Related papers: Modernism, Fiction and Mathematics
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
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…
This is an extended version of my 2018 Heinemann prize lecture describing the work for which I got the prize. The citation is very broad so this describes virtually all my work prior to 1995 and some afterwards. It discusses work in…
Mathematical models are an important tool for neuroscientists. During the last thirty years many papers have appeared on single neuron description and specifically on stochastic Integrate and Fire models. Analytical results have been proved…
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…
This paper summarizes the current status of the electromagnetic data libraries, reviews recent experimental validation results, highlights open issues and introduces new perspectives for the future of these data libraries taking shape in…
This essay, originally published in the Sept 1990 Notices of the AMS, discusses problems of our mathematical education system that often stem from widespread misconceptions by well-meaning people of the process of learning mathematics. The…
This draft book offers a comprehensive and rigorous treatment of the mathematical principles underlying modern deep learning. The book spans core theoretical topics, from the approximation capabilities of deep neural networks, the theory…
Review of the book: Distribution modulo one and Diophantine approximation, by Yann Bugeaud, Cambridge University Press 2012. ISBN 978-0521111690, 316 pp.
In recent years, promising mathematical models have been suggested which aim to describe conscious experience and its relation to the physical domain. Whereas the axioms and metaphysical ideas of these theories have been carefully…
The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…
This report describes the development and use of an online teaching tool giving students exercises in logical modelling, or \emph{formalisation} as it is called in the older literature. The original version of the site, `Logic for Fun',…
In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for…
A review of the Annual Review of Astronomy and Astrophysics Volume 52, 2014 (Ed. S.M. Faber, Ewine van Dishoeck, and John Kormendy) is given, with a perspective of understanding the current trends in Astronomy and Astrophysics. The impact…
Comment: Elaboration on Two Points Raised in ``Classifier Technology and the Illusion of Progress'' [math.ST/0606441]
Mathematical oncology is an interdisciplinary research field where the mathematical sciences meet cancer research. Being situated at the intersection of these two fields makes mathematical oncology highly dynamic, as practicing researchers…
We review some of Olivier Messiaen's use of mathematics in his composition and his theoretical writings. The final version of this paper appeared in the book Twentieth-Century Music and Mathematics, R. Illiano (ed.), Brepols, Turnhout,…
Despite the effort put into the detection of academic plagiarism, it continues to be a ubiquitous problem spanning all disciplines. Various tools have been developed to assist human inspectors by automatically identifying suspicious…
Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…