Related papers: Observations about Leonardo's drawings for Luca Pa…
After a short introduction to Pillai's work on Diophantine questions, we quote some later developments and we discuss related open problems.
Duerer's engraving ``MELENCOLIA I'' was circulated in two versions not previously distinguished. Besides their conspicuous early Renaissance scientific instruments and tools, they contain numerous apparently unreported concealments whose…
Leonid Levin (arxiv.org/abs/cs/0503039v14, p.7) published a new (and very nice) proof of G\'acs-Ku\v{c}era's theorem that occupies only a few lines when presented in his style. We try to explain more details and discuss the connection of…
As is well known, several Roman sources report on the existence of a town foundation ritual, inherited from the Etruscans, which allegedly included astronomical references. However, the possible existence of astronomical orientations in the…
On the basis of Galilean invariance and the Doppler formula, combined with an observational condition, it is shown that the constancy of the velocity of light {\it in vacuo} can be derived, together with time-dilatation and Lorentz…
Drawing (a multiset of) coloured balls from an urn is one of the most basic models in discrete probability theory. Three modes of drawing are commonly distinguished: multinomial (draw-replace), hypergeometric (draw-delete), and Polya…
In this article (it's only in italian, but I'm translating it) I will try to solve some questions about a mathematical problem that my friend Patrizio Frederic, a researcher in statistics at the University of Modena, proposed to me. Given…
In this article I will address some questions about a mathematical problem that my friend Patrizio Frederic, a researcher in statistics at the University of Modena, proposed to me. Given some parallel line segments, is there at least one…
We define certain arithmetic derivatives on $\mathbb{Z}$ that respect the Leibniz rule, are additive for a chosen equation $a+b=c$, and satisfy a suitable non-degeneracy condition. Using Geometry of Numbers, we unconditionally show their…
Euclid uses an undefined notion of "equal figures", to which he applies the common notions about equals added to equals or subtracted from equals. When (in previous work) we formalized Euclid Book~I for computer proof-checking, we had to…
This note is concerned with the disproof of the most general case of Parker's conjecture. The conjecture relates a certain group theoretic objects to the field of moduli of a Dessin d'enfant.
This essay demonstrates the key role of Astronomy in Botticelli's "Venus and Mars-NG915" painting, to date only very partially understood. Worthwhile coincidences among the principles of the Ficinian philosophy, the historical characters…
In no other epoch of Western history like in the Middle Ages, cosmology was so key an element of culture and, one way or another, the motion of the heavens ended up impregnating the literature of that time. Among the most noteworthy poets…
This article considers the Dissertatio de Arte Combinatoria, published in 1666 and relatively neglected by Leibniz s scholars. However in recent times the tide seems to be changing. Our work presents three main parts (sections II, III and…
An account is given of some topical unpublished work by Ettore Majorana, revealing his very deep intuitions and skilfulness in Theoretical Physics. The relevance of the quite unknown results obtained by him is pointed out as well.
This note is the transcription of an interview with Professor Luigi Rodino, on the occasion of the ISAAC-ICMAM Conference of Analysis in Developing Countries (December 2, 2024 - Bogot\`a), that was dedicated to him. Luigi Rodino is at…
E394 in the Enestrom index. Translated from the Latin original, "De partitione numerorum in partes tam numero quam specie datas" (1768). Euler finds a lot of recurrence formulas for the number of partitions of $N$ into $n$ parts from some…
We survey Vojta's higher-dimensional generalizations of the $abc$ conjecture and Szpiro's conjecture as well as recent developments that apply them to various problems in arithmetic dynamics. In particular, the "$abcd$ conjecture" implies a…
Unusual features of water waves that Galileo described in a letter to Cardinal Orsini in 1616 are revisited from the perspectives of singular optics and geometric analysis.
We explicitly derive the Christoffel symbols in terms of adapted frame fields for the Levi-Civita connection of a Lorentzian $n$-manifold $(M, g)$, equipped with a prescribed optical geometry of K\"ahler-Sasaki type. The formulas found in…