How to Read Mathematics

Re:How to Read Mathematics by alderssc on Tuesday June 28, 2011 @03:55PM (#2707025)

As a math major, my view is probably biased, but I feel like one of the reasons mathematics is so widely used and applied in other fields such as physics, CS, and even biology these days is that they express or model, to a high degree of accuracy, patterns that recur in all these fields. The mathematical notation is the most general and abstract form of expressing these patterns. My feeling is that to not learn the language of math dooms one to reinvent the wheel because they don't realize that the problem she is working on has been solved before in a more general case by some one else. In those cases where the problem hasn't been solved before, the solution leads to new areas or notation which can show up in unexpected ways in different branches of science.

Without this common language, we would have a specialized language for every field, allowing little "cross-pollination". As an example, in evolutionary biology, take the NK model of epistatic interactions which models gene interactions. It just so happens that this model is extremely similar to a thing in statistical physics called a spin-glass. Without mathematics the biologist would have to sit and work out all the details of these epistatic interactions before getting to actually do biology. So in short, mathematics saves you time by expressing common patterns or ideas.

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Re:How to Read Mathematics by ColinWright on Tuesday June 28, 2011 @04:19PM (#2707114)

There was an example not so long ago of a paper published in, I think, biology, where the author had invented a wonderful new technique for more accurate estimates of the area under a curve.

It was Simpson's rule.

CORRECTION:

It was worse than that. It was the trapezoidal rule:

http://care.diabetesjournals.org/content/17/2/152.abstract

The author named it after themselves:

    ... The Tai model allows flexibility
    in experimental conditions ...

and got 75 citations ...

http://fliptomato.wordpress.com/2007/03/19/medical-researche...

Unbelievable.

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Re:How to Read Mathematics by slowpoke on Tuesday June 28, 2011 @04:59PM (#2707306)

>So in short, mathematics saves you time by expressing common patterns or ideas.

I wasn't arguing that. In fact, I said that math is lending me and students of other fields tools to use and apply. The problem lies in the expression of said tools (which is exactly what I mean with "arcance notations") and the inability of many mathematicians - no offense - to separate those two concepts (tools/mechanics and expression) from another. They assume that they are completely inseparable, which is not only part, but a major source of the problem. Any attempts to somehow make math less obscure (or even just suggest it) is met, in great parts, with conservative hostility. I've seen mathematicans claim "that I was telling them that their profession is pointless and should be abolished" when all I was saying that a majority of the expression of math is incredibly obscure/arcance to most people which are not mathematicians and mostly not suited for practical appliance (as in, appliance in fields of science other than math).

Also, it's a valid point to say that we shouldn't have special syntax/language for every appliance of math imaginable. That would indeed not only be stupid, but actually /increase/ obscurity. We should, however, stop excusing the obscurity of math with "it's shorter to write". Readability and - most importantly - comprehensibility should /always/ come before convenience. Even in math.

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