相关论文: Georg Cantor and his heritage
$ $[This paper is a (self contained) chapter in a new book, Mathematics and Computation, whose draft is available on my homepage at https://www.math.ias.edu/avi/book ]. We survey some concrete interaction areas between computational…
Following the processing of individual topics of elementary school mathematics as content of empirical theories the question is adressed wether the associated conception of mathematics finds itself under established concepts, and how it can…
We review the life and remarkable contributions to Physics of Gregor Wentzel.
Theory of Probability is distinguished by several high-level philosophical attitudes, some stressed by Jeffreys, some implicit. By reviewing these we may recognize the importance in this work in the historical development of statistics.…
Academic biography of Karl Weierstrass, his basic works, influence of his doctrine on the development of mathematics.
Following an idea due to Euler, we evaluate the alternating sums of powers of consrcutive integers.
Remarks on mathematical proof and the practice of mathematics.
We study a generalization of Mor\'an's sum sets, obtaining information about the $h$-Hausdorff and $h$-packing measures of these sets and certain of their subsets.
According to Cantor, a set is a collection into a whole of defined and separate (we shall say distinct) objects. So, a natural question is ``How to treat as `sets' collections of indistinguishable objects?". This is the aim of quasi-set…
This is a short overview of the contribution of Leonid Kantorovich into the formation of the modern outlook on the interaction between mathematics and economics.
Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…
Remarks on the Cantor's nondenumerability proof of 1891 that the real numbers are noncountable will be given. By the Cantor's diagonal procedure, it is not possible to build numbers that are different from all numbers in a general assumed…
In this note for the joint meeting of DMV and GDM we illustrate with examples the role of computer algebra in university mathematics education. We discuss its potential in teaching algebra, but also computer algebra as a subject in its own…
This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like…
The aim of this article has been to put together various aspects of the personality of the Italian mathematician Francesco Severi: the mathematical, the political, the institutional, academic and philosophical one. We tried in particular to…
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
In 1994, J.Cobb described a Cantor set in $\mathbb{R}^3$ each of whose projections into 2-planes is one-dimensional. A series of works by other authors developing this field followed. We present another very simple series of Cantor sets in…
This article critically reappraises arguments in support of Cantor's theory of transfinite numbers. The following results are reported: i) Cantor's proofs of nondenumerability are refuted by analyzing the logical inconsistencies in…
We seek to elucidate the philosophical context in which one of the most important conceptual transformations of modern mathematics took place, namely the so-called revolution in rigor in infinitesimal calculus and mathematical analysis.…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.