Writing history is more difficult than writing
mathematics.
In mathematics, you can
always improve the way things are done
if you are dissatisfied. There is some
inner core of material that
has some intrinsic reality,
but in the end mathematics is largely a human invention.
You don't get to improve history.
Nor should you want to.
The way things actually happened is always
more interesting than the way someone feels
they might or, in a reasonable world,
would have happened. The whole point of history
is to recount how and why things happened
the way they did. In the history of
mathematics, this translates to the problem
of understanding the historical
development of ideas.
Many mathematicians (and for that matter
other scientists) don't understand this - they
often write about things as they feel they
should have been, rather than the way they were.
This short changes truth.
What historians do get to do is
change the interpretation of what facts
they get. Very often the facts themselves say little.
But it is important to separate fact from interpretation.
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