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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

@colorx6030

27 күн бұрын

That's really cool if it's real

@Neater_profile

19 күн бұрын

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

13 күн бұрын

@@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.

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

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 !

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

25 күн бұрын

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❤❤

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."

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

Amazing quote for Fourier in the beginning ! Thank you!

way too underrated, you explained it well

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!!

@DrWillWood

27 күн бұрын

Thank you! Appreciate the support 🙂

Thank you so much for your videos!.

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.

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

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...

Hi Dr. Wood! Great teaching!

One of the best explanations!

Excellent! Thank you very much.

great work!

thank you DR.

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!

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.

Thanks

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?

What a legend

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

27 күн бұрын

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

25 күн бұрын

@@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

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?

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 😔

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

Having to study this and Laplace transforms rn in school 😂

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

what a genius

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

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

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

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.

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

@DrWillWood

26 күн бұрын

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

19 күн бұрын

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

14 күн бұрын

Im confused in that section too :v

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

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

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?

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

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

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

@hambonesmithsonian8085

27 күн бұрын

Never doubt human ingenuity.

@samueldeandrade8535

27 күн бұрын

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

@salvit6024

27 күн бұрын

Amor fati and high self-efficacy

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

@Katchi_

25 күн бұрын

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

@themightyquinn100

24 күн бұрын

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

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.

@redaboussaadi1412

27 күн бұрын

The equation he wrote also isn’t homogenous

Nope

why do you say "zee" and not "zed"? 🧐

@gaopinghu7332

27 күн бұрын

It's standard in the US.

@LambOfDemyelination

27 күн бұрын

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

@yuseifudo6075

27 күн бұрын

Because it's one way to say it

@LambOfDemyelination

26 күн бұрын

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