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UNDERSTANDING PROOFS JEREMY AVIGAD
 

Summary: UNDERSTANDING PROOFS
JEREMY AVIGAD
"Now, in calm weather, to swim in the open ocean is as easy to the practised
swimmer as to ride in a spring-carriage ashore. But the awful lonesomeness is
intolerable. The intense concentration of self in the middle of such a heartless
immensity, my God! who can tell it? Mark, how when sailors in a dead calm bathe
in the open sea--mark how closely they hug their ship and only coast along her
sides." (Herman Melville, Moby Dick, Chapter 94)
Introduction
What does it mean to understand mathematics? How does mathematics help us
understand?
These questions are not idle. We look to mathematics for understanding, we
value theoretical developments for improving our understanding, and we design
our pedagogy to convey understanding to students. Our mathematical practices
are routinely evaluated in such terms. It is therefore reasonable to ask just what
understanding amounts to.
The issue can be addressed at different levels of generality. Most broadly, we
need to come to terms with the sort of thing that understanding is, and the sort of
thing that mathematics is, in order to discuss them in an appropriate manner. We
can narrow our focus by noticing that the term "understanding" is used in different

  

Source: Avigad, Jeremy - Departments of Mathematical Sciences & Philosophy, Carnegie Mellon University

 

Collections: Multidisciplinary Databases and Resources; Mathematics