What is it that mathematicians say? Something like, "One page of symbols and formula is better than 100 pages of text"

We may say it, but it's not always true.

In my experience, a lot of the reason mathematics is so inaccessible to the masses is the focus on obscure notional tricks, rather than the underlying reasoning.

It was quite a jarring experience when I finally had a mathematics teach in my final year of high school start teaching counting arguments using plain english; it all felt seemed somehow suspect, less logical somehow.

It also demonstrated just how much time I was taught to spend translating real world problems into formal mathematical notation before I began reasoning about the solution.

As a mathematician, I understand the power of a good notation; but I also understand how quickly formal notation can become a barrier to understanding. I was taught to always break reasoning down into discrete steps; synthesis is almost always easier than reduction. The same idea applies to coding: break code into small, discrete, provably correct steps whenever possible.

The exact opposite of this is the mathematics trick a few undergrads pulled on their TA. Not knowing how to solve the problem correctly, they wrote the beginning, worked ahead a few stesp, wrote the desired conclusion, worked back a few steps, and linked the two sections with the words: "Trivially, the result follows", and relied on the TA to agree that the result was "trivially correct". Since their TA was a genius (with a 90%+ average in the hardest university math courses every single year), he would often agree that it was "obviously correct", and they'ld get full marks through sheer guesswork.

Too much coding I see these days ends up being of the "trivally correct" stripe: people stare at code for three days, can't find the bug, finally decipher the flaw and fix it, and then declare what the code does to be "obviously correct now".

Me, I learned the hard way: better a series of small steps where you can find your mistakes, than a complex expression of interwoven logic that don't quite work, though your not sure why...
-- Ytreq Q. Uiop

In reply to Re^8: Thread on Joel on software forum : "I hate Perl programmers." by Anonymous Monk
in thread Thread on Joel on software forum : "I hate Perl programmers." by techcode

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