Related papers: De Divino Errore
In their "How proper are Bayesian models in the astronomical literature?" [arXiv:1712.03549], Hyungsuk Tak, Sujit K. Ghosh and Justin A. Ellis criticised my work with false statements. This is an infamous case of straw man fallacy. They…
We discuss the statistics involved in the legal case of the nurse Lucia de B. in The Netherlands, 2003-2004. Lucia de B. witnessed an unusually high number of incidents during her shifts, and the question arose as to whether this could be…
It is argued that Goedel's incompleteness theorem should be seen as self-evident, rather than unexpected or surprising.
Some Goedel centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. [Enriques lecture given…
In spite of its title, the book mostly treats probability theory: the law of large numbers (regarded as a principle); formal definition of a random variable and law of distribution; the misnamed Cauchy distribution; functions now named…
Quantum mechanics represents one of the greatest triumphs of human intellect and, undoubtedly, is the most successful physical theory we have to date. However, since its foundation about a century ago, it has been uninterruptedly the center…
We correct an error in [I. Kangasniemi, and J. Onninen, On the heterogeneous distortion inequality. Math. Ann. 384 (2022), no. 3-4, 1275-1308.]
In 1927 Heisenberg discovered that the ``more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa''. Four years later G\"odel showed that a finitely specified, consistent formal…
A re-examination of a well-known iconographic source, the "Allegory of Sight" by Jan Brueghel the Elder and Peter Paul Rubens, reveals that one of the two telescopes depicted in the painting has a highly unusual,and until now unknown to the…
Van der Waerden's theorem, published in Nieuw. Arch. Wisk. 15 (1927), acted as a catalyst for major further developments in Ramsey theory. In this survey, we delve into the legacy of this mathematical gem, tracing its historical origin,…
We explore Leibniz's understanding of the differential calculus, and argue that his methods were more coherent than is generally recognized. The foundations of the historical infinitesimal calculus of Newton and Leibniz have been a target…
I have noted a number of errors, most of them quite minor, in the {\em Encyclopedia of Cosmology} (New York and London: Garland), 1993, Norriss S. Hetherington, ed. The majority occur in my mathematically verbose article, ``Fundamental…
Paul Erdos conjectured that for every n in N, n>1, there exist a, b, c natural numbers, not necessarily distinct, so that 4/n=1/a+1/b+1/c (see \cite{rg}). In this paper we prove an extension of Mordell's theorem and formulate a conjecture…
We investigate the implications of a curious biconditional involving divisors of odd perfect numbers, if Dris conjecture that $q^k < n$ holds, where $q^k n^2$ is an odd perfect number with Euler prime $q$. We then show that this…
Can we really falsify truth by dictat? A critical note on J. R. Lucas' 1996 remarks concerning non-standard models of first-order Peano Arithmetic.
The famous van der Waerden theorem states that if partition N into finitely many cells then one of them will contain arbitrary length arithmetic progressions. It has a polynomial version also. In this article we will prove the near 0…
This paper has been withdrawn by the author because Conjecture 1 is false. Please see arXiv:0901.2093 for a justification that Conjecture 1 is false. The other main results are also available from the above URL.
In his paper on the incompleteness theorems, G\"odel seemed to say that a direct way of constructing a formula that says of itself that it is unprovable might involve a faulty circularity. In this note, it is proved that 'direct'…
We correct Miyabe's proof of van Lambalgen's Theorem for truth-table Schnorr randomness (which we will call uniformly relative Schnorr randomness). An immediate corollary is one direction of van Lambalgen's theorem for Schnorr randomness.…
Remarks on mathematical proof and the practice of mathematics.