On the shape of a curve

✍ Scribed by Raoul Bott

• Publisher: Elsevier Science
• Year: 1975
• Tongue: English
• Weight: 766 KB
• Volume: 16
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1016/0001-8708(75)90147-4

✦ Synopsis

DEDICATED

TO STAN ULAM

The dubious honor of being your anti-keynote speaker1 has no doubt fallen to me because I am an engineer and applied mathematician gone astray-a victim of the seductive wiles of pure mathematics.

Of course the days of penitence in matters of chastity are long gone, so do not expect me to be contrite. Rather my theme will be that the temptation was simply too great. However let me say this concerning the various branches of our subject. Subjectively I find no difference among any of them. When I worked on networks with Duffin I found them as fascinating as I found Lie groups later on in my work with Samelson, fixed point theory in my work with Atiyah, and as I find foliations in my work with Haefliger at the moment.

But to get on with it, let me cite an instance of the "Pure Temptation" in mathematics which was eminently successful:

We start from the "practical" question: How many solutions does a real polynomial equation of degree 12 have ?

A little experimentation then shows that such an equation, say,