相关论文: Der rechnende Dichter (The calculating poet)

Formulas for calculating the Riesz function, introduced by Marcel Riesz in connection with the Riemann hypothesis, are derived; and the behavior of the Riesz function is discussed.

Since the discovery of differential calculus by Newton and Leibniz and the subsequent continuous growth of its applications to physics, mechanics, geometry, etc, it was observed that partial derivatives in the study of various natural…

In a forthcoming book, professional computer scientist and physicist Paul Budnik presents an exposition of classical mathematical theory as the backdrop to an elegant thesis: we can interpret any model of a formal system of Peano Arithmetic…

This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and…

The fundamental role of mathematics as an inspiration for artists, but also as a tool for art creation, is presented in this paper following different art fields, like architecture, sculpture, painting, photography, literature and poetry,…

Math is widely considered as a powerful tool and its strong appeal depends on the high level of abstraction it allows in modelling a huge number of heterogeneous phenomena and problems, spanning from the static of buildings to the flight of…

The fact that classical mathematical proofs of simply existential statements can be read as programs was established by Goedel and Kreisel half a century ago. But the possibility of extracting useful computational content from classical…

"Mathematicians, like physicists, are pushed by a strong fascination. Research in mathematics is hard, it is intellectually painful even if it is rewarding, and you would not do it without some strong urge." [D. Ruelle]. We shall give some…

In the words of the esteemed mathematician Paul Erd\"os, the mathematician's task is to \emph{prove and conjecture}. These two processes form the bedrock of all mathematical endeavours, and in the recent years, the mathematical community…

These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural…

This book covers the history of probability up to Kolmogorov with essential additional coverage of statistics up to Fisher. Based on my work of ca. 50 years, it is the only suchlike book. Gorrochurn (2016) is similar but his study of events…

We give an informal introduction to the authors' work on some conjectures of Kazhdan and Lusztig, building on work of Soergel and de Cataldo-Migliorini. This article is an expanded version of a lecture given by the second author at the…

This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…

This is a short overview of the influence of mathematicians and their ideas on the creative contribution of Mikhailo Lomonosov on the occasion of the tercentenary of his birth.

This paper is a criticism on "A Mathematician's Apology" by G. H. Hardy.

Steven Weinberg was a giant of late 20th Century physics on whose shoulders we stand while groping for the science of the 21st Century. This article provides a too-brief summary of a selection of his many achievements -- eight decades of…

This paper presents TextComplexityDE, a dataset consisting of 1000 sentences in German language taken from 23 Wikipedia articles in 3 different article-genres to be used for developing text-complexity predictor models and automatic text…

This article discusses epistemological problems in the philosophy of mathematics and issues concerning the reliability of the mathematical literature.

We study some combinatorial and algebraic properties of certain quadratic algebras related with dynamical classical and classical Yang-Baxter equations. One can find more details about the content of present paper in Extended Abstract.

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of…