Related papers: Some multifaceted aspects of mathematical physics,…
The purpose of this project is to outline various philosophies on the metaphysics of mathematics that have been prominent since the time of Cantor, highlighting some biographical aspects that have influenced these ideas as well. The main…
We briefly recount the long friendship that developed between Ludwig and us (Moshe Flato and I), since we first met at ICM 1966 in Moscow. That friendship extended to his school and family, and persists to this day. Its strong personal…
Despite its amazing quantitative successes and contributions to revolutionary technologies, physics currently faces many unsolved mysteries ranging from the meaning of quantum mechanics to the nature of the dark energy that will determine…
Both metamathematics and physics are posited to emerge from samplings by observers of the unique ruliad structure that corresponds to the entangled limit of all possible computations. The possibility of higher-level mathematics accessible…
A fundamental paper of Elliott Lieb from 1973 has been the basis for much beautiful work on matrix inequalities by many people over the following years. We review a well-connected set of these developments. Some new proofs are provided.
Laymen and sometimes even physicists think of natural sciences, in particular of theoretical and mathematical physics often as subjects, which unfold according to an intrinsic logical pattern, with the limitations being set only by the…
The information-theoretic point of view proposed by Leibniz in 1686 and developed by algorithmic information theory (AIT) suggests that mathematics and physics are not that different. This will be a first-person account of some doubts and…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
On the occasion of Elliott Lieb being awarded the Gauss Prize 2022, we give a non-technical overview over some of his seminal works in mathematical physics. We emphasize, in particular, his work on Coulomb many-body systems and functional…
Courses in mathematical methods for physics students are not known for including too much in the way of mathematical rigour and, in some ways, understandably so. However, the conditions under which some quite commonly used mathematical…
Mel Levy and Elliott Lieb are two of the most prominent researchers who have dedicated their efforts to the investigation of fundamental questions in many-electron theory. Their results have not only revolutionized the theoretical approach…
Personal view of author on goals and content of Mathematical Physics.
Lev Davidovich Landau was arguably one of the greatest and most versatile physicists. His work spans a very wide range and has had a considerable impact on all areas of physics including condensed matter physics, plasma, high energy and…
Central to our understanding of quantum many particle physics are two ideas due to Landau. The first is the notion of the electron as a well-defined quasiparticle excitation in the many body state. The second is that of the order parameter…
This is a philosophy-intense physics article, or, if you wish, a physics-intense philosophy article. Also, being a mathematician, I tend to view the physics, in particular the essence of quantum physics, in emphasizing the mathematical…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching ---…
Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find…
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…
[Taken from the "README" in the book] My goal with this book is to provide some kind of bridge for mathematics between the high-school-level and college-level for physics students. From my perspective, our job as physicists is to observe…