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This volume covers one of the most thrilling two-year periods in twentieth-century physics, as matrix mechanics - developed chiefly by W. Heisenberg, M. Born, and P. Jordan - and wave mechanics - developed by E. Schr\"odinger - supplanted…

This is an expository paper about the Borel complexity of structure and classification theorems. It sorts several classical problems relative to known benchmarks of complexity. As a corollary various problems proposed by people such as von…

Dynamical Systems · Mathematics 2023-04-14 Matthew Foreman

The Bohr--Einstein debate is one of the more remarkable protracted intellectual exchanges in the history of physics. Its influence has been lasting: One of the few clear patterns in a 2013 survey about quantum foundations was that the…

Quantum Physics · Physics 2020-04-02 Blake C. Stacey

An account of the careers of the five women who completed a doctorate in mathematics in France before 1960 and became internationally known scientists, followed by a more general description of the place of women on the mathematical scene…

History and Overview · Mathematics 2015-02-27 Yvette Kosmann-Schwarzbach

Translated from the Latin original, "De numeris amicabilibus" (1747). E100 in the Enestroem index. Euler starts by saying that with the success of mathematical analysis, number theory has been neglected. He argues that number theory is…

History and Overview · Mathematics 2009-08-11 Leonhard Euler , Jordan Bell

This Introduction opens the book {\sl Standing Together in Troubled Times} which presents a story of friendship between Wolfgang Pauli, one of the greatest theoretical physicists of the 20th century, and Charlotte Houtermans. They met at…

History and Philosophy of Physics · Physics 2016-11-11 M. Shifman

Reviewing Piaget's psychology of reasoning by the mathematical educators of the Federal Republic of Germany late in the 1960th the concept of grouping has been understood similar to a mathematical structure. Possibly to consider empirical…

History and Overview · Mathematics 2015-04-07 Hans Joachim Burscheid , Horst Struve

Mathematical challenges punctuate the history of early modern mathematics. While cultural historians have attempted to contextualize these challenges among contemporary practices, in particular duels or advertisements in a competitive…

History and Overview · Mathematics 2012-09-25 Catherine Goldstein

At the 1927 Solvay conference, Einstein presented a thought experiment intended to demonstrate the incompleteness of the quantum mechanical description of reality. In the following years, the thought experiment was picked up and modified by…

Quantum Physics · Physics 2009-11-10 Travis Norsen

After reminding the main issues at stake in the famous Einstein-Bohr debate initiated in 1935, we tentatively propose a way to get them closer, thus shedding a new light on this historical discussion.

History and Philosophy of Physics · Physics 2022-01-04 Nayla Farouki , Philippe Grangier

In this article we present diverse experiences of Polish mathematicians (in a broad sense) who during World War I fought for freedom of their homeland or conducted their research and teaching in difficult wartime circumstances. We first…

History and Overview · Mathematics 2020-01-16 Stanislaw Domoradzki , Malgorzata Stawiska

Seven mathematicians and one political scientist met at the Cambridge Apportionment Meeting in January 2011. They agreed a unanimous recommendation to the European Parliament for its future apportionments between the EU Member States. This…

History and Overview · Mathematics 2011-08-23 Geoffrey R. Grimmett

Re-evaluation of the evidence (some of it unpublished) shows that experimenters conducting Einstein-Podolsky-Bohm (EPR) experiments may have been deceived by various pre-conceptions and artifacts. False or unproven assumptions were made…

Quantum Physics · Physics 2007-05-23 Caroline H. Thompson

This paper was accepted for Comment. Math. Univ. Carolinae in 1968 but then got lost during the military occupation of Prague and surrounding events. My own long-lost carbon copy of it turned up in my Columbia office. The only changes to…

Rings and Algebras · Mathematics 2018-08-21 Walter D Neumann

Einstein at the Z\"urich Polytechnic: he skipped classes, did not attend all the lectures of his Professors, and before going to the examinations he studied instead from the notebooks of his good friend from class, Marcel Grossmann.…

History and Philosophy of Physics · Physics 2012-05-22 Galina Weinstein

I attempted to write the full translation of this article to make the remarkable proof of Pierre Deligne available to a greater number of people. Overviews of the proofs can be found elsewhere. I especially recommend the notes of James…

Algebraic Geometry · Mathematics 2019-01-29 Evgeny Goncharov

In 1930 Einstein argued against consistency of the time-energy uncertainty relation by discussing a thought experiment involving a measurement of mass of the box which emitted a photon. Bohr seemingly triumphed over Einstein by arguing that…

Quantum Physics · Physics 2015-06-04 H. Nikolic

This reviews the econophysics activities in Belgium from my admittedly biased point of view. Unknown historical notes or facts are presented for the first time explaining the aims, whence evolution of the research papers and friendly…

General Finance · Quantitative Finance 2012-12-11 Marcel Ausloos

In this article, I trace the early historical developments that ultimately led to the creation of the atomic bomb. Even after the completion of weapons, many scientists continued to argue that nuclear armaments were indispensable for…

History and Philosophy of Physics · Physics 2026-03-30 Shoji Nagamiya

Historical literature has traced US efforts to bring Latin American countries over to the side of the Allies in WWII. Following a period of hesitation and negotiation with the US and Germany, the Brazilian government aligned itself with the…

History and Philosophy of Physics · Physics 2014-07-28 Olival Freire Junior , Indianara Silva