Economy of Thought: A Neglected Principle of Mathematics Education

  • Alexandre V. BorovikEmail author
Part of the Mathematics, Culture, and the Arts book series (MACUAR)


The aim of science is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest. The guiding motto in the life of every natural philosopher should be, “Seek simplicity and distrust it.”



I thank my mathematics homeschooler colleagues Maria Droujkova (see her book [24]) and Julia Brodsky—their heroism is a source of inspiration for me, and this paper is written with them as readers in mind. Maria Droujkova’s new project, Avoid Hard Work!, [16], focuses on simplicity as a guiding principle of mathematics education.

I am grateful to Roman Kossak and Philip Ording, the initiators and editors of this volume, for their patience and persistence.

Ron Aharoni, Natasha Artemeva, John Baldwin, Rick Booth, Julia Brodsky, Ronald Brown, David Corfield, Yagmur Denizhan, Maria Droujkova, Julian Gilbey, Daniel S. Helman, Roman Kossak, Brendan Larvor, Josef Lauri, Azadeh Neman, David Pierce, Wes Raikowski, Peter Ransom, Carlos Santacruz, Seb Schmoller, Anna Sfard, Chris Stephenson, Natasa Strabic, Adam Sulich, Yusuf Ünlü, and the anonymous referee provided most useful feedback and corrections. Tony Gardiner kindly corrected my translation of a fragment from Igor Arnold’s paper.

Some parts of the paper were written thanks to my involvement with CMEP, the Cambridge Mathematics Education Project. I thank my CMEP colleagues, and especially Martin Hyland and Tony Gardiner, for many useful discussions—but neither they nor CMEP are responsible for my views expressed here.

This paper was completed when I enjoyed the warm hospitality offered to me in the Nesin Mathematics Village13 in Şirince, Izmir Province, Turkey; my thanks go to Ali Nesin and to all volunteers and staff who have made the Village a mathematics research paradise, an oasis of proper mathematics education, and a garden of philosophy and arts [1, 19]. Simplicity is the cultural dominant of the Village.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of MathematicsUniversity of ManchesterManchesterUK

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