Related papers: De Divino Errore
The "paradox" arises in the Two Envelopes Paradox from the incorrect formulation of the argument. The infomation given is misused and therefore the results are incorrect for the question asked. The key is to be clear on what question we are…
In his encyclopedic work on astronomy, the 1651 Almagestum Novum, the Italian Jesuit Giovanni Battista Riccioli (1598-1671) argued against the movement of the Earth on the grounds that (among other things), if the Earth rotated, that…
What is the largest number accessible to the human imagination? The question is neither entirely mathematical nor entirely philosophical. Mathematical formulations of the problem fall into two classes: those that fail to fully capture the…
We give some lectures on the work on formal logic of Jacques Herbrand, and sketch his life and his influence on automated theorem proving. The intended audience ranges from students interested in logic over historians to logicians. Besides…
The idea of using measure theoretic concepts to investigate the size of number theoretic sets, originating with E. Borel, has been used for nearly a century. It has led to the development of the theory of metrical Diophantine approximation,…
Review of the book: Distribution modulo one and Diophantine approximation, by Yann Bugeaud, Cambridge University Press 2012. ISBN 978-0521111690, 316 pp.
This essay, originally published in the Sept 1990 Notices of the AMS, discusses problems of our mathematical education system that often stem from widespread misconceptions by well-meaning people of the process of learning mathematics. The…
I try to clarify several confusions in the popular literature concerning chaos, determinism, the arrow of time, entropy and the role of probability in physics. Classical ideas going back to Laplace and Boltzmann are explained and defended…
Given an inaccessible J\'onsson cardinal $\lambda$, a sequence of results due to Shelah from Cardinal Arithmetic and Sh413 tell us that $\lambda$ must be at least $\lambda\times\omega$-Mahlo. We may then ask ourselves whether we can improve…
Wigner's famous and influential claim that mathematics is "unreasonably effective" in physics is founded on unreasonable assumptions about the nature of mathematics and its independence of physics. Here I argue that what is surprising is…
The \textit{Collatz's conjecture} is an unsolved problem in mathematics. It is named after Lothar Collatz in 1973. The conjecture also known as Syrucuse conjecture or problem. Take any positive integer $ n $. If $ n $ is even then divide it…
Let $\mathcal{D}=(d_n)_{n=1}^\infty$ be a bounded sequence of integers with $d_n\ge 2$ and let $(i, j)$ be a pair of strictly positive numbers with $i+j=1$. We prove that the set of $x \in \RR$ for which there exists some constant $c(x) >…
The fundamental aim of the paper is to correct an harmful way to interpret a Goedel's erroneous remark at the Congress of Koenigsberg in 1930. Despite the Goedel's fault is rather venial, its misreading has produced and continues to produce…
More than a paper, this is just a little divertissement about coauthoring, the Hirsch h-index, and bibliometric evaluation in general. Without pretending to yield any general conclusions, what I found rummaging through the physics…
In a recent paper, Svante Janson has considered a conjecture suggested by Va\v{s}ek Chv\a'atal dealing with the probability that a binomial random variable with parameters $n$ and $m/n$ - where $m$ is an integer - exceeds its expectation…
This is a reply to Johansen's comment on `Are Financial Crashes Predictable?', by L. Laloux, M. Potters, R. Cont, J.P. Aguilar, J.P. Bouchaud, Europhys. Lett. 45, p. 1 (1999).
We use a logical device called the Dutch Book to establish epistemic confidence, defined as the sense of confidence \emph{in an observed} confidence interval. This epistemic property is unavailable -- or even denied -- in orthodox…
In this paper, we show that the single deletion correcting Varshamov-Tenengolts code, with minor modifications, can also correct an ordered deletion-erasure pattern where one deletion and at most one erasure occur and the deletion always…
During the last centuries of human history, many questions was repeated in connection with the great problems of the existence and origin of human beings, and also of the Universe. The old questions of common sense and philosophy have not…
This is an English translation from the Latin original of Leonhard Euler's ``Solutio facilior problematis Diophantei circa triangulum, in quo rectae ex angulis latera opposita bisecantes rationaliter exprimantur''. In this paper, Euler…