The Analyst by Bishop George Berkeley, the famous pamphlet against vagueness of early Analysis, ends with a list of 67 Queries. Quite a number of them, in my humble opinion, remain unanswered, this one in particular:
Qu. 38. Whether tedious Calculations in Algebra and Fluxions be the likeliest Method to improve the Mind? And whether Mens being accustomed to reason altogether about Mathematical Signs and Figures, doth not make them at a loss how to reason without them?
To answer the first part of this question with, I would remark that there is usually some meaning behind these calculations that drives and motivates them. It’s like a pianist doesn’t just press the keys, but does so to make music. As for the second part, I’m not sure, there might be some truth to that observation.
By: Misha on December 26, 2008
at 8:01 pm
we were *already* at a loss how to reason
without ’em; introducing the symbols
hasn’t done any actual *harm* …
but i exaggerate. the trouble arises,
in my opinion, because practice in maths
leads to the idea that every statement
should have a well-defined *meaning*.
this is very seldom the case outside
of mathematics and makes us
hard to “reason” with because we keep
expecting people to care about things
like logical consequences.
like i tell my students:
a lot of people think math is hard–
and it *is* hard — it’s just easier
than anything else.
By: vlorbik on January 7, 2009
at 4:07 pm