Hey baby, let me indent your contour

Today was the last day of Complex Variables before the final next Wednesday. SAD!

A huge topic we’ve been focusing on for the past few weeks has been the residue theorem. Because I’ve been OBSCENELY BUSY, I haven’t had a chance to look up the dude behind the theorem (and behind pretty much everything we’ve talked about in this class): AUGUSTIN-LOUIS CAUCHY!!   

So that’s what I did tonight. Cauchy was born in Paris in 1789. He worked under Laplace and was pretty familiar with Lagrange during the period when Napoleon was in power. Because of Lagrange’s urging, he entered secondary school in 1802 (at age 13) and it quickly became apparent that the dude was SUPER smart. He started winning all these academic competitions and basically out performed everyone else at the school.

When he was 36, he published one of his most important and well-known theorems: Cauchy’s Integral Theorem. A year later, in 1826, he gave the first formal definition of a residue of a function and shortly thereafter gave the residue theorem in another paper.

But that’s not all! Here are some other things Cauchy is responsible for:

  • He was the first to rigorously prove Taylor’s Theorem
  • He gave the necessary and sufficient condition for a limit to exist—the form of this condition is the one that’s still taught today!
  • He created a test for absolute convergence
  • He defined the concept of stress in elasticity
  • He gave an explicit definition of infinitesimals in terms of sequences tending to zero.

And more! According to a biography written by Hans Freudenthal, more concepts and theorems have been named after Cauchy than for any other mathematician.


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