Related papers: MacLaurin and Morality
Number theory as a coherent mathematical subject started with the work of Fermat in the decade from 1630 to 1640, but modern number theory, that is, the systematic and mathematically rigorous development of the subject from fundamental…
Three years ago, we initiated a programme of research in which ideas and tools from statistical physics and network theory were applied to the field of comparative mythology. The eclecticism of the work, together with the perspectives it…
I am most honoured to have the privilege to present the Foreword to this fascinating and wonderfully varied collection of contributions, concerning the nature of computation and of its deep connection with the operation of those basic laws,…
The erroneous prediction of the speed of light in dispersive media has been looked upon historically as unequivocal proof that Newton's corpuscular theory is incorrect. Examination of his arguments shows that they were only directly…
The thought experiment (called the clock paradox or the twin paradox)proposed by Langevin in 1911 of two observers, one staying on Earth and the other making a trip toward a star with a velocity near the light velocity is very well known…
In 1866, Charles Ludwidge Dodgson published a paper concerning a method for evaluating determinants called the condensation method. His paper documented a new method to calculate determinants that was based on Jacobi's Theorem. The…
William Oliver Martin published "The Order and Integration of Knowledge" in 1957 to address the problem of the nature and the order of various kinds of knowledge; in particular, the theoretical problem of how one kind of knowledge is…
In a recent article, Luciano Floridi explains his view of Turing's legacy in connection to the philosophy of information. I will very briefly survey one of Turing's other contributions to the philosophy of information and computation,…
In a 1985 commentary to his collected works, Kolmogorov remarked that his 1932 paper "was written in hope that with time, the logic of solution of problems [i.e., intuitionistic logic] will become a permanent part of a [standard] course of…
Scientists have long aimed to discover meaningful formulae which accurately describe experimental data. A common approach is to manually create mathematical models of natural phenomena using domain knowledge, and then fit these models to…
Summary. The 'trait {\`a} preuves' is a 17th century expression that refers to drawings rigorously justified by mathematics. This work is a reflection on the principle of purity of methods from a historical, mathematical and epistemological…
We report on a pedagogical experiment to make mathematics easy by changing its philosophy. The Western philosophy of math originated in religious beliefs about mathesis, cursed by the church. Later, mathematics was "reinterpreted", in a…
We summarize the papers published by Einstein in the Annalen der Physik in the years 1902-04 on the derivation of the properties of thermal equilibrium on the basis of the mechanical equations of motion and of the calculus of probabilities.…
The Stirling approximation formula for $n!$ dates from 1730. Here we give new and instructive proofs of this and related approximation formulae via tools of probability and statistics. There are connections to the Central Limit Theorem and…
We present a novel unity of logic, viz., a single sequent calculus that embodies classical, intuitionistic and linear logics. Concretely, we define classical linear logic negative (CLL$^-$), a new logic that is classical and linear yet…
In this article Denis Diderot's Fifth Memoir of 1748 on the problem of a pendulum damped by air resistance is discussed. Diderot wrote the Memoir in order to clarify an assumption Newton made without further justification in the first pages…
The two of us have shared a fascination with James Victor Uspensky's 1937 textbook $Introduction \, to \, Mathematical \, Probability$ ever since our graduate student days: it contains many interesting results not found in other books on…
This paper introduces a refinement of the sequent calculus approach called cirquent calculus. While in Gentzen-style proof trees sibling (or cousin, etc.) sequents are disjoint sequences of formulas, in cirquent calculus they are permitted…
David Brink was one of the leading theoretical nuclear physicists of his generation. He made major contributions to the study of all aspects of nuclear physics embracing nuclear structure, nuclear scattering, and nuclear instability. His…
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 ---…