Related papers: An Explicit Conjectured Determinant Evaluation Who…

Presented here are over one hundred conjectures ranging from easy to difficult, from many mathematical fields. I also summarize briefly methods and tools that have led to this collection.

In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.

In this work, we empirically examine human-AI decision-making in the presence of explanations based on predicted outcomes. This type of explanation provides a human decision-maker with expected consequences for each decision alternative at…

A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.

A determinant evaluation is proven, a special case of which establishes a conjecture of Bombieri, Hunt, and van der Poorten (Experimental Math\. {\bf 4} (1995), 87--96) that arose in the study of Thue's method of approximating algebraic…

We give a more strong heuristic justification of our conjecture on the excess of the odious primes.

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

A considerable body of work in AI has been concerned with aggregating measures of confirmatory and disconfirmatory evidence for a common set of propositions. Claiming classical probability to be inadequate or inappropriate, several…

The On-Line Encyclopedia Of Integer Sequences , that wonderful resource that most combinatorialists, and many other mathematicians and scientists, use at least once a day, is a treasure trove of mathematical information, and, one of its…

The remarkable success of Artificial Intelligence in advancing automated decision-making is evident both in academia and industry. Within the plethora of applications, ranking systems hold significant importance in various domains. This…

We give an identity which is conjectured and proved by using an implementation in Multi-WZ.

We give a generalization and a short mechanized proof of determinant conjectured by G. Kuperberg and J. Propp. Further generalizations and applications of the method to some q-analogues may be found in http://www.math.temple.edu/~tewodros

We numerically estimate the critical exponents of certain enumeration sequences that naturally generalize the famous Catalan and super-Catalan sequences, and raise deep and original questions about their exact values, and whether they are…

Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research. A mitigation is using LLMs to generate formal proofs in languages like Lean. We perform the…

We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.

Mathematical proof aims to deliver confident conclusions, but a very similar process of deduction can be used to make uncertain estimates that are open to revision. A key ingredient in such reasoning is the use of a "default" estimate of…

This is a complement to my previous article "Advanced Determinant Calculus" (S\'eminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described…

Explainable recommendation has shown its great advantages for improving recommendation persuasiveness, user satisfaction, system transparency, among others. A fundamental problem of explainable recommendation is how to evaluate the…

We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.

As AI systems advance, AI evaluations are becoming an important pillar of regulations for ensuring safety. We argue that such regulation should require developers to explicitly identify and justify key underlying assumptions about…