I often heard that late medieval scholastic philosophy became absurd in the questions it asked, the example always given is that philosophers would debate ‘how many angels could dance on the head of a pin’. Did any serious philosopher ever actually ask this question? Or was this just an absurd question dreamed up by the opponents of scholasticism?
And if anyone ever did seriously ask the question, what’s the answer?
No, it's a bit of folklore. In fact it's even a bit of folklore who supposedly invented the folklore as it's commonly attributed to Rabelais, who didn't write about it. The earliest known source (per Marshall and Walsham) is William Chillingworth's 1638 book The religion of Protestants: a safe way to salvation (link) is the earliest known statement of it; whether a million of angels may not sit upon a needle's point. In the 19th century it was brought up again for instance by the English writer Isaac D'Israeli (father of the Prime Minister Benjamin) who put it (in Curiosities of Literature) in the early 19th century “how many angels can dance on the head of a very fine needle without jostling one another?”.
There were, however, discussions that could indeed provide the fodder for this kind of satire. Thomas Aquinas, who discussed in Summa Theologica (c. 1270) on whether two angels could exist in the same space or not. The contemporary Franciscan, Saint Bonaventure, also discussed in his Commentary on the Sentences (Book 2, Distinction 2, Part 2, Article 2) a whole number of related points:
Question 1: Whether Angels are in a corporeal place?
Question 2: Whether an Angel is ever and at once in several places?
Question 3: Whether an Angel is in an indivisible or point-like place?
Question 4: Whether several Angels are together in the same place?
(or perhaps in modern physics terms, whether angels were elementary particles or composite, and whether they were Bosons or Fermions) Bonaventure was however perhaps the most thorough of angelologists in the 13th century, which was also the height of medieval angelology. (although angels and demons would make a huge comeback in different ways in the Renaissance)
But although they seem easy to mock, as Keck puts it: "the question of an angel's relationship to space was a legitimate and significant question, in part because it was interwoven with devotional concerns such as the angelic ministries." It was part of an systematic attempt at determining from scripture the nature of angels and their in the creation. (although if you want the full context, that's what the whole book is..)
Peter Marshall, Alexandra Walsham, Angels in the Early Modern World, Cambridge University Press, 2006
David Keck, Angels and Angelology in the Middle Ages, Oxford University Press, 1998