[tokenadult]

Thanks for sharing this particular Feynman lecture. The treatment here, using what are basically the Peano postulates to derive the field properties of the real numbers and then the basic structure of secondary school mathematics, follows the treatment of Landau's Grundlagen der Analysis (Foundations of Analysis), a concise book that Feynman was probably aware of as he presented his lecture. Feynman of course added a sense of excitement and wonder that makes this lecture charming to read. Such treatments of the foundations of secondary school mathematics are fairly commonplace in the better university textbooks of mathematics. I first learned of Landau's book in a discussion of mathematics education in a Usenet newsgroup back in the 1990s, and bought the German edition on the recommendation of Michael Spivak's famous textbook Calculus, which follows a similar approach (but starting from the field properties of real numbers taken as axioms). In those days, I'm pretty sure, the standard calculus textbook at Caltech, where Feynman taught, was Apostol's textbook, which starts a little bit differently but also takes a theorem-proof approach.

https://maa.org/press/maa-reviews/calculus-4

[WalterBright]

> the standard calculus textbook at Caltech, where Feynman taught, was Apostol's textbook

It remained so in the late 70's when I attended.

The prices it still fetches on Amazon shows its timeless worth.

[haskellandchill]

Nice I was going to mention Spivak but you beat me to it. I stumbled on it in a library 20 years ago and was hooked. I bought the Differential Geometry books with the pretty covers and lost my book collection before I could do much with them. I'll have to check out Apostol, I only know the Number Theory book.