My papers and books

This list includes my papers about and around mathematics, but not my mathematics research papers.

A. Borovik, Mathematics for teachers of mathematics, The De Morgan Gazette 10 no. 2 (2018), 11-25. 

A. V. Borovik,  Mathematics for makers and mathematics for users, in Humanizing Mathematics and its Philosophy: Essays Celebrating the 90th Birthday of Reuben Hersh (B. Sriraman ed.), Birkhauser, 2017, pp. 309–327. DOI 10.1007/978-3-319-61231-7_22. ISBN 978-3-319-61231-7.   A version of the paper as it was accepted for publication on 02 May 2017, with some minor typographic corrections, and with this bibliographic note added.  Later changes made by the editors are not shown in this version. Typesetting in \(\LaTeX\) is done by the author. 

T. Bascelli, P. B. Laszczyk, A. Borovik, V. Kanovei, K. U. Katz, M. G. Katz, S. S. Kutateladze, T. Mcgaffey, D. M. Schaps, and D. Sherry,  Cauchy’s infinitesimals, his sum theorem, and foundational paradigms. Online: Bascelli, T., Błaszczyk, P., Borovik, A. et al. Found Sci (2017), 1-30. doi:10.1007/s10699-017-9534-y. Final pre-publication version: 

A. Borovik, What can specialist mathematics schools give to students that mainstream schools cannot? The De Morgan Gazette 9 no. 3 (2017), 17–25

A. Borovik, What students like, The De Morgan Gazette 9 no. 1 (2017), 1–6

A. V. Borovik, Comments on “Stop Ruining Math! Reasons and Remedies for the Maladies of Mathematics Education” by Rachel Steinig, The De Morgan Gazette 8 no. 2 (2016) 9-18.

A. V. Borovik, Being in control. In Understanding Emotions in Mathematical Thinking and Learning (U. Xolocotzin (ed.). Academic Press, San Diego, 2017, pp. 77–96. DOI: 10.1016/B978-0-12-802218-4.0003-0. ISBN: 9780128022184 (print), 9780128024898 (electronic). URL The final pre-publication version:

A. V. Borovik,  Economy of thought: a neglected principle of mathematics education,  in Simplicity: Ideals of Practice in Mathematics and the Arts  (R. Kossak and Ph. Ording, eds.).  Springer, 2017, pp. 241 – 265. DOI 10.1007/978-3-319-53385-8_18. ISBN 978-3-319-53383-4. A pre-publication version (without editorial changes made by publishers):   . (Typeset in \(\LaTeX\) by the author.)

A. V. Borovik, Sublime Symmetry: Mathematics and Art, The De Morgan Gazette, 8 no. 1 (2016) 1-8. ISSN 2053-1451

A. V. Borovik,  Makers and Users (extended abstract of a talk at the ISIS Summit in Vienna, June 2015)

A. V. Borovik, Calling a spade a spade: Mathematics in the new pattern of division of labour, Mathematical Cultures: The London Meetings 2012-14 (B. Larvor, ed.). Trends in the History of Science. Springer, 2016, pp. 347-374. ISBN 978-3-319-28580-1. DOI 10.1007/978-3-319-28582-5_20. A pre-publication version (without editorial changes made by publishers): . (Typeset in \(\LaTeX\) by the author.)

A. V. Borovik, Free Maths Schools”: some international parallels, The De Morgan Journal 2 no. 2 (2012) 23-35

A. V . Borovik and A. D. Gardiner, Mathematical abilities and mathematical skills, The De Morgan Journal 2 no. 2 (2012)  75-86.

A. V. Borovik, Information and Communication Technology in University Level Mathematics Teaching, The De Morgan Journal 2 no. 1 (2012) 9-39.


A. V. Borovik, Mathematics under the Microscope: Notes on Cognitive Aspects of Mathematical Practice. Amer. Math. Soc., Providence, RI. 317 pp. ISBN-10: 0-8218-4761-9. ISBN-13: 978-0-8218-

A. V. Borovik and A. S. Borovik, Mirrors and Reflections: The Geometry of Finite Reflection Groups. Springer, 2010.  ISBN 978-0-387-79065-7.