Related papers: From Euler to AI: Unifying Formulas for Mathematic…
Motivated by the remarkable success of artificial intelligence (AI) across diverse fields, the application of AI to solve scientific problems, often formulated as partial differential equations (PDEs), has garnered increasing attention.…
A large-scale experiment was conducted to find formulas relating to the base $e^\pi$. The numbers in this base are $$x = \sum_{n=0}^\infty {a(n)\over e^{\pi n}}$$ where $a(n)$ is taken from the OEIS catalog. These experiments were inspired…
Retrieving mathematical knowledge is a central task in both human-driven research, such as determining whether a result already exists, finding related results, and identifying historical origins, and in emerging AI systems for mathematics,…
AI for Mathematics (AI4Math) is not only intriguing intellectually but also crucial for AI-driven discovery in science, engineering, and beyond. Extensive efforts on AI4Math have mirrored techniques in NLP, in particular, training large…
We present a large number of analytic evaluations of Euler sums, namely sums such as \begin{align} M(m,n_0,n_1,n_2, \ldots, n_t) &= \sum_{k=1}^\infty \frac{H(k)^m}{k^{n_0} (k+1)^{n_1} (k+2)^{n_2} \cdots (k+t)^{n_t}}, \nonumber \end{align}…
We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for interactive theorem proving and discovery with LLMs. Human…
A series of formula is presented that are all inspired by the Ramanujan Notebooks [6]. One of them appears in the notebooks II about Zeta(3). That formula inspired others that appeared in 1998, 2006 and 2009 on the author's website and…
Mathematical concepts emerge through an interplay of processes, including experimentation, efforts at proof, and counterexamples. In this paper, we present a new multi-agent model for computational mathematical discovery based on this…
The recent LEP data for gauge coupling constants constrain many grand unified models. In this paper, we study several possibilities for unification of gauge coupling constants. Without an intermediate mass scale, the minimal supersymmetric…
Can artificial intelligence truly contribute to creative mathematical research, or does it merely automate routine calculations while introducing risks of error? We provide empirical evidence through a detailed case study: the discovery of…
AI for Mathematics (AI4Math) has emerged as a distinct field that leverages machine learning to navigate mathematical landscapes historically intractable for early symbolic systems. While mid-20th-century symbolic approaches successfully…
Many Artificial Intelligence tasks cannot be evaluated with a single quality criterion and some sort of weighted combination is needed to provide system rankings. A problem of weighted combination measures is that slight changes in the…
Lists, multisets, and sets are well-known data structures whose usefulness is widely recognized in various areas of Computer Science. These data structures have been analyzed from an axiomatic point of view with a parametric approach in (*)…
We study mathematical discovery through the lens of neurosymbolic reasoning, where an AI agent powered by a large language model (LLM), coupled with symbolic computation tools, and human strategic direction, jointly produced a new result in…
An investigation of the comparative efficiency of the different methods in which {\pi} is cal- culated. This thesis will compare and contrast five different methods in calculating {\pi} by first deriving the various proofs to each method…
Mathematical reasoning skills are essential for general-purpose intelligent systems to perform tasks from grocery shopping to climate modeling. Towards evaluating and improving AI systems in this domain, we propose LILA, a unified…
Large Language Models (LLMs) have shown impressive progress in mathematical reasoning. While data augmentation is promising to enhance mathematical problem-solving ability, current approaches are predominantly limited to instance-level…
In 2007, A.I.Aptekarev and his collaborators discovered a sequence of rational approximations to Euler's constant $\gamma$ defined by a linear recurrence. In this paper, we generalize this result and present an explicit construction of…
Across languages, numeral systems vary widely in how they construct and combine numbers. While humans consistently learn to navigate this diversity, large language models (LLMs) struggle with linguistic-mathematical puzzles involving…
Advances in large language models (LLMs) have spurred research into enhancing their reasoning capabilities, particularly in math-rich STEM (Science, Technology, Engineering, and Mathematics) documents. While LLMs can generate equations or…