Related papers: Karl Weierstrass Bicentenary
Insofar as Sir Karl Raimund Popper's writings deal with political statements, they are evident; yet insofar as they deal with scientific issues, they are misleading. If applied to the concrete implementation of science, such as distribution…
Mathematics cannot anymore be assimilated to a linguistic game, where formal proofs are strongly differentiated with conjectural thinking, without building any category of knowledge to understand the passage (Wittgenstein's gist). Nowadays,…
Supportive attitudes can bring to a blossoming science, while neglect can quickly make science absent from everyday life and provide a very primitive view of the world. We compare one important Greek achievement, the computation of the…
This talk presents a short review of David Brink's most important achievements and of my own experience working with him.
This is a textbook about elementary number theory, with emphasis on classical topics around the Euklidean Algorithm.
Remarks on mathematical proof and the practice of mathematics.
The Weihrauch degrees are a tool to gauge the computational difficulty of mathematical problems. Often, what makes these problems hard is their discontinuity. We look at discontinuity in its purest form, that is, at otherwise constant…
I write about H\'ector, his contributions to the early work in the quark model, and a general discussion of quantum statistics
Carl Friedrich Gauss is often given credit for providing the first correct proof of the fundamental theorem of algebra in his 1799 doctoral dissertation. However, Gauss's proof contained a significant gap. In this paper, we give an…
The nineteenth century Russian author Leo Tolstoy based his egalitarian views on sociology and history on mathematical and probabilistic views, and he also proposed a mathematical theory of waging war.
This paper contains a case study of the work and self-definition of two important mathematicians during the rise of modern mathematics: Felx Hausdorff (1868--1942) and Hermann Weyl (1885--1955). The two had strongly diverging positions with…
The ability to read, write, and speak mathematics is critical to students becoming comfortable with statistical models and skills. Faster development of those skills may act as encouragement to further engage with the discipline. Vocabulary…
We establish a version of the Landen's transformation for Weierstrass functions and invariants that is applicable to general lattices in complex plane. Using it we present an effective method for computing Weierstrass functions, their…
The development of a mathematics for living systems is one of the most challenging prospects of this century. The search began with the pioneering contribution of Ilia Prigogine, who developed methods from statistical physics to describe…
Over the past 20 years, Wikipedia has gone from a rather outlandish idea to a major reference work, with more than 60 million articles across all languages, including nearly 7 million in English [Wiki01]. Around 27,000 of these articles…
We give a survey on the Weierstrass representations of surfaces in three- and four-dimensional spaces, their applications to the theory of the Willmore functional and on related problems of spectral theory of the two-dimensional Dirac…
This is a former PhD student's take on his teacher's scientific philosophy. I describe a set of 'principles' that I believe are conducive to good applied mathematics, and that I have learnt myself from observing Hans van Duijn in action.
The impact of the computer on present and especially future mathematics is illustrated by means of the iconic example of WZ theory.
John Mather is a great scholar who was dedicated to mathematics in his whole life. His works in mathematics can be characterized as original and foundational. He laid out the foundation of singularity theory while he was a graduate student.…
The analytical aspects of the "Trait\'e des \'equations" of Sharaf al-D\^in al-T\^us\^i (2nd half of the XIIth century) have been underlined by R. Rashed (1974, 1986). In the present paper, we consider again some of those aspects, when…