Related papers: Problems with Popper
Egbert Brieskorn died on July 11, 2013, a few days after his 77th birthday. He was an impressive personality who has left a lasting impression on all who knew him, whether inside or outside of mathematics. Brieskorn was a great…
I present some reminiscences, both personal and scientific, over a lifetime of admiration of, and friendship with, one of the Grandmasters of our subject.
Published between 1760 and 1770, Bielfeld's writings prove that scholars of the time were acquainted with the concepts of both political arithmetic and German statistik, long before they merged into a new discipline at the beginning the…
A recent essay [1] reminds us of how richly Boltzmann deserves to be admiringly commemorated for the originality of his ideas on the occasion of his 150th birthday. Without any doubt, the scientific community owes Boltzmann a great debt 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…
This article is a summary of a talk about Richard Feynman, given at a conference Polymaths across the Eras organized in November 2023 by the St Cross Centre for the History and Philosophy of Physics (HAPP) in Oxford. It describes Feynman as…
This paper is devoted to Poincar\'e's work in probability. Though the subject does not represent a large part of the mathematician's achievements, it provides significant insight into the evolution of Poincar\'e's thought on several…
G\"unter Hellwig was the author of influential textbooks on PDEs and differential operators of mathematical physics, an enthusiastic and inspiring teacher to generations of engineers, organiser of PDE conferences at Oberwolfach and a…
This survey article on Hilbert's first and second problems is adapted from a one-hour colloquium lecture given at the University of Auckland in May, 2000, just three months before the 100th anniversary of Hilbert's lecture. It includes an…
We revisit Popper's falsifiability criterion. A tester hires a potential expert to produce a theory, offering payments contingent on the observed performance of the theory. In our model, instead of knowing the true data-generating process,…
The notion that we live in an evolving universe was established only in the twentieth century with the discovery of the recession of galaxies by Hubble and with the Lemaitre and Friedmann's interpretation in the 1920s. However, the concept…
This paper is concerned with a dialogue between Rabindranath Tagore and Albert Einstein, where Tagore argued that our knowledge is essentially human, while Einstein maintained that some kinds of knowledge are more objective. Arguments by…
What is the largest number accessible to the human imagination? The question is neither entirely mathematical nor entirely philosophical. Mathematical formulations of the problem fall into two classes: those that fail to fully capture the…
Niels Bohr's doctrine of the primacy of "classical concepts" is arguably his most criticized and misunderstood view. We present a new, careful historical analysis that makes clear that Bohr's doctrine was primarily an epistemological…
After some brief biographical notes, Wolfgang Pauli's main contributions to general relativity, quantum theory, quantum field theory, and elementary particle physics are reviewed. A detailed description is given how Pauli descovered -…
Kazuo Kondo (1911-2001) was Chair of the Department of Mathematical Engineering at the University of Tokyo, Japan. Over a period of 50 years, he and a few colleagues wrote and published a voluminous series of papers and monographs on the…
Al Cameron, who died recently (October 3, 2005) at 80, was one of the giants in astrophysics. His insights were profound and his interests were wide-ranging. Originally trained as a nuclear physicist, he made major contributions in a number…
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 authors discuss the role of controversy in mathematics as a preface to two opposing articles on computational complexity theory: "Some basic information on information-based complexity theory" by Beresford Parlett [math.NA/9201266] and…
The classical platonist/formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: is new mathematics discovered or invented? Using an example from my own mathematical life, I argue that…