From Analysis

The Beauty of the Fourier

Thanks to twitter I stumbled upon a beautiful Fast Fourier Transform video, here it is:

Fast Fourier Transform from peter menich on Vimeo.

In case you want to know some more about Fourier Transforms, Larry Hardesty from MIT has a really nice Explained article on them:

In 1811, Joseph Fourier, the 43-year-old prefect of the French district of Isère, entered a competition in heat research sponsored by the French Academy of Sciences. The paper he submitted described a novel analytical technique that we today call the Fourier transform, and it won the competition; but the prize jury declined to publish it, criticizing the sloppiness of Fourier’s reasoning. According to Jean-Pierre Kahane, a French mathematician and current member of the academy, as late as the early 1970s, Fourier’s name still didn’t turn up in the major French encyclopedia the Encyclopædia Universalis.

Now, however, his name is everywhere. The Fourier transform is a way to decompose a signal into its constituent frequencies, and versions of it are used to generate and filter cell-phone and Wi-Fi transmissions, to compress audio, image, and video files so that they take up less bandwidth, and to solve differential equations, among other things. It’s so ubiquitous that “you don’t really study the Fourier transform for what it is,” says Laurent Demanet, an assistant professor of applied mathematics at MIT. “You take a class in signal processing, and there it is. You don’t have any choice.”(Rest of the Article)

150 Years of Unprovability: The Reimann Hypothesis

It is 150 years to the day since the Riemann Hypothesis was first presented to the Monatsberichte der Berliner Akademie. So in honor of this most important of unsolved mathematical problems, and one that has a 1 million dollar bounty on its head(so yeah you should probably go solve it like right now) here is a video clip from the BBC’s Story of Maths that tells Riemann’s Story

And another that talks of the Riemann Hypothesis itself