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**1 - 5**of**5**### How mathematicians obtain conviction: Implications for mathematics instruction and research on epistemic cognition

, 2014

"... The received view of mathematical practice is that mathematicians gain certainty in mathematical assertions by deductive evidence rather than empirical or authoritarian evidence. This assumption has influenced mathematics instruction where students are expected to justify assertions with deductive ..."

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The received view of mathematical practice is that mathematicians gain certainty in mathematical assertions by deductive evidence rather than empirical or authoritarian evidence. This assumption has influenced mathematics instruction where students are expected to justify assertions with deductive arguments rather than by checking the assertion with specific examples or appealing to authorities. In this paper, we argue that the received view about mathematical practice is too simplistic; some mathematicians sometimes gain high levels of conviction with empirical or authoritarian evidence and sometimes do not gain full conviction from the proofs that they read. We discuss what implications this might have, both for for mathematics instruction and theories of epistemic cognition.

### Future Prospects for Computer-Assisted Mathematics

, 2005

"... The recent rise of “computer-assisted” and “experimental” mathematics raises intriguing questions as to the future role of computation in mathematics. These results also draw into question the traditional distinctions that have been drawn between formal proof and computationally-assisted proof. This ..."

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The recent rise of “computer-assisted” and “experimental” mathematics raises intriguing questions as to the future role of computation in mathematics. These results also draw into question the traditional distinctions that have been drawn between formal proof and computationally-assisted proof. This article explores these questions in the context of the growing consensus among computer technologists that Moore’s Law is likely to continue unabated for quite some time into the future, producing hardware and software much more powerful than what is available today.

### Some reflections on mathematics and its relation to computer science

, 2014

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### Exploratory experimentation in experimental mathematics: A glimpse at the PSLQ algorithm

"... From a philosophical viewpoint, mathematics has traditionally been dis-tinguished 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, in the ..."

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From a philosophical viewpoint, mathematics has traditionally been dis-tinguished 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, in the