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The Internet of Mirrors (IoM) is an emerging IoT ecosystem of interconnected smart mirrors designed to deliver personalised services across a three-tier node hierarchy spanning consumer, professional, and hub nodes. Determining where…
The paper collects preparatory work for interdisciplinary collaboration between three partners, between (1) expertise in improving accessibility of studies for impaired individuals, (2) expertise in developing educational mathematics…
Olympiad-level physics problem-solving significantly challenges both humans and artificial intelligence (AI), as it requires integrating appropriate modeling, application of physical principles, and precise calculation within long reasoning…
Computing olympiads contain some of the most challenging problems for humans, requiring complex algorithmic reasoning, puzzle solving, in addition to generating efficient code. However, it has been understudied as a domain to evaluate…
Hybrid is a formal theory implemented in Isabelle/HOL that provides an interface for representing and reasoning about object languages using higher-order abstract syntax (HOAS). This interface is built around an HOAS variable-binding…
Artificial intelligence (AI) has demonstrated impressive progress in mathematical reasoning, yet its integration into the practice of mathematical research remains limited. In this study, we investigate how the AI Mathematician (AIM) system…
We present an ongoing effort to build a framework and a library in Isabelle/HOL for formalising primal-dual arguments for the analysis of algorithms. We discuss a number of example formalisations from the theory of matching algorithms,…
We significantly improve the performance of the E automated theorem prover on the Isabelle Sledgehammer problems by combining learning and theorem proving in several ways. In particular, we develop targeted versions of the ENIGMA guidance…
Recently, the physical capabilities of (M)LLMs have garnered increasing attention. However, existing benchmarks for physics suffer from two major gaps: they neither provide systematic and up-to-date coverage of real-world physics…
Large language models (LLM), such as Google's Minerva and OpenAI's GPT families, are becoming increasingly capable of solving mathematical quantitative reasoning problems. However, they still make unjustified logical and computational…
This paper presents a framework for the implementation of online programming competitions, including a set of principles for the design of the multiplayer game and a practical framework for the construction of the competition environment.…
We present a formalization of basics related to infinite words in the generic proof assistant Isabelle/HOL. Furthermore, we present a formalization of purely morphic and morphic languages. Finally, we present a formalized definition of…
The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO and have made significant progress. This paper focuses on formal verification,…
We present AlphaGeometry2 (AG2), a significantly improved version of AlphaGeometry introduced in (Trinh et al., 2024), which has now surpassed an average gold medalist in solving Olympiad geometry problems. To achieve this, we first extend…
Recent progress in large language models (LLMs) has moved the frontier from puzzle-solving to science-grade reasoning-the kind needed to tackle problems whose answers must stand against nature, not merely fit a rubric. Physics is the…
An interactive theorem prover, Isabelle, is under development. In LCF, each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a…
The formalisation of mathematics is continuing rapidly, however combinatorics continues to present challenges to formalisation efforts, such as its reliance on techniques from a wide range of other fields in mathematics. This paper presents…
In this paper, we introduce a combination of novel and exciting tasks: the solution and generation of linguistic puzzles. We focus on puzzles used in Linguistic Olympiads for high school students. We first extend the existing benchmark for…
Interactive machine learning (IML) is a field of research that explores how to leverage both human and computational abilities in decision making systems. IML represents a collaboration between multiple complementary human and machine…
OpenAI and DeepMind's AIs recently got gold at the IMO math olympiad and ICPC programming competition. We show frontier AI is similarly good at hacking by letting GPT-5 compete in elite CTF cybersecurity competitions. In one of this year's…