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Computers in mathematical inquiry
 in The Philosophy of Mathematical Practice
, 2008
"... Computers are playing an increasingly central role in mathematical practice. What are we to make of the new methods of inquiry? In Section 2, I survey some of the ways that computers are used in mathematics. These raise questions that seem to have a generally epistemological character, ..."
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Computers are playing an increasingly central role in mathematical practice. What are we to make of the new methods of inquiry? In Section 2, I survey some of the ways that computers are used in mathematics. These raise questions that seem to have a generally epistemological character,
What’s experimental about experimental mathematics? ∗
, 2008
"... From a philosophical viewpoint, mathematics has often and traditionally been distinguished from the natural sciences by its formal nature and emphasis on deductive reasoning. Experiments — one of the corner stones of most modern natural science — have had no role to play in mathematics. However, dur ..."
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From a philosophical viewpoint, mathematics has often and traditionally been distinguished from the natural sciences by its formal nature and emphasis on deductive reasoning. Experiments — one of the corner stones of most modern natural science — have had no role to play in mathematics. However, during the last three decades, high speed computers and sophisticated software packages such as Maple and Mathematica have entered into the domain of pure mathematics, bringing with them a new experimental flavor. They have opened up a new approach in which computerbased tools are used to experiment with the mathematical objects in a dialogue with more traditional methods of formal rigorous proof. At present, a subdiscipline of experimental mathematics is forming with its own research problems, methodology, conferences, and journals. In this paper, I first outline the role of the computer in the mathematical experiment and briefly describe the impact of high speed computing on mathematical research within the emerging subdiscipline of experimental mathematics. I then consider in more detail the epistemological claims put forward within experimental mathematics and comment on some of the discussions that experimental mathematics has provoked within the mathematical community in recent years. In the second part of the paper, I suggest the notion of exploratory experimentation as a possible framework for understanding experimental mathematics. This is illustrated by discussing the socalled PSLQ algorithm.
11 Computers in Mathematical Inquiry
"... Computers are playing an increasingly central role in mathematical practice. What are we to make of the new methods of inquiry? In Section 11.2, I survey some of the ways in which computers are used in mathematics. These raise questions that seem to have a generally epistemological ..."
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Computers are playing an increasingly central role in mathematical practice. What are we to make of the new methods of inquiry? In Section 11.2, I survey some of the ways in which computers are used in mathematics. These raise questions that seem to have a generally epistemological
Chapter 1 Checking proofs
"... Argumentative practice in mathematics evidently takes a number of shapes. An important part of understanding mathematical argumentation, putting aside its special subject matters (numbers, shapes, spaces, sets, functions, etc.), is that mathematical argument often tends toward formality, and it ofte ..."
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Argumentative practice in mathematics evidently takes a number of shapes. An important part of understanding mathematical argumentation, putting aside its special subject matters (numbers, shapes, spaces, sets, functions, etc.), is that mathematical argument often tends toward formality, and it often has superlative epistemic goals: