My calculus book is not a book for formalistic pedants who want to know the exact restrictions on the types of regions Green’s Theorem applies to. In my opinion it is deplorable that “honors” calculus have come to be synonymous with foundational hair-splitting. Only through the dogmatic eyes of the 20th century war on intuition is there nothing to calculus between rote calculations on the one hand and epsilons and deltas on the other. Open-minded students who want to genuinely understand things in an intuitively satisfying way are being robbed of a beautiful world by effectively being fast-tracked into real analysis as soon as they want to understand more about the calculus. The foundational investigation and arithmetisation of the calculus is a fascinating subject. I love real analysis and I think “baby Rudin” is a paragon of beauty. But real analysis is not calculus. It is a completely separate subject, as history shows. It is not “calculus for smart people,” as most modern honors efforts try to scam students into thinking.

Connected with this is the prevalent but harmful attitude that “mathematicians” demand rigour whereas “physicists” prefer more intuitive arguments. This false dichotomy should not be accepted, for it is based on a self-righteous and narrow-minded notion of “mathematician.” Its stupidity should be apparent from the fact that the set of “mathematicians” so defined is confined to a snobbish 20th-century clique, and in effect excludes every single discoverer of every single result in all of undergraduate calculus.