alt Hacker NewsThe purpose of this article was, secretly, to tell the reader about another class of Diophantine equations which leads to the Langlands program, which studies from incredibly intricate hidden structure inside of number theory. The Langlands program studies Diophantine equations of the form
This is not what the Langlands program is
This is of course an oversimplification by graduate students trying to reach a broad audience, but one could argue that it in fact is. Langlands himself viewed his program as part of an attempt to achieve non-abelian reciprocity laws. See for instance: https://www.phys.ens.psl.eu/~kashani/slides_chenevier.pdf