}\left(e^{-i\arccos\sqrt{z}}+e^{i\arccos\sqrt{z}}-i\left(e^{-i\arccos\sqrt{w}}+e^{i\arccos\sqrt{w}} ight) ight). Consider also product_(n=0)^(k) (x + i n) and the particular products with which this product converges as k goes to infinity. All of this leads me to believe that perhaps there's some simple sort of representation by generalizing the imaginary unit if not the complexes in a particular way such that something simple along the lines of f(z)^n = Gamma(f(z) + n)/Gamma(f(z)). With that, and with being able to represent any Gamma(z) for z in the rectangular region [0, 1 + i] (or really any such region [n+ik, n+1 + ij] for integers n, k and j), both representing Gamma sufficiently with which to create some sort of symbolic arithmetic (provided certain comparative operations can be performed symbolically), as well as computing arbitrarily good approximations of Gamma(z), would be trivialized-and that's just what I'm looking for. Am still sad I didn't get addicted to complex arithmetic sooner 😔

What a legend

Having to study this and Laplace transforms rn in school 😂

Can you transfer heat through a photon? Or how about a frequency like gamma or infrared. Or is heat strictly bound to physical matter?

Dear Dr Will Wood. Can you explain the relationship between equation at 4:27 and Newton's cooling law? At first glance it seems to make sense, but in Newton Law of Cooling there is no spacial variable? Also the unit of 2 equations is not the same. For Newton's law of cooling, the unit of dQ/dt is Watt, but for the second equation, the unit is W/m. Can you help explain this?

Can you tell about decomposition over Bernstein polynomials? Is it even possible?

I learned in detail how the Fourier transform works and even implemented it, but I'm still convinced it's magic and not real maths

Typo at 5:50. You cannot add (dT/dx) and (dT). The units conflict.

its amazing that fourier dreamed this all up 200 years ago while napoleon was conquering europe.....there seems to be a tendency toward great intellectual discoveries when a nation is in the highest geopolitical ascendancy in its history

This will only work as long as the PDE is linear, right?

Cant see any bound between Fourier's lifestory and his maths solution. I dont mean that autor was wrong when added history to this video, but it need better connection of scenario parts.

I'm a huge fan of Fourier's jelly for ten minutes.

what a genius

Involved in the Reign of Terror.......imprisoned and survived prison? So, he wasn't "involved" in the Reign of Terror but he WAS imprisoned during the Reign of Terror. Why was this?

Only problem i've seen with the video is it's assertion that you can derive fourier's law from newton's law of cooling. You can not, in the video he slipped in dT/dx instead of just dT, which is newton's original formulation, such a move is unjustified though

Great content. The pronunciation is more like « Foorier ».

I just don't understand how anyone can come up with this

wish i could listen to this but your decision to add unneeded background music interferes with understanding.

Crazy how times change. Today if you go to prison, you'll never get a job at a college or university.

Who ate all the Pi's = 0

Sorry, but I'm sure the explanations were clearer when I studied Fourier 45 years ago in Electrical Engineering math at University, that or I'm just getting old.

why do you say "zee" and not "zed"? 🧐

Nope