Related papers: Martin Gardner's Mistake
The treatment of systematic errors is often mishandled. This is due to lack of understanding and education, based on a fundamental ambiguity as to what is meant by the term. This note addresses the problems and offers guidance to good…
In this article, we study rates of convergence of the generalization error of multi-class margin classifiers. In particular, we develop an upper bound theory quantifying the generalization error of various large margin classifiers. The…
The finite satisfiability problem of two-variable logic extended by a linear order successor and a preorder successor is shown to be undecidable.
Starting from the first Hardy-Littlewood conjecture some topics will be covered: an empirical approach to the distribution of the twin primes in classes mod(10) and a simplified proof of the Bruns theorem . Finally, it will be explored an…
Developing a better understanding of surprising or counterintuitive phenomena has constituted a significant portion of deep learning research in recent years. These include double descent, grokking, and the lottery ticket hypothesis --…
Overfitting and generalization is an important concept in Machine Learning as only models that generalize are interesting for general applications. Yet some students have trouble learning this important concept through lectures and…
Decades of research suggest that information exchange in groups and organizations can reliably improve judgment accuracy in tasks such as financial forecasting, market research, and medical decision-making. However, we show that improving…
The ternary Goldbach conjecture, or three-primes problem, states that every odd number $n$ greater than $5$ can be written as the sum of three primes. The conjecture, posed in 1742, remained unsolved until now, in spite of great progress in…
Since the seminal paper by Tversky and Kahneman, the conjunction fallacy has been the subject of multiple debates and become a fundamental challenge for cognitive theories in decision-making. In this article, we take a rather uncommon…
Our interest is whether two binomial parameters differ, which parameter is larger, and by how much. This apparently simple problem was addressed by Fisher in the 1930's, and has been the subject of many review papers since then. Yet there…
This paper is one of a series in which elementary-education practice is analyzed by comparison with the history of mathematics, mathematical structure, modern practice, and (occasionally) cognitive neuroscience. The primary concerns are:…
Consider a person trying to spread an important message on a social network. He/she can spend hours trying to craft the message. Does it actually matter? While there has been extensive prior work looking into predicting popularity of…
Triality theory is proved for a general unconstrained global optimization problem. The method adopted is simple but mathematically rigorous. Results show that if the primal problem and its canonical dual have the same dimension, the…
Scattered factor (circular) universality was firstly introduced by Barker et al. in 2020. A word $w$ is called $k$-universal for some natural number $k$, if every word of length $k$ of $w$'s alphabet occurs as a scattered factor in $w$; it…
In this paper a result of Latala about the tail behavior of Gaussian polynomials will be discussed. Latala proved an interesting result about this problem in paper [2]. But his proof applied an incorrect statement at a crucial point. Hence…
There have been many attempts over the years to derive the Born Rule from the wave equation since Everett's Many Worlds Interpretation was proposed; however, none of these have been satisfactory as shown when critics pointed out loopholes…
Two prominent conjectures by Herbert J. Ryser have been falsely attributed to a somewhat obscure conference proceedings that he wrote in German. Here we provide a translation of that paper and try to correct the historical record at least…
In a recent preprint on ArXiv, Bacher introduced a twisted version of the Stern sequence. His paper contains in particular three conjectures relating the generating series for the Stern sequence and for the twisted Stern sequence. Soon…
In 1979, Weitzman introduced Pandora's box problem as a framework for sequential search with costly inspections. Recently, there has been a surge of interest in Pandora's box problem, particularly among researchers working at the…
High-quality distractors are crucial to both the assessment and pedagogical value of multiple-choice questions (MCQs), where manually crafting ones that anticipate knowledge deficiencies or misconceptions among real students is difficult.…