Let us look at some specific examples of mathematical work and see what philosophical lessons we can draw from them. We will find that the activity of mathematical research forces a recognition of the objectivity of mathematical truth. The "Platonism" of the working mathematician is not really a belief in Plato's myth; it is just an awareness of the refractory nature, the stubbornness of mathematical facts. They are what they are, not what we wish them to be.
KeywordsSimple Group Mathematical Object Rigorous Proof Riemann Hypothesis Finite Simple Group
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