Related papers: Joseph Carter Corbin: Arkansas's "Profound Mathema…
This paper is about two things: (i) Charles Sanders Peirce (1837-1914) -- an iconoclastic philosopher and polymath who is among the greatest of American minds. (ii) Abductive inference -- a term coined by C. S. Peirce, which he defined as…
We introduce the concept of an academic genealogy, or AG, and illustrate how AG charts may be constructed and then demonstrate how this methodology can be used by applying it to create the partial or full AG charts to two scientists, Paul…
The article is dedicated to thye memory of a distinguished mathematician Professor Misha Shubin
The study of computability has its origin in Hilbert's conference of 1900, where an adjacent question, to the ones he asked, is to give a precise description of the notion of algorithm. In the search for a good definition arose three…
We are grateful to all discussants of our re-visitation for their strong support in our enterprise and for their overall agreement with our perspective. Further discussions with them and other leading statisticians showed that the legacy of…
A short biographical note on the life and works of K. Ramachandra, one of the leading mathematicians in the field of analytic number theory in the second half of the twentieth century.
Irving John ("Jack") Good (9 December 1916 - 5 April 2009) was one of my greatest heroes and influencers. On Oct. 25, 2009, I gave a twenty-three minute talk with the present title, and this article is an extended transcript of that talk.…
This is an expanded version of a write-up of a talk given in the fall of 2000 in Oberwolfach. A large part of it is intended to be understandable by non-number theorists with a mathematical background. The talk covered some of the history,…
This paper presents a systematic study of the prehistory of the traditional subsystems of second-order arithmetic that feature prominently in the reverse mathematics program of Friedman and Simpson. We look in particular at: (i) the long…
This is a complement to my previous article "Advanced Determinant Calculus" (S\'eminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described…
In May 2022 ICRANet organized the Workshop dedicated to the 80th anniversary of Professor Ruffini. This paper is based on the talk delivered at the meeting. Professor Ruffini was well known for Soviet scientific community not only due to…
We discuss the legacy of Alan Turing and his impact on computability and analysis.
A brief account of interesting moments in the genesis of the quark paradigm is presented.
Professor Sir Karl Popper (1902-1994) was one of the most influential philosophers of science of the twentieth century. However, in his most famous work he displays misunderstandings of science and mathematics at a basic level.
We prove three conjectures concerning the evaluation of determinants, which are related to the counting of plane partitions and rhombus tilings. One of them was posed by George Andrews in 1980, the other two were by Guoce Xin and Christian…
Invented by Kurt Hensel at the very end of 19th century on the model of power series in one indeterminate, the $p$-adic numbers have not only become an indispensable tool of contemporary arithmetic, but a research topic per se. In this…
This is a historical introduction to the theory of Stirling numbers of the second kind S(n,k) from the point of view of analysis. We tell the story of their birth in the book of James Stirling (1730) and show how they mature in the works of…
An outline of J\"org Eschmeier's main mathematical contributions is organized both on a historical perspective, as well as on a few distinct topics. The reader can grasp from our essay the dynamics of spectral theory of commutative tuples…
This book is the final version of a course on algorithmic information theory and the epistemology of mathematics and physics. This is camera-ready copy prepared for publication as a book, but at the last minute I decided to publish it…
Karl Pearson is the leading figure of XX century statistics. He and his co-workers crafted the core of the theory, methods and language of frequentist or classical statistics -- the prevalent inductive logic of contemporary science.…