The Limits of Mathematics
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http://www.maa.org/mathland/mathtrek_2_23_98.html  


Ivars Peterson (MathTrek)  
In Godel's realm, no matter what the system of axioms or rules is, there will always be some assertion that can be neither proved nor invalidated within the system. Indeed, mathematics is full of conjectures assertions awaiting proof with no assurance that definitive answers even exist... Hilbert, Goedel, Turing, Chaitin: mathematics [is] much more of an experimental science than many mathematicians would be willing to admit.  


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