Illustrations for Quanta magazine - describing a concept called The Langlands program; which provides a beautifully intricate set of connections between various areas of mathematics, pointing the way toward novel solutions for old problems.
Imagine the world of mathematics as a physical world - with different continents representing different fields of mathematics...
...One of these being the field of Number Theory.
The Land of Number Theory is described as a lush, mysterious and largely uncharted forest. This forest is home to mathematical concepts such as Arithmetics, prime numbers, polynomial equations and whatnot.
Another one of these continents is the land of Harmonic Analysis...
...This is a world of Symmetry, geometry, repeating patterns and modular forms.
These vastly different fields was long thought to exist totally separate from each other - mathematicians who studied them could never really prove any interconnectedness between them. That is, not until 1967 when, in a letter to the number theorist André Weil, a 30-year-old mathematician named Robert Langlands outlined striking conjectures that predicted a correspondence between two objects from these separate fields. The Langlands program was born.
And finally - a bridge connecting the continents is revealed in glimpses through the proverbial fog existing between these fields.
One of the mathematicians trying to prove the connection between these fields was Shrinivasa Ramanujan, who studied in the field of Harmonic Analysis.
And in the field of Number theory, also looking to prove this connection we find Mathematicians Andrew Wiles and Taniyama Shimura Well (among others).
Some initial sketches for the Langlands Explainer, some of them which made it further and some of them which ended up with some alterations in the end.
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