To the Editor:
I enjoyed reading Nick Trefethen’s opinions on complex variables and taking his quiz (“What's so Special About Complex Variables,” October 2012). Although I can parallel park and speak French, I could have failed such a quiz in other areas of mathematics. I was able to ace this one, having taught 18.04 (Complex Variables with Applications) at MIT (some years after Nick himself). I share his love of the subject, and frankly, it was my desire to teach it that helped me decide on a career in applied mathematics, after a getting PhD in physics.
I once started a paper with the corny line, “Complex analysis is one of the most beautiful subjects in mathematics, and, despite involving imaginary numbers, it has remarkable relevance for ‘real’ applications.” Indeed, complex analysis is fundamental not only in mathematics, but throughout science and engineering. Although Nick laments the fading familiarity with complex variables among applied mathematicians, the sickness is more advanced elsewhere. Even at a place like MIT, science and engineering curricula reflect a different sort of “mission creep” away from mathematical depth. Entire classes (like 18.04) are being replaced by a few lectures in “Math for Engineers,” where Nick’s quiz would not go over so well! Although complex variables may seem arcane in the computer age, the subject provides the language of quantum mechanics, signal processing, and much useful mathematics and deserves to be taught more broadly in the future.
—Martin Z. Bazant, MIT