Related papers: From Euler to AI: Unifying Formulas for Mathematic…
There is an overwhelmingly large literature and algorithms already available on `large scale inference problems' based on different modeling techniques and cultures. Our primary goal in this paper is \emph{not to add one more new…
The purpose of this paper is to present series expansions for even powers of the number $\pi$. This is accomplished by generalizing Euler's method for solving the Basel Problem, which was published in 1735. We employ elementary symmetric…
Symmetry is present throughout nature and continues to play an increasingly central role in physics and machine learning. Fundamental symmetries, such as Poincar\'{e} invariance, allow physical laws discovered in laboratories on Earth to be…
LLM-based formal proof assistants (e.g., in Lean) hold great promise for automating mathematical discovery. But beyond syntactic correctness, do these systems truly understand mathematical structure as humans do? We investigate this…
We develop a method to recognize admissibility of $\Pi_{2}$-rules, relating this problem to a specific instance of the unification problem with linear constants restriction, called here "unification with simple variable restriction". It is…
Tools of Topological Data Analysis provide stable summaries encapsulating the shape of the considered data. Persistent homology, the most standard and well studied data summary, suffers a number of limitations; its computations are hard to…
This paper presents a comprehensive overview on the applications of artificial intelligence (AI) in mathematical research, highlighting the transformative role AI has begun to play in this domain. Traditionally, AI advancements have heavily…
We investigate the special class of formulas made up of arbitrary but finite com- binations of addition, multiplication, and exponentiation gates. The inputs to these formulas are restricted to the integral unit 1. In connection with such…
Automatically generating high-quality step-by-step solutions to math word problems has many applications in education. Recently, combining large language models (LLMs) with external tools to perform complex reasoning and calculation has…
Systems of equations with sets of integers as unknowns are considered. It is shown that the class of sets representable by unique solutions of equations using the operations of union and addition $S+T=\makeset{m+n}{m \in S, \: n \in T}$ and…
The ability to replicate predictions by machine learning (ML) or artificial intelligence (AI) models and results in scientific workflows that incorporate such ML/AI predictions is driven by numerous factors. An uncertainty-aware metric that…
The increasing complexity of AI systems has made understanding their behavior critical. Numerous interpretability methods have been developed to attribute model behavior to three key aspects: input features, training data, and internal…
We introduce universal neural likelihood inference (UNLI): enabling a single model to provide data-grounded, conditional likelihood predictions for arbitrary targets given any collection of observed features, across diverse domains and…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
There has recently been considerable interest in addressing the problem of unifying distributed statistical analyses into a single coherent inference. This problem naturally arises in a number of situations, including in big-data settings,…
Although many series exist for $\pi$ and $\pi^2$, very few are known for $\pi^3$. In this article, we derive, using a trigonometric identity obtained by Euler, two representations of $\pi^3$ involving infinite sums and the golden ratio. The…
Large Reasoning Models (LRMs) have made significant progress in mathematical capabilities in recent times. However, these successes have been primarily confined to competition-level problems. In this work, we propose AI Mathematician (AIM)…
The advancement in generative AI could be boosted with more accessible mathematics. Beyond human-AI chat, large language models (LLMs) are emerging in programming, algorithm discovery, and theorem proving, yet their genomics application is…
The vast corpus of physics equations forms an implicit network of mathematical relationships that traditional analysis cannot fully explore. This work introduces a graph-based framework combining neural networks with symbolic analysis to…