Explanation and Proof in Mathematics

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.

Gyozo G. Lang is Professor at the Eotvos Lorand University in Budapest, Hungary, President of the Electrochemical Committee of the Hungarian Academy of Sciences, he has been Regional Representative for Hungary of the International Society of Electrochemistry 2005-2010. He is a member of the Editorial Board of the Journal of Electrochemical Science and Engineering.Cesar A. Barbero is presently full professor and head of the Advanced Materials Program at UNRC. He is a permanent research fellow of the Argentinian Research National Council (CONICET) since 1995. Barbero received the Tajima Prize of the International Society of Electrochemistry (ISE) in 1996, the Rafael Labriola Prize of the Argentinian Chemistry Society (AQA) in 2004 and the Maria Cristina Giordano Prize of the Argentinian Society for Physical Chemistry Research (AAIFQ) in 2007. He is an IUPAC Fellow since 2000. In 2007 he received the John Simon Guggenheim Fellowship (USA). He has been invited professor at the universities of Paris VII (France), Alicante (Spain), La Laguna (Spain), Wales at Bangor (UK) and Buenos Aires (Argentina).