# New book: Philosophy makes better mathematicians

May 28, 2013Does 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."

According to Jessica Carter it is important to stamp out the long-lived myth that mathematics is indisputable.

"There are many examples of matters within mathematics that can be discussed. I do not believe that the rigor of mathematics is up for discussion, but I think we should deal with the fact that it is changing and evolving as all other sciences."

A philosophical question, that can evoke many thoughts from a mathematician, is: "Has mathematics always existed, and do we know about it, because we have discovered it? Or has man created mathematics? "

The Greek philosopher Plato believed that mathematics is eternal, because concepts and ideas have their own existence. Opposite to this idea later philosophers believed that concepts and ideas cannot exist independently of man, and therefore mathematics is something that has been invented.

"When I teach philosophy to our mathematics students and ask them to think about this question, my main point is not to give them an answer to the question. The aim is rather to teach the mathematics students to think philosophically about mathematics, to think critically, to ask questions, to analyze arguments and to assess assumptions. Mathematics is a subject which, like all other subjects has undergone development, and mathematicians, too, get smarter by thinking philosophically, reflecting and putting the subject into perspective."

Several centuries before Christ the Greek thinker Pythagoras believed that numbers were the basis of everything in the world. He explained the world from natural numbers and operated only with these and fractions (the ratio of natural numbers).

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.

"This story illustrates that mathematics is not fixed. Even mathematics has undergone an evolution, and it will continue to do so. Today's mathematicians are in the process of developing new mathematics, and mathematics students should be made aware of this, "says Jessica Carter.

-end-

**Philosophy and Mathematics at the University of Southern Denmark**

All students at the University of Southern Denmark are taught philosophy of science. The course runs over seven weeks and is 5 ECTS (European Credit Transfer System. 300 ECTS corresponds to a typical five-year university degree).

**Contact:**Jessica Carter, Department of Mathematics and Computer Science, University of Southern Denmark. Tel: +45 6550 2358th Email: jessica@imada.sdu.dk

This press release was written by press officer Birgitte Svennevig.

University of Southern Denmark

**Related Mathematics Articles:**

Could mathematics help to better treat cancer?

Impaired information processing may prevent cells from perceiving their environment correctly; they then start acting in an uncontrolled way and this can lead to the development of cancer.

Impaired information processing may prevent cells from perceiving their environment correctly; they then start acting in an uncontrolled way and this can lead to the development of cancer.

People can see beauty in complex mathematics, study shows

Ordinary people see beauty in complex mathematical arguments in the same way they can appreciate a beautiful landscape painting or a piano sonata.

Ordinary people see beauty in complex mathematical arguments in the same way they can appreciate a beautiful landscape painting or a piano sonata.

Improving geothermal HVAC systems with mathematics

Sustainable heating, ventilation, and air conditioning systems, such as those that harness low-enthalpy geothermal energy, are needed to reduce collective energy use and mitigate the continued effects of a warming climate.

Sustainable heating, ventilation, and air conditioning systems, such as those that harness low-enthalpy geothermal energy, are needed to reduce collective energy use and mitigate the continued effects of a warming climate.

How the power of mathematics can help assess lung function

Researchers at the University of Southampton have developed a new computational way of analyzing X-ray images of lungs, which could herald a breakthrough in the diagnosis and assessment of chronic obstructive pulmonary disease (COPD) and other lung diseases.

Researchers at the University of Southampton have developed a new computational way of analyzing X-ray images of lungs, which could herald a breakthrough in the diagnosis and assessment of chronic obstructive pulmonary disease (COPD) and other lung diseases.

Mathematics pushes innovation in 4-D printing

New mathematical results will provide a potential breakthrough in the design and the fabrication of the next generation of morphable materials.

New mathematical results will provide a potential breakthrough in the design and the fabrication of the next generation of morphable materials.

More democracy through mathematics

For democratic elections to be fair, voting districts must have similar sizes.

For democratic elections to be fair, voting districts must have similar sizes.

How to color a lizard: From biology to mathematics

Skin color patterns in animals arise from microscopic interactions among colored cells that obey equations discovered by Alan Turing.

Skin color patterns in animals arise from microscopic interactions among colored cells that obey equations discovered by Alan Turing.

US educators awarded for exemplary teaching in mathematics

Janet Heine Barnett, Caren Diefenderfer, and Tevian Dray were named the 2017 Deborah and Franklin Tepper Haimo Award winners by the Mathematical Association of America (MAA) for their teaching effectiveness and influence beyond their institutions.

Janet Heine Barnett, Caren Diefenderfer, and Tevian Dray were named the 2017 Deborah and Franklin Tepper Haimo Award winners by the Mathematical Association of America (MAA) for their teaching effectiveness and influence beyond their institutions.

Authors of year's best books in mathematics honored

Prizes for the year's best books in mathematics were awarded to Ian Stewart and Tim Chartier by the Mathematical Association of America (MAA) on Jan.

Prizes for the year's best books in mathematics were awarded to Ian Stewart and Tim Chartier by the Mathematical Association of America (MAA) on Jan.

The mathematics of coffee extraction: Searching for the ideal brew

Composed of over 1,800 chemical components, coffee is one of the most widely-consumed drinks in the world.

Composed of over 1,800 chemical components, coffee is one of the most widely-consumed drinks in the world.

## Top Science Podcasts

We have hand picked the**top science podcasts of 2019**.

**Now Playing: TED Radio Hour**

**Risk**

Why do we revere risk-takers, even when their actions terrify us? Why are some better at taking risks than others? This hour, TED speakers explore the alluring, dangerous, and calculated sides of risk. Guests include professional rock climber Alex Honnold, economist Mariana Mazzucato, psychology researcher Kashfia Rahman, structural engineer and bridge designer Ian Firth, and risk intelligence expert Dylan Evans.

**Now Playing: Science for the People**

**#540 Specialize? Or Generalize?**

Ever been called a "jack of all trades, master of none"? The world loves to elevate specialists, people who drill deep into a single topic. Those people are great. But there's a place for generalists too, argues David Epstein. Jacks of all trades are often more successful than specialists. And he's got science to back it up. We talk with Epstein about his latest book, "Range: Why Generalists Triumph in a Specialized World".

**Now Playing: Radiolab**

**Dolly Parton's America: Neon Moss**

Today on Radiolab, we're bringing you the fourth episode of Jad's special series, Dolly Parton's America. In this episode, Jad goes back up the mountain to visit Dolly's actual Tennessee mountain home, where she tells stories about her first trips out of the holler. Back on the mountaintop, standing under the rain by the Little Pigeon River, the trip triggers memories of Jad's first visit to his father's childhood home, and opens the gateway to dizzying stories of music and migration. Support Radiolab today at Radiolab.org/donate.