Related papers: BourbOulipo. Relazioni tra Oulipo e Bourbaki
I briefly consider the Kuhnian notion of "paradigm shifts" applied to the history of mathematics and argue that the succession and intergenerational continuity of mathematical thought was undeservedly neglected in the historical studies. To…
We examine some recent scholarship on Leibniz's philosophy of the infinitesimal calculus. We indicate difficulties that arise in articles by Bassler, Knobloch, and Arthur, due to a denial to Leibniz's infinitesimals of the status of…
There exists a remarkable connection between the quantum mechanical Landau-Zener problem and purely classical-mechanical problem of a ball rolling on a Cornu spiral. This correspondence allows us to calculate a complicated multiple…
I coined the term anabelomorphy (pronounced as anabel-o-morphy) as a concise way of expressing Mochizuki's idea of "anabelian way of changing ground field, rings etc." which was he has introduced in his work on his Inter-Universal…
The 19th century impressionist movement, as a reaction to "art pompier", is proposed as a comparison with modern evolutions in mathematics.
With a bird's-eye view, we survey the landscape of Calabi-Yau threefolds, compact and non-compact, smooth and singular. Emphasis will be placed on the algorithms and databases which have been established over the years, and how they have…
I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…
Remarks on mathematical proof and the practice of mathematics.
Pierre Bourdieu discussed how an individual's taste relates o his or her social environment, and how the classification of \emph{distinct} and \emph{vulgar}, among others, arises from at the same time as shapes this taste in his work called…
Quantum physics has intrigued scientists and philosophers alike, because it challenges our notions of reality and locality--concepts that we have grown to rely on in our macroscopic world. It is an intriguing open question whether the…
Given two non-zero integers $a$ and $b$ there exist integers $m$ and $n$ for which $am-bn =(a,b)$. An increasing number of mathematicians have been calling this `B\'ezout's identity', some encouraged by finding "identit\'e de B\'ezout" in…
This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…
J{\'e}r{\^o}me Lalande, a famous French astronomer in the 18th century, collaborated throughout his career with several female calculators in astronomy: Nicole Reine Lepaute, Marie Louise Dupi{\'e}ry and Marie Jeanne Lefran{\c c}ois. Taking…
QBism is a novel interpretation of quantum mechanics. With its radical emphasis on the subject, QBism provides a welcome corrective to popular misrepresentations of the epistemological reflections of Niels Bohr, while Bohr, rightly…
Charles Peirce develops a scheme for classifying different kinds of monadic, dyadic and triadic relations. His account of these different classes of relations figures prominently in the development of his algebraic and diagrammatic systems…
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? Using an example from my own mathematical life, I argue that…
This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern…
This article discusses epistemological problems in the philosophy of mathematics and issues concerning the reliability of the mathematical literature.
How students use mathematics in their physics classes has been studied extensively in the physics education literature. In addition to specific mathematical methods in specific physics contexts, possible effects of more general "cultural"…