49 citations · 185 across the 47 of their papers we have counts for
13 papers · 1 filter
'Decolonisation' of the curricula and some related issues
Alexandre Borovik
University level mathematics in a number of countries is under pressure to `decolonise the curriculum'. This paper considers, as a test case, a possible `decolonisation' of linear…
Is pluralism in the history of mathematics possible?
Jacques Bair, Alexandre Borovik, Vladimir Kanovei +6
Leibniz scholarship is currently an area of lively debate. We respond to some recent criticisms by Archibald et al.
The Kolmogorov Reform of Mathematics Education in the USSR
Alexandre Borovik
In the Soviet Union a reform movement in mathematics education was triggered by Andrey Kolmogorov in the 1970s, and followed by a counter-reform. This movement was rooted in the ve…
Historical infinitesimalists and modern historiography of infinitesimals
Jacques Bair, Alexandre Borovik, Vladimir Kanovei +5
In the history of infinitesimal calculus, we trace innovation from Leibniz to Cauchy and reaction from Berkeley to Mansion and beyond. We explore 19th century infinitesimal lores,…
Mathematics and Mathematics Education in the 21st Century
Alexandre Borovik, Zoltan Kocsis, Vladimir Kondratiev
Mathematics enters the period of change unprecedented in its history, perhaps even a revolution: a switch to use of computers as assistants and checkers in production of proofs. Th…
Mathematics education policy as a high stakes political struggle: The case of Soviet Russia of the 1930s
Alexandre V. Borovik, Serguei D. Karakozov, Serguei A. Polikarpov
This paper is an introduction to our ongoing more comprehensive work on a critically important period in the history of Russian mathematics education; it provides a glimpse into th…
A mathematician's view of the unreasonable ineffectiveness of mathematics in biology
Alexandre Borovik
This paper discusses, from a mathematician's point of view, the thesis formulated by Israel Gelfand, one of the greatest mathematicians of the 20th century, and one of the pioneers…
A view from lockdown: mathematics discovered, invented, and inherited
Alexandre Borovik
The classical platonist / formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: \emph{Is new mathematics discovered or inven…
Cauchy's infinitesimals, his sum theorem, and foundational paradigms
Tiziana Bascelli, Piotr Blaszczyk, Alexandre Borovik +7
Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and…
A non-standard analysis of a cultural icon: The case of Paul Halmos
Piotr Blaszczyk, Alexandre Borovik, Vladimir Kanovei +4
We examine Paul Halmos' comments on category theory, Dedekind cuts, devil worship, logic, and Robinson's infinitesimals. Halmos' scepticism about category theory derives from his p…
Calling a spade a spade: Mathematics in the new pattern of division of labour
Alexandre V. Borovik
The growing disconnection of the majority of population from mathematics is becoming a phenomenon that is increasingly difficult to ignore. This paper attempts to point to deeper r…
Mathematics discovered, invented, and inherited
Alexandre Borovik
The classical platonist/formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: is new mathematics discovered or invented? Usi…
Who Gave you the Cauchy-Weierstrass Tale? The Dual History of Rigorous Calculus
Alexandre Borovik, Mikhail G. Katz
Cauchy's contribution to the foundations of analysis is often viewed through the lens of developments that occurred some decades later, namely the formalisation of analysis on the…