Krantz described a number of mathematical discoveries which characterize mathematical uniqueness from all other disciplines, whereby he indicated that mathematics discipline is distinguished from all others by its characteristic feature of proof. Krantz incorporates the idea of critical thinking in mathematics as a major factor that helps mathematicians to prove their work. He documents several works exemplifying the idea of proof and its benefits in mathematics including Euclid, Eudoxus, Pythagoras work among others. He discussed other works which were shown to be against proof in the mathematic study. Further, he endeavored to show how such proof in mathematics has been integrated and advanced in other disciplines in recent centuries. In his conclusion after the discussion of proof under different perspectives, he suggests that proof in mathematics will be perpetuated through expansion through the systems of interdisciplinary work.
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