Related papers: Der rechnende Dichter (The calculating poet)

Through the use of a system-building approach, an approach that includes finding common ground for the various philosophical paradigms within statistics, Erich L. Lehmann is responsible for much of the synthesis of classical statistical…

The decomposition of representations of compact classical Lie groups into representations of finite subgroups is discussed. A Mathematica package is presented that can be used to compute these branching rules using the Weyl character…

This article is about life and work of Otto Toeplitz, who was influenced by the ideas of Felix Klein and David Hilbert.

This is an introduction (in German) to projective geometry by the late Heinz Lueneburg. Projective spaces are treated as lattices with particular properties, and finite geometries receive special attention. The final chapters deal with…

In this note a characterization of anallytically Riesz operators is given. This work completes the article [1].

A flexible unified framework for both classical and quantum Schubert calculus is proposed. It is based on a natural combinatorial approach relying on the Hasse-Schmidt extension of a certain family of pairwise commuting endomorphisms of an…

We revisit in a probabilistic framework the umbral approach of Bernoulli, Euler and Carlitz Hermite polynomials by Gessel [1].

We present a research mathematician's perspective on current developments around in K-12 mathematics. We share activities, and highlight the different ways in which students' reasoning can progress, such as amount of abstraction,…

I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of…

Monsters lurk within mathematical as well as literary haunts. I propose to trace some pathways between these two monstrous habitats. I start from Jeffrey Jerome Cohen's influential account of monster culture and explore how well…

Some Goedel centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. [Enriques lecture given…

We re-evaluate the great Leibniz-Newton calculus debate, exactly three hundred years after it culminated, in 1712. We reflect upon the concept of invention, and to what extent there were indeed two independent inventors of this new…

We compare several approaches to the history of mathematics recently proposed by Blasjo, Fraser--Schroter, Fried, and others. We argue that tools from both mathematics and history are essential for a meaningful history of the discipline. In…

A focused modernization of Sophus Lie's brilliant writings about the foundations of geometry that every contemporary geometer should have at least once a look at. Translated, updated, commented.

Leibniz scholarship is currently an area of lively debate. We respond to some recent criticisms by Archibald et al.

As David Berlinski writes (1997), the existence and nature of mathematics is a more compelling and far deeper problem than any of the problems raised by mathematics itself. Here we analyze the essence of mathematics making the main emphasis…

Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore,…

This is in some sense an addendum to the book Relational Mathematics by the first-named author. It originated from work on diverse other topics during which a lot of purely relational results with broad applicability have been produced.…

A new calculus of planar diagrams involving diagrammatics for biadjoint functors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose Grothendieck ring contains an integral form of…

The results received in works [Centsov N.N. [N.N. Chentsov], Statistical decision rules and optimal inference, 1982 Amer. Math. Soc. (Translated from Russian); Morozova, E. A., Chentsov, N. N. Natural geometry of families of probability…