A nice article on the history of mathematical proof
I recently read an article on the history and concept of mathematical proof. I think it is a nice intro to the history of mathematics.
What I found particularly interesting was the fact that mathematics is built on only a small set of axioms. An axiom (or postulate), by the way, is a mathematical statement of fact, formulated using the terminology that has been defined in the definitions, that is taken to be self-evident. Group theory, for example, is built on just three axioms, the subject of real variables on twelve axioms, set theory on eight axioms, and Euclidean geometry on five axioms. David Hilbert in fact believed fervently that there ought to be a universal (and rather small) set of axioms for mathematics, and that all mathematical theorems should be derivable from those axioms.
The author explains basic concepts of mathematics clearly and I am sure readers who do not have background in mathematics will know more about mathematics and its rather amusing history after reading the article.
In closing, the author also gave his thoughts on how mathematics would look like in many years to come. He observes that as the field of applied mathematics is growing, interdisciplinary collaborations of scientists from a variety of backgrounds will become the panorama for modern research. I personally take this remark to be positive since I believe that all science should be integrated. I rejoice to see men from various fields working together to discover the truths of God hidden in His creation.
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- January 23, 2008 / 02:21