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A series of chapters all set in the eighteenth century consider topics such as John Marsh's techniques for the computation of decimal fractions, Euler's efforts to compute the surface area of scalene cones, a little-known work by John Playfair on the practical aspects of mathematics, and Monge's use of descriptive geometry.

The remaining chapters deal with the philosophy of twentieth-century mathematics through topics such as an historically informed discussion of finitism and its limits; a reexamination of Mary Leng's defenses ofmathematical fictionalism through an alternative, anti-realist approach to mathematics; and a look at the reasons that mathematicians select specific problems to pursue.

Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.

Full citation:

The definitions and theorems of the spherics of theodosios

Thomas R S D

1-21

John Marsh and the curious world of decimal arithmetic

Melville Duncan J.

23-42

Euler's discovery and resolution of d'Alembert's paradox

Hackborn William W.

43-57

Euler's work on the surface area of scalene cones

Curtin Daniel J.

59-67

What mathematics Rittenhouse knew

Alexander Marion W.

69-89

John Playfair's approach to "the practical parts of the mathematics"

Ackerberg-Hastings Amy

91-107

Monge's descriptive geometry in three examples

Baltus Christopher

109-120

The culture of research mathematics in 1860s Prussia

Fraser Craig

121-140

The axiom of choice as paradigm shift

Therrien Valérie Lynn

141-155

Boltzmann et Vlasov

Godard Roger

157-166

Takeuti's well-ordering proof

Darnell Eamon; Thomas-Bolduc Aaron

167-180

A non-error theory approach to mathematical fictionalism

Bériault Phil

181-189

Mathematical problem choice and the contact of minds

Ashton Zoe

191-203