In the four decades since Imre Lakatos declared mathematics a
"quasi-empirical science," increasing attention has been paid to
the process of proof and argumentation in the field -- a
development paralleled by the rise of computer technology and the
mounting interest in the logical underpinnings of mathematics.
Explanantion and Proof in Mathematics assembles perspectives from
mathematics education and from the philosophy and history of
mathematics to strengthen mutual awareness and share recent
findings and advances in their interrelated fields. With examples
ranging from the geometrists of the 17th century and ancient
Chinese algorithms to cognitive psychology and current educational
practice, contributors explore the role of refutation in generating
proofs, the varied links between experiment and deduction, the use
of diagrammatic thinking in addition to pure logic, and the uses of
proof in mathematics education (including a critique of
"authoritative" versus "authoritarian" teaching styles).
A sampling of the coverage:
- The conjoint origins of proof and theoretical physics in
ancient Greece.
- Proof as bearers of mathematical knowledge.
- Bridging knowing and proving in mathematical reasoning.
- The role of mathematics in long-term cognitive development of
reasoning.
- Proof as experiment in the work of Wittgenstein.
- Relationships between mathematical proof, problem-solving, and
explanation.
Explanation and Proof in Mathematics is certain to attract a
wide range of readers, including mathematicians, mathematics
education professionals, researchers, students, and philosophers
and historians of mathematics.
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