In a paper entitled “Tight single-change covering designs — the inside story”, published in the Bulletin of the Institute of Combinatorics and its Applications, Donald Preece described how a piece of mathematical research actually gets done, forgotten, revived, extended, and finally published.
Content of the Bull. ICA is not easily available. I am sorry to report that my copies ended up in the skip. But thanks to the kind offices of Ian Anderson, I have my hands on a copy of the paper. The opening paragraph is well worth quoting, for the light it throws both on its subject and on its author.
“But how do you DO research in mathematics?”, people often wonder. Even a distinguished laboratory scientist may be unable to comprehend how research can be possible without test-tubes, pipettes, and bubbling flasks of evil-smelling brews. Well, you scratch your head; you scratch the back of an envelope with a pencil; you scratch a blackboard with a piece of chalk. You lie in the bath and gaze alternately at the ceiling and at your navel. You do the washing-up or go to sleep and you leave your subconscious to do your thinking for you – often astonishingly successfully. And a good old screaming-match with your colleagues can sometimes help too.
If you can get your hands on it, read the whole paper. It explains something I hadn’t known, the origins of the tight single-change covering design problem in the early days of computing, when only a few rows of a matrix could be stored in memory at a time.