Related papers: The Wild Number Problem: math or fiction?
Mathematics cannot anymore be assimilated to a linguistic game, where formal proofs are strongly differentiated with conjectural thinking, without building any category of knowledge to understand the passage (Wittgenstein's gist). Nowadays,…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
Quantum mechanics led to spectacular technological developments, discovery of new constituents of matter and new materials. However there is still no consensus on its interpretation and limitations. Some scientists and scientific writers…
Recently, the educational initiative TED-Ed has published a popular brain teaser coined the 'frog riddle', which illustrates non-intuitive implications of conditional probabilities. In its intended form, the frog riddle is a reformulation…
In this article, I discuss the relationship of mathematics to the physical world, and to other spheres of human knowledge. In particular, I argue that Mathematics is created by human beings, and the number $\pi$ can not be said to have…
This paper was withdrawn by the authors.
This paper looks at how ancient mathematicians (and especially the Pythagorean school) were faced by problems/paradoxes associated with the infinite which led them to juggle two systems of numbers: the discrete whole/rationals which were…
The "Millennium Prize Problems" have a place in the history of mathematics. Here we tell some little-known anecdotes from the perspective of the planner of that project. These stories are far from their end; more likely they are just at…
In the last decade a huge amount of articles has been published studying pattern avoidance on permutations. From the point of view of enumeration, typically one tries to count permutations avoiding certain patterns according to their…
The "interior goat problem" is a numerical puzzle which has haunted mathematicians for nearly three centuries. Closed-form solutions have only been found for the two-dimensional case, and although approximations have been established for…
I argue that we must distinguish between: (0) the Three-Doors-Problem Problem [sic], which is to make sense of some real world question of a real person. (1) a large number of solutions to this meta-problem, i.e., many specific…
There is much interest in providing probabilistic semantics for defaults but most approaches seem to suffer from one of two problems: either they require numbers, a problem defaults were intended to avoid, or they generate peculiar side…
Throughout this article the major idea and conclusion is about comparing this method with some very famous methods like fourier series and wavelet, to show that the power of this approximation method is as much as to predicate many natural…
A strong link between complexity theory and literature is possible, i.e. feasible, under one proviso, namely that total novels be considered. However, neither in literature at large nor in complexity science has been literature seriously…
Thirty original and collected problems, puzzles, and paradoxes in mathematics and physics are explained in this paper, taught by the author to the elementary and high school teachers at the University of New Mexico - Gallup in 1997-8 and…
A recent paper proposing a model of the limiting speed of the domino effect is discussed with reference to its need and the need of models in general for validation against experimental data. It is shown that the proposed model diverges…
Can mathematics help us find our way through all the wonders and mysteries of the universe? When physicists describe the laws governing the physical world, mathematics is always involved. Is this due to the fact that the universe is, at…
It is argued that the occurrence of disproportionately ("un-natural") large (or small) numbers, as well as deep cancellations, are comparatively natural traits of the way Nature is geared to operate in most complex systems. The idea is…
This paper has been withdrawn by the author. In this article I review W\"ust's recent handbook on mathematical physics from a philosophical standpoint. It emerges a structural approach to mathematics which evidences the utility of logic in…
This PhD thesis deals with a number of different problems in mathematical physics with the common thread that they have probabilistic aspects. The problems all stem from mathematical studies of lattice systems in statistical and quantum…