Related papers: PC4 at Age 40
This communication contributes to research on proof validation as a lens for uncovering didactical phenomena related to proof and proving. We revisit the puzzling case of lower secondary students in France who validate circular proofs. That…
In this Digest we review a recent study released by the Google Scholar team on the apparently increasing fraction of citations to old articles from studies published in the last 24 years (1990-2013). First, we describe the main findings of…
A determinant evaluation is proven, a special case of which establishes a conjecture of Bombieri, Hunt, and van der Poorten (Experimental Math\. {\bf 4} (1995), 87--96) that arose in the study of Thue's method of approximating algebraic…
In this paper we investigate the recent advances by Zhang, Maynard and Pintz towards Polignac's conjecture and give some new results concerning the relationship between Polignac numbers and arithmetic progressions.
This is an attempt to illustrate the glorious history of logical foundations and to discuss the uncertain future.
The title of this article is partially taken from writings of A. Einstein. In the 1932 ICM at Z\"urich, when E. \vCech gave a seminar on higher homotopy groups of a pointed space and proved they were abelian for n > 1. On these grounds, H.…
Some facts about 4-spinors listed and discussed. None, well perhaps some, of the work is original. However, locating formulas in other places has proved a time-consuming process in which one must always worry that the formulas found in any…
Explanations are inherently contrastive: E happened rather than E' because of C rather than C'. However, these contrasts, or "foils", are rarely mentioned explicitly but have to be inferred in context. Here, we investigate how people select…
In this short review I present my personal reflections on QBism. I have no intrinsic sympathy neither to QBism nor to subjective interpretation of probability in general. However, I have been following development of QBism from its very…
We comment on the claimed observation [arXiv:arXiv:2005.05301] of sterile neutrino oscillations by the Neutrino-4 collaboration. Such a claim, which requires the existence of a new fundamental particle, demands a level of rigor commensurate…
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…
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
This is a Comment on the Article ``Aging, phase ordering and conformal invariance'' by M.Henkel, M.Pleimling, C.Godr\`eche and J.M.Luck [Phys.Rev.Lett. 87, 265701 (2001)].
This is a collection of variants of Schanuel's conjecture and the known dependencies between them. It was originally written in 2007, and made available for a time on my webpage. I have been asked by a few people to make it available again…
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
In the absence of empirical confirmation, scientists may judge a theory's chances of being viable based on a wide range of arguments. The paper argues that such arguments can differ substantially with regard to their structural similarly to…
This paper reconstructs the derivations underlying the kinematical part of Einstein's 1905 special relativity paper, emphasizing their operational clarity and minimalist use of mathematics. Einstein employed modest tools-algebraic…
We describe a case of an interplay between human and computer proving which played a role in the discovery of an interesting mathematical result. The unusual feature of the use of computers here was that a computer generated but human…
We discuss several existing proofs of the value of a quartic integral and present a new proof that evolved from rational Landen transformations.
Analogue of Springer's formula for the Poincar\'e series of the algebra invariants of ternary form is found.