The Language of Mathematics: Making the Invisible Visible by Keith J. Devlin
My rating: 4 of 5 stars
This is a fairly concise book. Devlin attempts to show us the construction of mathematics by its application and by demonstrating its conceptual genealogy. Of course, history of how a field grows is going to reveal its construction to us, although the language itself is at the highest level, hopelessly erudite.
Devlin’s prose is concise, easy to read and yet sacrifices very little complexity for its clarity. The task he has undertaken however is a difficult one. In striving to show us applicability, Delvin allows us glimpses of what math can do for us in the daily routines of the world in which we live. Delvin doesn’t strive to make a philosophical statement about math, yet it seems that he wants to posit mathematic’s reality as being on par with the one in which we live. To do this would require a more concise approach, directed by principles. The chapters in this book suggest that Devlin wishes to pursue such an endeavor and yet at times, he seems unable to present us little more than examples and applications. In fact, his last chapter, about the ‘Hidden Patterns of the Universe’ seems to attempt to encapsulate an argument that Mathematics is as real as the universe is; although Delvin never makes this remark.
I don’t have a problem with his content, or how he talks about it. I do have an issue with his organization. If anything, he seems to want to make his argument without making it; to throw at us a barrage of ideas so that we submit. Unfortunately, in his presentation of this massive amount of data, he lacks any kind of metaphysical or over arching ideal by which we can grasp that mathematics is real. Isn’t it his point that inductive examples, examples by experience there may be plenty of, but a real proof is one that rationally equates two values so that their identity of relation is assured?
If we were to take mathematics as being as real as the universe, we would have to see a mathematical proof of it somehow. And so to that end, Devlin does not make this statement, although he seems to suggest it with many vague chapter titles and ruminations on how various patterns in the universe are at least explainable in mathematics. Devlin does not, however, explore that all patterns are explainable in mathematics, just that math is so applicable. Such an undertaking would be, in a sense, near impossible without a cogent understanding of exactly what a pattern is in the first place.
Still, I did enjoy reading this book, and learned a few things in the process. If you think this is an interesting topic, you may also enjoy reading this book.
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