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We present a tool for reasoning in and about propositional sequent calculi. One aim is to support reasoning in calculi that contain a hundred rules or more, so that even relatively small pen and paper derivations become tedious and error…
If scientific discovery is one of the main driving forces of human progress, insight is the fuel for the engine, which has long attracted behavior-level research to understand and model its underlying cognitive process. However, current…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
Can outreach inspire and lead to research and vice versa? In this work, we introduce our approach to the gamification of research in mathematics and computer science through three illustrative examples. We discuss our primary motivations…
This is a theoretical and computational strategy exploration of the visually attractive game IQ-Link. Not all games which are visually appealing are worthy of your time as a puzzlist. This analysis gives a would-be addict some idea of what…
Pebble games were extensively studied in the 1970s and 1980s in a number of different contexts. The last decade has seen a revival of interest in pebble games coming from the field of proof complexity. Pebbling has proven to be a useful…
This paper introduces MazeBase: an environment for simple 2D games, designed as a sandbox for machine learning approaches to reasoning and planning. Within it, we create 10 simple games embodying a range of algorithmic tasks (e.g. if-then…
Can AI solve all math? What do we actually mean by doing mathematics? How do we communicate mathematics? What is mathematics beyond problem solving? This essay is my attempt to answer these questions.
Thirty original and collected problems, puzzles, and paradoxes in mathematics and physics are explained in this paper, taught by the author to the elementary and high school teachers at the University of New Mexico - Gallup in 1997-8 and…
Questions concerning origin of mathematical knowledge and roles of language and intuition (imagery) in mathematical thoughts are long standing and widely debated. By introspection, mathematicians usually have some beliefs regarding these…
In this article, we present our findings from ten years of research on intelligent educational games. We discuss the architecture of our training environments for learning spelling and mathematics, and specifically focus on the…
The Jump-Jump game, as a simple yet challenging casual game, provides an ideal testing environment for studying LLM decision-making capabilities. The game requires players to precisely control jumping force based on current position and…
Children are one of the groups most influenced by COVID-19-related social distancing, and a lack of contact with peers can limit their opportunities to develop social and collaborative skills. However, remote socialization and collaboration…
In this article, we employ mathematical concepts as a tool to examine the phenomenon of consciousness experience and logical phenomena. Through our investigation, we aim to demonstrate that our experiences, while not confined to…
We introduce GuessWhat?!, a two-player guessing game as a testbed for research on the interplay of computer vision and dialogue systems. The goal of the game is to locate an unknown object in a rich image scene by asking a sequence of…
This article contains a selection of problems from the American Mathematics Competitions.
We present a pilot study on crea.blender, a novel co-creative game designed for large-scale, systematic assessment of distinct constructs of human creativity. Co-creative systems are systems in which humans and computers (often with Machine…
I discuss puzzles that require thinking outside the box. I also discuss the box inside of which many people think.
We present iBall, a basketball video-watching system that leverages gaze-moderated embedded visualizations to facilitate game understanding and engagement of casual fans. Video broadcasting and online video platforms make watching…