## Implications of Experimental Mathematics for the Philosophy of Mathematics,” chapter to appear

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Venue: | Current Issues in the Philosophy of Mathematics From the Viewpoint of Mathematicians and Teachers of Mathematics, 2006. [D-drive Preprint 280 |

Citations: | 2 - 1 self |

### BibTeX

@INPROCEEDINGS{Borwein_implicationsof,

author = {Jonathan Borwein},

title = {Implications of Experimental Mathematics for the Philosophy of Mathematics,” chapter to appear},

booktitle = {Current Issues in the Philosophy of Mathematics From the Viewpoint of Mathematicians and Teachers of Mathematics, 2006. [D-drive Preprint 280},

year = {}

}

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### Abstract

Christopher Koch [34] accurately captures a great scientific distaste for philosophizing: “Whether we scientists are inspired, bored, or infuriated by philosophy, all our theorizing and experimentation depends on particular philosophical background assumptions. This hidden influence is an acute embarrassment to many researchers, and it is therefore not often acknowledged. ” (Christopher Koch, 2004) That acknowledged, I am of the opinion that mathematical philosophy matters more now than it has in nearly a century. The power of modern computers matched with that of modern mathematical software and the sophistication of current mathematics is changing the way we do mathematics. In my view it is now both necessary and possible to admit quasi-empirical inductive methods fully into mathematical argument. In doing so carefully we will enrich mathematics and yet preserve the mathematical literature’s deserved reputation for reliability—even as the methods and criteria change. What do I mean by reliability? Well, research mathematicians still consult Euler or Riemann to be informed, anatomists only consult Harvey 3 for historical reasons. Mathematicians happily quote old papers as core steps of arguments, physical scientists expect to have to confirm results with another experiment. 1 Mathematical Knowledge as I View It Somewhat unusually, I can exactly place the day at registration that I became a mathematician and I recall the reason why. I was about to deposit my punch cards in the ‘honours history bin’. I remember thinking “If I do study history, in ten years I shall have forgotten how to use the calculus properly. If I take mathematics, I shall still be able to read competently about the War of 1812 or the Papal schism. ” (Jonathan Borwein, 1968) The inescapable reality of objective mathematical knowledge is still with me. Nonetheless, my view then of the edifice I was entering is not that close to my view of the one I inhabit forty years later. 1 The companion web site is at www.experimentalmath.info