The following is from:
Körner, T. W. (2004). A Companion to Analysis: A Second First and First Second Course in Analysis (Graduate Studies in Mathematics Vol. 62). American Mathematical Society. On the first page of the first chapter, the author states
“It is surprising how many people think that analysis consists in the difficult proofs of obvious theorems. All we need know, they say, is what a limit is, the definition of continuity and the definition of the derivative. All the rest is `intuitively clear’1.”
The corresponding footnote (footnote 1) states
“A good example of this view is given in the book [J. R. Brown. Philosophy of Mathematics. Routledge and Kegan Paul, 1999.]. The author cannot understand the problems involved in proving results like the intermediate value theorem and has written his book to share his lack of understanding with a wider audience.”
Note that Körner doesn’t say the author (Brown) doesn’t understand, but cannot understand. This guy used one of the only forms of communication that would reach a broad audience composed BOTH of graduate students in mathematics or fields involve advanced mathematics, AND his colleagues (professional mathematicians, professors who teach upper level mathematics, etc.) to plaster a scathingly dismissively insulting comment on a colleagues intellect and his work on the first page. For those who forget (or never wished to learn) the intermediate value theorem and one or more proofs of it, it involves calculus. Students are introduced to it in their first calculus course, but even if whatever text they use includes a proof, the proof rests on hidden assumptions as it is too advanced. However, it is not beyond the level of undergraduate mathematics (a first course in real analysis, “advanced calculus”, higher mathematics, etc., will give a proof). Thus Körner is essentially saying that Brown, in the book Körner cites, is incapable of understanding upper-level undergraduate mathematics/beginning graduate level mathematics and his book is a demonstration to the world of his intellectual deficiencies and ignorance.
I’ve seen some very thinly veiled insults, jabs, backhanded compliments, etc., in academic literature before. I don’t think I’ve ever seen something so explicitly and thoroughly insulting to both another academic and that academic’s work before (and this isn’t even a paper; Brown’s work, which I obtained in its 2nd edition just to find out what Körner refers to, is a textbook on proofs for philosophers of mathematics that was years in the making- twice).
I don’t know whether to cheer or to object.