Lately I've been thinking about number theory, Hilbert's program, and arithmetic. And I've been wondering if the axioms of arithmetic constitute a mathematical description of the cognitive processes underlying arithmetic. Hilbert's program was simply (although it wasn't simple) an effort to formalize mathematics in axiomatic form and to show the consistency of the system. Godel threw a bomb into the effort with his Incompleteness theorem.
A more thorough and better description of Hilbert's program is available at The Stanford Encyclopedia of Philosophy - Hilbert's Program.
Today's tags: math, mathcog
6 comments:
Nothing like a little light reading on a Saturday Night. ;)
There's always a juicy romance novel to calm things down. *grin*
Hmmm... I'm wondering (after reading the opening of the Hilbert article) if it might just be that Hilbert liked order and method and this was his attempt to codify mathematics as he desired.
After all, proofs (the mathematician's best friend) are a logical progression of steps. A mind that likes order and method, would certainly be looking for such a solution to just about everything in life. (I'm sure he would have hated the "God playing dice with the universe" thing too *grin*)
Or it could just be that I'm tired and can't think straight right now. You never know...
Teresa - It's the curse of geometers. *grin*
When the Clay Institute created their Millenium Problems program, they were in part paying homage to Hilbert's 1900 challenge to the math community. I forget now if the 7 Millemium Problems include one (Riemann Hypothesis) or two of Hilbert's original 23 open problems.
I'm out of my depth here.
However, I *do* recognize Godel's name from this book:
http://www.amazon.com/gp/product/0465026567/sr=8-1/qid=1143748036/ref=pd_bbs_1/104-6199166-4467105?%5Fencoding=UTF8
Give me time, Harvey, and you'll be swimming with the sharks. :-)
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