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Conventional Wisdom
• There is a sort of “standard story” of what mathematics is, that most of us are taught as be take math classes.
• Mathematics is:– Pure– Abstract– Absolutely True– Timeless– Etc.
The Mathematical Experience
• Your text for this section has, I think, two aims:– To give the reader some feeling for what it is like to do mathematics, and to be part of the mathematical community, with all its joys, frustrations, dilemmas, the thrill of victory, the agony of defeat.
– To explore some (philosophical) beliefs about the nature of mathematics and in particular, to argue for a particular philosophical position they call humanist mathematics. At the same time, they argue against many parts of the “standard story.”
The Authors
• It’s important to remember that the authors are successful professional mathematicians, so they do know what it’s like to do mathematics, and they are committed to the importance of mathematics.
Reuben Hersh
• Reuben Hersh’smathematical specialty is partial differential equations, and so he is very sympathetic to applied mathematics.
Phillip J. Davis
• Phillip J. Davis worked in numerical analysis and approximation theory, and so he is also very sympathetic to applied mathematics.
Davis & Hersh
• They have some good‐natured fun at the expense of mathematicians, but it is for a purpose: To make their philosophical point about what mathematics is.