Journal

Selected Passages From Correspondence With Friends

On Mathematics, Philosophy, and Education

This page lists the contents of my Journal.

Volume 14 ( 2026)

  1. Expertise and Incompetence , pp. 1-5.

I comment on a thesis which belongs to the tradition set in the famous book  Anti-Intellectualism in American Life (1963) by American historian and politolog Richard
Hofstadter (1916–1970):

`The complexity of modern life makes it difficult for ordinary citizens to participate independently and meaningfully in the governance of society, which
undermines trust in democratic institutions.’

and argue that it is outdated: the damning formulation now applies equally to politicians—as well as to all kinds of administrators, managers in softer lines of business (where rigorous criteria, based on principles of physics and exact sciences are absent), and the like—amidst what amounts to a pandemic of incompetence.

I call on all my colleagues in exact sciences and rigorous engineering and medical disciplines: mathematicians, computer scientists, physicists, chemists, biologists, medical practitioners, engineers, …, everyone who know that they deal with the objective reality, and have sufficiently clear and efficient criteria to distinguish between true and false, probable and improbable, possible and impossible –to be more politically active, and try to infuse a bit of rationality and common sense into the current brain-dead political discourse and practice.

Who else in this world retains this endangered skill — to think rationally?

Volume 13 ( 2025)

  1. The tool/weapon duality of mathematics.  pp. 1-17.

Abstract. This paper outlines the principal moral and ethical issues of mathematics and existential choices a mathematician may face in his professional life. My text is a manifesto; it is a list of declarations rather than a systematic development of the theme. Indeed each section could be expanded into a paper on its own. I hope to write fairly soon a more detailed exposition.

Trigger Warning. This paper contains an honest description of the role of mathematics in history which could be emotionally challenging for some readers and lead to intrusive thoughts about the future of mathematics and the future of humanity.

Comment. The paper appeared in J. Humanistic Mathematics, 16 no. 1 (2026), 365–392. DOI: 10.5642/jhummath.UZBE3851.  Available at:
https://scholarship.claremont.edu/jhm/vol16/iss1/24.

Volume 12 ( 2024)

  1. Why does the mirror change left and right but does not change up and down?    pp. 1-8.

Abstract. It does not.

Volume 11 (2023)

  1. The elephant in the room: The role of the subconscious in everyday mathematical work. pp. 1-18.

Volume 10 (2022)

 

Volume 6 (2018)

Volume 1 (2013)

  1. A monotonous bounded sequence as a metaphor for mathematics education. pp. 1-2
  2. Elementary Calculus: Real vs Analytic. pp. 3-8.
  3. The strange fate of abstract thinking. pp. 9-12.
  4. Mathematics discovered, invented, and inherited. pp. 13-28.
  5. A personal take on synthetic phonics.   pp.  29-44.
  6. Relationality of teaching, the Khan Academy, and word problems. pp. 45-50.