Related papers: Current Mathematics Appears to Be Inconsistent
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
G\"odel's second incompleteness theorem is standardly understood as showing that no sufficiently strong, consistent theory of arithmetic can prove its own consistency, a result typically interpreted against a model-theoretic background in…
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
In Mathematics is common to make a mistake and therefore a false conclusion arises. In each case it is important to recognize the mistake in order to avoid a similar one in the future. Geometric figures provide decisive help in order to…
Practicing mathematicians often assume that mathematical claims, when they are true, have good reasons to be true. Such a state of affairs is "unreasonable", in Wigner's sense, because basic results in computational complexity suggest that…
In the past century many fundamental results on unpredictability, undecidability and uncertainty have compelled scientists to grapple with the idea that some questions may never be resolved within our current theories. While this…
The paper presents a counterexample to the Hodge conjecture.
It appears paradoxical that science is producing outstanding new results and theories at a rapid rate at the same time that researchers are identifying serious problems in the practice of science that cause many reports to be irreproducible…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
The goal of this paper is to experiment new math concepts and theories, especially if they run counter to the classical ones. To prove that contradiction is not a catastrophe, and to learn to handle it in an (un)usual way. To transform the…
While explainability is a desirable characteristic of increasingly complex black-box models, modern explanation methods have been shown to be inconsistent and contradictory. The semantics of explanations is not always fully understood - to…
It is shown that the multiplicative anomaly in the vector-axial-vector model, which apparently has nothing to do with the breaking of classical current symmetries, nevertheless is strictly related to the well known consistent and covariant…
A disagreement of the empirical results with quantum mechanical predictions is pointed out in the experiment by M. Giustina et al. [arXiv:1212.0533].
We present in an informal way some recent results concerning a possible overlapping between classical unpredictability and quantum indeterminism.
Continued fractions are used to give an alternate proof of $e^{x/y}$ is irrational.
Natural language inference requires reasoning about contradictions, negations, and their commonsense implications. Given a simple premise (e.g., "I'm mad at you"), humans can reason about the varying shades of contradictory statements…
There have been a number of developments in measuring inconsistency in logic-based representations of knowledge. In contrast, the development of inconsistency measures for computational models of argument has been limited. To address this…
We present here a note which synthesizes our previous ideas concerning some problems in cosmology, and the numerical correspondences between the physical constants that we could deduce.
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
The derivation of the quantum retrodictive probability formula involves an error, an ambiguity. The end result is correct because this error appears twice, in such a way as to cancel itself. In addition, however, the usual expression for…