Introduction by *Reuben Hersh ...........................................................................* vii

About the Authors............................................................................................. xvii

**Chapter 1**

A Socratic Dialogue on Mathematics ................................................................ 1

*Alfréd Rényi*

**Chapter 2**

“Introduction” to *Filosofia e matematica*........................................................... 17

*Carlo Cellucci*

**Chapter 3**

On Proof and Progress in Mathematics ............................................................. 37

*William P. Thurston*

**Chapter 4**

The Informal Logic of Mathematical Proof ...................................................... 56

*Andrew Aberdein*

**Chapter 5**

Philosophical Problems of Mathematics in the Light

of Evolutionary Epistemology........................................................................... 71

*Yehuda Rav*

**Chapter 6**

Towards a Semiotics of Mathematics ................................................................ 97

*Brian Rotman*

**Chapter 7**

Computers and the Sociology of Mathematical Proof....................................... 128

*Donald MacKenzie*

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**Chapter 8**

From G.H.H. and Littlewood to XML and Maple:

Changing Needs and Expectations in Mathematical Knowledge Management....... 147

*Terry Stanway*

**Chapter 9**

Do *Real* Numbers Really Move? Language, Thought, and Gesture:

The Embodied Cognitive Foundations of Mathematics .................................... 160

*Rafael Núñez*

**Chapter 10**

Does Mathematics Need a Philosophy? ............................................................. 182

*William Timothy Gowers*

**Chapter 11**

How and Why Mathematics Is Unique as a Social Practice .............................. 201

*Jody Azzouni*

**Chapter 12**

The Pernicious Influence of Mathematics upon Philosophy.............................. 220

*Gian-Carlo Rota*

**Chapter 13**

The Pernicious Influence of Mathematics on Science........................................ 231

*Jack Schwartz*

**Chapter 14**

What Is Philosophy of Mathematics Looking for? ............................................ 236

*Alfonso C. Ávila del Palacio*

**Chapter 15**

Concepts and the Mangle of Practice Constructing Quaternions...................... 250

*Andrew Pickering*

**Chapter 16**

Mathematics as Objective Knowledge and as Human Practice.......................... 289

*Eduard Glas*

**Chapter 17**

The Locus of Mathematical Reality:

An Anthropological Footnote ........................................................................... 304

*Leslie A. White*

**Chapter 18**

Inner Vision, Outer Truth.................................................................................. 320

*Reuben Hersh*