New book: Philosophy makes better mathematicians [View all]

May 28, 2013 - 4:00:00 AM

Pythagorean numbers were only positive integers, and this limited toolbox worked fine until one of his students discovered that the diagonal of a square with sides being integers could not be described only using integers. The problem was that the square root of 2 was not a rational number, but an irrational number. Immediately the problem was removed by throwing the presumptuous student in the sea, where he drowned - a radical, though not long-lasting solution. There was no getting around the fact that integers and fractions were not enough to describe the world. The mathematical way to solve the problem was to expand the concept of numbers and introduce irrational numbers. Negative numbers were also needed, but they came only later.

By University of Southern Denmark
Does mathematics consist of absolute truths, and are mathematical results always indisputable? Most people would probably respond yes without thinking twice, but the answer is actually also in part no. Mathematics can also be approached from a philosophical angle - and it is important to do so. Otherwise, we cannot ask the big, important questions in life, writes University of Southern Denmark-scientist in a new book.

The author is Jessica Carter, Associate Professor at the Department of Mathematics and Computer Science at University of Southern Denmark. She teaches philosophy, and together with Tinne Hoff Kjeldsen from Roskilde University Center in Denmark she has written about the importance of learning some philosophy and history in order to become a competent and reflective mathematician.

The book is called International Handbook of Research in History, Philosophy and Science Teaching and it will be published by Springer Verlag in June 2013. The two authors have contributed with the chapter: The Role of History and Philosophy in University Mathematics Education.

Many believe that mathematics cannot be discussed. But it can - and it is important to do so. When discussing mathematics from a philosophical point of view, we stop learning equations and formulas by heart and start talking about all the different ways we can work with mathematics and the places it can take us.

http://www.rxpgnews.com/research/New-book-Philosophy-makes-better-mathematicians_638875.shtml