The Revolutionary Genius Of Joseph Fourier

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In this video, we explore the life and work of Fourier, culminating in the famous Fourier Series.
FAQ : How do you make these animations?
Animations are mostly made in Apple Keynote which has lots of functionality for animating shapes, lines, curves and text (as well as really good LaTeX). For some of the more complex animations, I use the Manim library. Editing and voiceover work in DaVinci Resolve.
Supporting the Channel.
If you would like to support me in making free mathematics tutorials then you can make a small donation over at
www.buymeacoffee.com/DrWillWood
Thank you so much, I hope you find the content useful.
This video was sponsored by Brilliant

[@DrWillWood]

To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/DrWillWood . You’ll also get 20% off an annual premium subscription.

[@spiderjerusalem4009]

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

[@colorx6030]

That's really cool if it's real

[@Neater_profile]

I think a lot of these stories surrounding Gauss are apocryphal and rooted more in wishful thinking rather than facts. Not denying that Gauss was a great mathematician tho.

[@rocksparadox]

@@Neater_profile Gauss and Euler had mathematical abilities so far beyond your comprehension that tales of them are interpreted by wishful thinking even if they had no computers to check the results. Euler stumped his teachers by adding numbers with a system instead of being a linear, step by step sheeple like the rest.

[@machoodin5172]

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

[@mhyria_]

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 !

[@Zejgar]

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.

[@BRunoAWAY]

Gaussian quadrature is like that, they belong tô the realm of brilhante simple ideias, I undering how manny of this ideias are still waiting for us tô imagine❤❤

[@AN-qk5st]

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

[@TerryGiblin]

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."

[@sciencefordreamers2115]

Amazing quote for Fourier in the beginning ! Thank you!

[@justaboringperson]

way too underrated, you explained it well

[@eaterofcrayons7991]

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

[@kgangadhar5389]

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

[@DrWillWood]

Thank you! Appreciate the support 🙂

[@hyperexplorer5355]

Thank you so much for your videos!.

[@General12th]

Hi Dr. Wood! Great teaching!

[@mustafaunal1834]

Excellent! Thank you very much.

[@iali361]

One of the best explanations!

[@Axenvyy]

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

[@bannguy]

great work!

[@leeris19]

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...

[@journeytotheinfinity440]

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

[@ronaldjorgensen6839]

thank you DR.

[@pectenmaximus231]

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.

[@ktkrelaxedscience]

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

[@larzcaetano]

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!

[@jasperantonelli4822]

Thanks

[@deakzoltan2714]

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.

[@ckq]

What a legend

[@atzuras]

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

[@andrewporter1868]

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

[@paradoxicallyexcellent5138]

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.

[@timothyvanrhein5230]

I was very confused around 6 min. I had to watch it several times and I didn't get it until the end of that sub-segmant when he declared it was the first order Taylor expansion. I still don't see clearly how he got there

[@marcoponzio1644]

@@timothyvanrhein5230 Yeah same. He kinda skimmed over the whole maths explanation and it's not easy for someone who's never seen this kind of stuff

[@andrewporter1868]

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 😔

[@supremebohnenstange4102]

Having to study this and Laplace transforms rn in school 😂

[@a.b3203]

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?

[@tuo9433]

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?

[@rexauer9896]

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

[@takyc7883]

what a genius

[@Embassy_of_Jupiter]

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

[@xelth]

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

[@oniondeluxe9942]

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

[@akashashen]

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

[@forrestcharnock3079]

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

[@DrWillWood]

You're right. Not a typo, just me being a bit loose with variable naming. Should've just given it a generic name like "a" or something in hindsight maybe!

[@belayadamu1473]

This was bugging me too. Not only the units but the maths does not work as well. @DrWillWood please correct it. Not to be an asshole but it just threw me a bit off.

[@rafiihsanalfathin9479]

Im confused in that section too :v

[@wdobni]

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

[@mks3782]

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.

[@tylerfoss3346]

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?

[@satishgupta2658]

Top 16 greatest mathematicians of all time 👇 Carl Friedrich Gauss Euler Newton Euclid Archimedes Leibniz Pierre Laplace Joseph Fourier Bernhard Riemann George Cantor Rene Descartes Alan Turing David Hilbert Kurt Gödel Fermat George Boole

[@JulienBorrel]

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

[@victormd1100]

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

[@sillystuff6247]

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

[@Daniel-li6gu]

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

[@hambonesmithsonian8085]

Never doubt human ingenuity.

[@samueldeandrade8535]

Thinking about it. You know. That's how everything is done.

[@salvit6024]

Amor fati and high self-efficacy

[@tomfreemanorourke1519]

Who ate all the Pi's = 0

[@themightyquinn100]

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

[@Katchi_]

That is a USA problem. Maybe visit the world. Learn something. Change your government.

[@themightyquinn100]

@@Katchi_ Did you get triggered by something I wrote?

[@rjlchristie]

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.

[@redaboussaadi1412]

The equation he wrote also isn’t homogenous

[@stighenningjohansen]

Nope

[@LambOfDemyelination]

why do you say "zee" and not "zed"? 🧐

[@gaopinghu7332]

It's standard in the US.

[@LambOfDemyelination]

@@gaopinghu7332 yeah but he's clearly not speaking American English

[@yuseifudo6075]

Because it's one way to say it

[@LambOfDemyelination]

@@yuseifudo6075 not in British English... Just funnily inconsistent, that's all