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Fourier: A Lifelong Passion

by Ricardo Pachon
3 minutes read

Long before Sheldon Cooper and his gang in “The Big Bang Theory,” and Ted Mosby in “How I Met Your Mother,” there was Ross Geller in “Friends” in the role of the geeky friend whose intellectual passions baffled everyone else. Ross is, of course, the best of them all, and I’ve happily re-watched the entire series now that Netflix is streaming it. I had forgotten that excellent final episode of the ninth season, where the whole group travels to Barbados to hear Ross give a talk at a paleontology conference. Watching the episode again today, I laughed remembering the time I put my own friends in the same situation.

It was during my last semester of a mathematics degree, and the occasion was the defense of my undergraduate thesis. For me, this moment marked the end of a year-long project, and for some reason, I thought it nobly fitting to ask family and friends to join me for the presentation. I’m not sure exactly when they realized the tremendous mistake they had made by accepting my invitation, but it was probably within the first minute, as I displayed the first slide with the pompous and cryptic title: “Construction of first and second generation biorthogonal wavelet systems and their application in the numerical solution of partial differential equations”. For the next hour, I bombarded the attendees with a slew of equations and graphs, and it’s a testament to how much they all love me that none of them fell asleep in the middle of my talk.

The “wavelets” mentioned in the title of my thesis are intimately related to a subject that sums up one of my greatest passions, which has connected in some way with almost every topic I’ve worked on over the last fifteen years: Fourier Analysis. This theory deals with the possibility, methods, and consequences of decomposing a block of information into characteristic frequencies. These frequencies can then be used to understand, manipulate, and reconstruct the original information.

I’ve spent years studying, applying, and teaching Fourier, and I know I could happily spend the rest of my life working in this area of mathematics and still have only scratched the surface of all that it hides behind. I’ve used Fourier to locate earthquake epicenters, produce images of tissues inside the human body with computed tomography, multiply numbers with millions of digits, speed up the simulation of the transient regime of integrated circuits, and calculate the prices of financial derivatives. Fourier is connected to Chebfun, that wonderful project I worked on for four years while at Oxford, and Fourier is linked to Artificial Intelligence, the new field I will now focus my career on.

Fourier analysis is behind the digital music we listen to every day, and in the perpetual motion of the stars. Fourier is studied in engineering because it is an incredibly useful technique for what electrical, civil, and mechanical engineers do. Yet, at the same time, Fourier can shed any mortal coil to become abstract harmonic analysis and be the focus of study for the purest mathematicians.

Jean-Baptiste Joseph Fourier was born this week 250 years ago and transformed the world. His theory is fascinating, and I can say without blushing that I am passionate about it. I will gladly invite you all again the next time I speak publicly about this. I know you won’t fall asleep.

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