August 3, 2007
Ambiguity and Paradox in Mathematics
Many people believe that mathematics provides a model of what thinking is, or should be. They imagine that mathematical thinking always proceeds in a logically rigorous, step-by-step fashion from one truth to another, like a formal proof or a computer program. In fact, insights in mathematics — whether they are the scholar's breakthroughs or the student's leap to a new level of understanding — involve a different mode of thinking that is essentially
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