Related papers: AlephZero and Mathematical Experience
AlphaZero learns to play go, chess and shogi at a superhuman level through self play given only the rules of the game. This raises the question of whether a similar thing could be done for mathematics -- a MathZero. MathZero would require a…
We cast aspects of consciousness in axiomatic mathematical terms, using the graphical calculus of general process theories (a.k.a symmetric monoidal categories and Frobenius algebras therein). This calculus exploits the ontological…
Fact-checking is the process of evaluating the veracity of claims (i.e., purported facts). In this opinion piece, we raise an issue that has received little attention in prior work -- that some claims are far more difficult to fact-check…
A new generation of educational mathematics software is being shaped in ThEdu and other academic communities on the side of computer mathematics. Respective concepts and technologies have been clarified to an extent, which calls for…
Artificial intelligence is transforming mathematics at a speed and scale that demand active engagement from the mathematical community. We examine five areas where this transformation is particularly pressing: values, practice, teaching,…
The ability to automatically generalise (interactive) proofs and use such generalisations to discharge related conjectures is a very hard problem which remains unsolved. Here, we develop a notion of goal types to capture key properties of…
Mathematical proof is undoubtedly the cornerstone of mathematics. The emergence, in the last years, of computing and reasoning tools, in particular automated geometry theorem provers, has enriched our experience with mathematics immensely.…
The impact of Machine Learning (ML) algorithms in the age of big data and platform capitalism has not spared scientific research in academia. In this work, we will analyse the use of ML in fundamental physics and its relationship to other…
Generative AI and Large Language Models (LLMs) hold promise for automating spreadsheet formula creation. However, due to hallucinations, bias and variable user skill, outputs obtained from generative AI cannot be assumed to be accurate or…
The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…
Objects are a centerpiece of the mathematical realm and our interaction with and reasoning about it, just as they are of the physical one (if not more). And humans' mathematical reasoning must ultimately be grounded in our general…
In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…
Multiple-choice questions (MCQs) offer the most promising avenue for skill evaluation in the era of virtual education and job recruiting, where traditional performance-based alternatives such as projects and essays have become less viable,…
It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…
The proliferation of artificial intelligence provides an opportunity to create psychological spaciousness in society. Spaciousness is defined as the ability to hold diverse interpersonal interactions and forms the basis for vulnerability…
This paper argues that, insofar as we doubt the bivalence of the Continuum Hypothesis or the truth of the Axiom of Choice, we should also doubt the consistency of third-order arithmetic, both the classical and intuitionistic versions.…
Partial-monitoring games constitute a mathematical framework for sequential decision making problems with imperfect feedback: The learner repeatedly chooses an action, opponent responds with an outcome, and then the learner suffers a loss…
Artificial agents now generate behavior rich enough to invite trust, surprise, and concern, yet our evaluation tools still privilege capability scores over psychological structure. This paper argues that the philosophical impasse between…
Artificial intelligence has impacted many aspects of human life. This paper studies the impact of artificial intelligence on economic theory. In particular we study the impact of artificial intelligence on the theory of bounded rationality,…
The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…