Jun 18, 2026 · 13 min · 11 segments
Amid the chaos of revolutionary France, one man’s mathematical obsession gave way to a calculation that now underpins much of mathematics and physics. The calculation, called the Fourier transform…
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The high-pitched flutter of the flute, the middle tones of the violin, and the low hum of the double bass fill the air with pressure waves of many different frequencies.
When the combined sound wave descends through the ear canal and into the spiral-shaped cochlea, hairs of different lengths resonate to the different pitches, separating the messy signal into buckets of elemental sounds.
In the early 1800s, French mathematician Jean-Baptiste Joseph Fourier discovered a way to take any function and decompose it into a set of fundamental waves, or frequencies.
Add these constituent frequencies back together, and you'll get your original function.
The technique, today called the Fourier transform, allowed the mathematician, previously an ardent proponent of the French Revolution, to spur a mathematical revolution as well.
Out of the Fourier transform grew an entire field of mathematics called harmonic analysis, which studies the components of functions.
Soon enough, mathematicians began to discover deep connections between harmonic analysis and other areas of math and physics from number theory to differential equations to quantum mechanics.
You can also find the Fourier transform at work in your computer, allowing you to compress files, enhance audio signals, and more.
The high-pitched flutter of the flute, the middle tones of the violin, and the low hum of the double bass fill the air with pressure waves of many different frequencies.
When the combined sound wave descends through the ear canal and into the spiral-shaped cochlea, hairs of different lengths resonate to the different pitches, separating the messy signal into buckets of elemental sounds.
In the early 1800s, French mathematician Jean-Baptiste Joseph Fourier discovered a way to take any function and decompose it into a set of fundamental waves, or frequencies.
Add these constituent frequencies back together, and you'll get your original function.
The technique, today called the Fourier transform, allowed the mathematician, previously an ardent proponent of the French Revolution, to spur a mathematical revolution as well.
Out of the Fourier transform grew an entire field of mathematics called harmonic analysis, which studies the components of functions.
Soon enough, mathematicians began to discover deep connections between harmonic analysis and other areas of math and physics from number theory to differential equations to quantum mechanics.
You can also find the Fourier transform at work in your computer, allowing you to compress files, enhance audio signals, and more.
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