That is a splendid 1996 book on mathematics and mathematical researchers, by Gian-Carlo Rota. I found philosophical, mathematical, and also managerial insights on most of the pages. It is playful and yet earnestly serious at the same time. Here is one bit:
He [Alonzo Church] looked like a cross between a panda and a large owl. He spoke in complete paragraphs which seemed to have been read out of a book, evenly and slowly enunciated, as by a talking machine. When interrupted, he would pause for an uncomfortably long period to recover the thread of the argument. He never made casual remarks: they did not belong in the baggage of formal logic. For example, he would not say “It is raining.” Such a statement, taken in isolation, makes no sense. (Whatever it is actually raining or not does not matter; what matters is consistence.) He would say instead: “I must postpone my departure for Nassau Street, inasmuch as it is raining, an act which I can verify by looking out the window.”
It is full of the sociology of everyday life, in mathematical communities that is, for instance:
How do mathematicians get to know each other? Professional psychologists do not seem to have studied this question; I will try out an amateur theory. When two mathematicians meet and feel out each other’s knowledge of mathematics, what they are really doing is finding out what each other’s bottom line is. It might be interesting to give a precise definition of a bottom line; in the absence of a definition, we will give some typical examples.
…I will shamelessly tell you what my bottom line is. It is placing balls into boxes, or as Florence Nightingale David put it with exquisite tact in her book Combinatorial Chance, it is the theory of distribution and occupancy.
The author fears the influence of philosophy on mathematics, which led to this paragraph:
Philosophical arguments are emotion-laden to a greater degree than mathematical arguments and written in a style more reminiscent of a shameful admission than of a dispassionate description. Behind every question of philosophy there lurks a gnarl of unacknowledged emotional cravings which act as a powerful motivation for conclusions in which reason plays at best a supporting role. To bring such hidden emotional cravings out into the open, as philosophers have felt it their duty to do, is to ask for trouble. Philosophical disclosures are frequently met with the anger that we reserve for the betrayal of our family secrets.
Definitely recommended, the book also has some of the best and most concrete discussions of Husserl’s philosophy I have seen, along with a meta-account of such, and also there is a discussion of the exoteric and esoteric readings of cosmology and black holes and indeed mathematics too. Here is further information on Gian-Carlo Rota the author.
For the pointer to the book I thank Patrick Collison.