Related papers: Arithmetic in Metamath, Case Study: Bertrand's Pos…
This is an exposition of facts about Arithmetic with an approach via mathematical logic. In Section 1 we present Peano Arithmetic, PA, and the complete theory of $\mathbb{N}$, and we show that $\mathbb{N}$ is a prime model of the theory of…
Current autoformalization benchmarks are largely focused on olympiad or undergraduate mathematics, while graduate and research-level mathematics remains underexplored. In this paper, we introduce MathAtlas, the first large-scale…
In this paper, we are going to prove a famous problem concerning prime numbers. Bertrand postulate states that there is always a prime p with n < p < 2n, if n > 1. Bertrand postulate is not a newer one to be proven, in fact, after his…
Despite the recent progress in automatic theorem provers, proof engineers are still suffering from the lack of powerful proof automation. In this position paper we first report our proof strategy language based on a meta-tool approach.…
Following decades of sustained improvement, metaheuristics are one of the great success stories of optimization research. However, in order for research in metaheuristics to avoid fragmentation and a lack of reproducibility, there is a…
While pre-trained language models achieve impressive performance on various NLP benchmarks, they still struggle with tasks that require numerical reasoning. Recent advances in improving numerical reasoning are mostly achieved using very…
In this paper we present the experimental results that more clearly than any theory suggest an answer to the question: when in detection of large (probably) prime numbers to apply, a very resource demanding, Miller-Rabin algorithm. Or, to…
We report on a pedagogical experiment to make mathematics easy by changing its philosophy. The Western philosophy of math originated in religious beliefs about mathesis, cursed by the church. Later, mathematics was "reinterpreted", in a…
I propose a system for Automated Theorem Proving in higher order logic using deep learning and eschewing hand-constructed features. Holophrasm exploits the formalism of the Metamath language and explores partial proof trees using a…
The overarching theme of the following pages is that mathematical logic -- centered around the incompleteness theorems -- is first and foremost an investigation of $\textit{computation}$, not arithmetic. Guided by this intuition we will…
We present a categorical framework for formal systems in which inference rules with $m$ metavariables over a category of syntax $\mathscr{S}$, taken to be a cartesian PROP, are represented by operations of arity $k \to n$ equipped with…
We present a new asynchronous model of computation named Stellar Resolution based on first-order unification. This model of computation is obtained as a formalisation of Girard's transcendental syntax programme, sketched in a series of…
In order to properly train a machine learning model, data must be properly collected. To guarantee a proper data collection, verifying that the collected data set holds certain properties is a possible solution. For example, guaranteeing…
Herbrand's theorem plays an important role both in proof theory and in computer science. Given a Herbrand skeleton, which is basically a number specifying the count of disjunctions of the matrix, we would like to get a computable bound on…
We formalise the pi-calculus using the nominal datatype package, based on ideas from the nominal logic by Pitts et al., and demonstrate an implementation in Isabelle/HOL. The purpose is to derive powerful induction rules for the semantics…
We introduce Aristotle, an AI system that combines formal verification with informal reasoning, achieving gold-medal-equivalent performance on the 2025 International Mathematical Olympiad problems. Aristotle integrates three main…
This note is mainly to point out, if needed, that uncertainty about models and their parameters has little to do with a `paradox'. The proposed `solution' is to formulate practical questions instead of seeking refuge into abstract…
We propose a new type of quantum computer which is used to prove a spectral representation for a class F of computable sets. When S in F codes the theorems of a formal system, the quantum computer produces through measurement all theorems…
Linear and semidefinite programming (LP, SDP), regularisation through basis pursuit (BP) and Lasso have seen great success in mathematics, statistics, data science, computer-assisted proofs and learning. The success of LP is traditionally…
In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that…