Why did Israel Gelfand say “You have to be fast only to catch fleas,” and how does this phrase apply to researchers?
To me, at least, the metaphor seems clear. Anyone can pick up pennies off the street, but it takes hard work and time to amass a fortune. Hmmm. Another metaphor.
If you want to make a reputation publishing trivial (or small) results, then you have to be fast, since they are available to most mathematicians in a subfield. But if you want to do great things (catch bears, for example), it will take time and effort. It will, necessarily be slower and that is ok as the results are more profound.
The word "only" in the quote is very important. Yes, you need to be fast to catch small, fleeting, things, but only for that. Without that word, the meaning would be entirely different.
Gelfand, of course, is known for some pretty profound work. They didn't result from 3 week research projects.
And, this is only my speculation, since he can't be asked directly.
This is just speculation, but as a native Russian speaker, I'm pretty sure this is a literal translation of a Russian saying, better translated as "You only need haste when catching fleas" (Спешка нужна только при ловле блох). Since Israel Gelfand had lived in USSR, I think it's pretty likely he was referencing it.
It's pretty much a generic "haste makes waste" proverb that means you shouldn't rush and that you should think before doing something.
Not an answer, but another "catch a flea" quote from a mathematician.
In guessing a conundrum, or in catching a flea, we do not expect the breathless victor to give us afterwards, in cold blood, a history of the mental or muscular efforts by which he achieved success; but a mathematical calculation is another thing.
A Tangled Tale
Answers to Knot 4
I am only speculating, but the meaning in this context seems clear to me: "You only need to be quick about generating and publishing material when the material is relatively trivial." The implication is that you can take your time, not only not rushing, but even being somewhat slow, when you are generating momentous material, that is to say, solving big problems.
Furthermore, "fleas" may allude to opportunities to generate trivial new mathematical content in the form of minor nitpicks, adjustments, corrections, and additions to a recently published big breakthrough. These "fleas" are thus perhaps small spin-offs from recent breakthroughs that are easily seen by everyone. There may be an allusion to a woolly mammoth or other large animal, brought down by some great hunter, that has fleas on it. You would need to be quick if you are to catch one or more of them before they have been caught by other hunters.
I also get a sense that catching fleas is not something to be proud of.
I don't think this is accurate any more, unfortunately people are expected to come up even with big results with a reasonable amount of speed. Wiles and Fermat's Last Theorem is a bit of an exception if I remember rightly, as he was salami slicing and publishing intermediate results as separate papers on the way to the proof to give the illusion of productivity (see the book by Singh).
I'm also interested in the extent to which this applies to scientific research and physics. I guess it still applies but then there really is a race for results and sometimes time is of the essence. In general a lot of emphasis is given towards those people that can make very quick (not necessarily non-trivial) extensions of other people's work or to come up with quick explanations of recent experimental results.
In physics, Einstein said he had no time for those physicists who 'find where the board is thin and drill lots of small holes' ie. he was interested in things which took a lot of thought and conceptual understanding rather than just choosing what looked to be an area with lots of quick results which can be obtained with relative ease and speed.