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William D'Alessandro
University of Illinois, Chicago (PhD)
  1. Proving Quadratic Reciprocity: Explanation, Disagreement, Transparency and Depth.William D'Alessandro - 2020 - Synthese:1-44.
    Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to Gauss (...)
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  2. Explanation in Mathematics: Proofs and Practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11).
    Mathematicians distinguish between proofs that explain their results and those that merely prove. This paper explores the nature of explanatory proofs, their role in mathematical practice, and some of the reasons why philosophers should care about them. Among the questions addressed are the following: what kinds of proofs are generally explanatory (or not)? What makes a proof explanatory? Do all mathematical explanations involve proof in an essential way? Are there really such things as explanatory proofs, and if so, how do (...)
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    Teaching and Learning Guide For: Explanation in Mathematics: Proofs and Practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11).
    This is a teaching and learning guide to accompany "Explanation in Mathematics: Proofs and Practice".
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