相关论文: Der rechnende Dichter (The calculating poet)
At a crossroads of calculus and combinatorics, the generating function of secant and tangent numbers (Euler numbers) provides enumeration of alternating permutations. In this article, we present a new refinement of Euler numbers to answer…
I present some reminiscences, both personal and scientific, over a lifetime of admiration of, and friendship with, one of the Grandmasters of our subject.
Remarks on mathematical proof and the practice of mathematics.
This text tries to give an elementary introduction to the mathematical properties of infinite sets. The aim is to keep the approach as simple as possible. Advanced knowledge of mathematics is not necessary for a proper understanding, and…
A portrait of Kurt Goedel with emphasis on his work on relativity theory and idealistic philosophy.
In spite of the wide range of his book, Cournot did not know some essential discoveries in natural sciences (William Herschel, Daniel Bernoulli, Humboldt) and his deliberations about measurement were almost useless. But he introduced the…
This text is based on an invited talk at the Dedekind Symposium at Braunschweig in October 2016. It summarizes views from my recent commented edition of Dedekinds two books on the foundations of mathematics.
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
An outline of J\"org Eschmeier's main mathematical contributions is organized both on a historical perspective, as well as on a few distinct topics. The reader can grasp from our essay the dynamics of spectral theory of commutative tuples…
Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching ---…
We give an overview of several of the mathematical works of Gilles Lachaud and provide a historical context. This is interspersed with some personal anecdotes highlighting many facets of his personality.
Free translation of the original abstract in Spanish: Some of the most relevant milestones due to, or instigated by, mathematicians concerning the creation, development and advances of Cosmology as a scientific discipline are presented and…
We try to understand and justify Schubert Calculus the way Schubert did it.
The first contribution of this paper is the presentation of a Pavelka - like formulation of possibilistic logic in which the language is naturally enriched by two connectives which represent negation (eg) and a new type of conjunction…
The author describes some of his experiences as a mathematician cooperating with diabetes specialists.
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.…
Three thinkers of the 19th century revolutionized the science of logic, mathematics, and philosophy. Edmund Husserl (1859-1938), mathematician and a disciple of Karl Weierstrass, made an immense contribution to the theory of human thought.…
In this paper, we present a series of mathematical problems which throw interesting lights on flamenco music. More specifically, these are problems in discrete and computational mathematics suggested by an analytical (not compositional)…
Fritz Gesztesy's varied and prolific career has produced many transformational contributions to the spectral theory of one-dimensional Schr\"odinger equations. He has often done this by revisiting the insights of great mathematical analysts…
It is a survey of the main results on abstract characterizations of algebras of $n$-place functions obtained in the last 40 years. A special attention is paid to those algebras of $n$-place functions which are strongly connected with groups…