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All of the analysts were eating in spirals, and the algebraists in rows
это очень смешно

Back when I was in grad school there was a department lunch with corn
on the cob. Partway through the meal one of the analysts looked around
the room and remarked, "That's odd, all of the analysts are eating
corn one way and the algebraists are eating corn another!" Everyone
looked around. In fact everyone was eating the corn in one of two
ways. One way was to munch over the length of the corn in a straight
line, back up, turn slightly, and do another row across. Kind of like
how an old typewriter goes. The other way was to go around in a
spiral. All of the analysts were eating in spirals, and the
algebraists in rows.

There were a number of mathematicians present whose fields of study
didn't make it clear whether they were on the analysis or algebra side
of things. We went around and asked, and in every case the way they
ate corn matched their preference. Since then I've made a point of
amusing myself by asking mathematicians I meet whether they prefer
algebra or analysis, and then predicting which way they will eat
corn. I'm probably up to 40 or so by now, and in every case but one
I've been able to correctly predict how they eat corn. The one
exception was a logician who claimed to be exactly on the fence
between the two. When I explained the corn thing to him he looked
surprised, and said that he had an unusual way of eating corn. He went
in loose spirals! In other words he truly was a perfect combination of
algebra and analysis!

If you have even a passing familiarity of probability, it is clear
that despite how unbelievable it initially is that the type of
mathematics you prefer is connected to how you eat corn, it is pretty
much certain that there actually is a very strong connection. If you
believe, as I do, that this difference is connected to how we think
about other things, then there must be some odd connection between how
we like to understand the world and how we eat corn. Why is another
matter.

How do I explain the distinction between algebra and analysis? Well
the best way to understand it is to ask you to study advanced
mathematics. You will have to take many courses with the word
"algebra" in the name, and others with "analysis" in the name. By the
time you're done you'll have experienced the difference, and you'll be
clear on which you prefer. Odds are you won't do that, but that is the
most reliable way to come to understand it.

If I have to wave my hands and explain it, I would explain it like
this. In algebra there are sequences of operations which have proven
to be important and effective in one circumstance. Algebraists try to
reuse these operations in different contexts in the hopes that what
proved effective in one situation will be effective again. By contrast
an analyst is likely to form an idiosyncratic mental model of specific
problems. Based on that mental model you have intuitions that let you
carry out long chains of calculations that are, in principle,
obviously going to lead to the right thing. Typically your intuition
is correct to within a constant factor, and you're only interested in
some sort of limiting behavior so that is fine.

дьяволы, ангелы.. кукуруза!

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