Related papers: Mathematics, Love, and Tattoos
The space of couplings of a given theory is the arena of interest in this article. Equipped with a metric ansatz akin to the Fisher information matrix in the space of parameters in statistics (similar metrics in physics are the…
This article, dedicated, with admiration to Reuben Hersh, for his forthcoming 90th birthday, argues that mathematics today is not yet a science, but that it is high time that it should become one.
We have developed a relativistically-accurate computer graphics code and have used it to produce photo-realistic images and videos of scenes where special relativistic effects dominate, either in astrophysical contexts or in imaginary…
We survey some recent applications of machine learning to problems in geometry and theoretical physics. Pure mathematical data has been compiled over the last few decades by the community and experiments in supervised, semi-supervised and…
Geometry is essentially a global language, which is fully understood in different times, countries and cultures. The proof of a geometric theorem (e.g. the Pythagorean Theorem) or a geometric construction (e.g. the construction of an…
In this paper, I explore what mathematical research can tell us about ourselves, and our role in the world, using examples from my own experience. The paper is a sequel to my piece "Mathematics is a Quest for Truth", published in the…
A formula for the apparent rotation of a relativistically moving object has been known for some time, but it seems not to have been realized that this formula has a very pretty interpretation in terms of formal group laws. Version 2…
A series of ceramic artworks are presented, inspired by the author's research connecting theoretical physics to the beautiful theory of Riemann surfaces. More specifically the research is related to the classification of curves on the…
A relativistic theory of surficial Love numbers, which characterize the surface deformation of a body subjected to tidal forces, was initiated by Damour and Nagar. We revisit this effort in order to extend it, clarify some of its aspects,…
Integer iteration rules such as n |-> {a n + b, c n +d} are studied as minimal examples of the general process of multicomputation. Despite the simplicity of such rules, their multiway graphs can be complex, exhibiting, for example,…
An opiniated essay on what pure mathematics is and why the adjective "pure" in "pure mathematics" is not a good choice.
A sketch of some of the fundamental notions related to the nature of knowledge is offered, with special focus on the role of mathematics and my own opinions. No single idea exposed here is entirely original; indeed, this topic has been…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
Operator matrices have played a significant role in studying Hilbert space operators. In this paper, we discuss further properties of operator matrices and present new estimates for the operator norms and numerical radii of such operators.…
This text is a survey on symmetric matrices. It serves as a script for a module to be taught at university.
This study examines the potential of using math-themed postage stamps in mathematics lessons as a tool to engage students and integrate the subject with history, art, and culture. Since the first mathematical stamps appeared in the early…
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.
We re-examine the old question to what extent mathematics may be compared with a game. Mainly inspired by Hilbert and Wittgenstein, our answer is that mathematics is something like a rhododendron of language games, where the rules are…
A review of selected topics in mathematical general relativity
The aim of this work is an analytic investigation of differential equations producing mirror maps as well as giving new examples of mirror maps; one of these examples is related to (rational approximations to) $\zeta(4)$. We also indicate…