Related papers: First Proof
Students in introductory physics courses often rely on ineffective strategies, focusing on final answers rather than understanding underlying principles. Integrating scientific argumentation into problem-solving fosters critical thinking…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
The highest level of mathematics research is traditionally seen as a solitary activity. Yet new innovations by mathematicians themselves are starting to harness the power of social computation to create new modes of mathematical production.…
The General AI Challenge is an initiative to encourage the wider artificial intelligence community to focus on important problems in building intelligent machines with more general scope than is currently possible. The challenge comprises…
Artificial intelligence (AI) technologies (re-)shape modern life, driving innovation in a wide range of sectors. However, some AI systems have yielded unexpected or undesirable outcomes or have been used in questionable manners. As a…
This paper collects some problems that I have encountered during the years, have puzzled me and which, to the best of my knowledge, are still open. Most of them are well-known and have been first stated by other authors. In this sad season…
Modern AI systems are reaping the advantage of novel learning methods. With their increasing usage, we are realizing the limitations and shortfalls of these systems. Brittleness to minor adversarial changes in the input data, ability to…
As automated reasoning systems advance rapidly, there is a growing need for research-level formal mathematical problems to accurately evaluate their capabilities. To address this, we present Formal Conjectures, an evolving benchmark of…
Despite significant developments in Proof Theory, surprisingly little attention has been devoted to the concept of proof verifier. In particular, the mathematical community may be interested in studying different types of proof verifiers…
A suite of impressive scientific discoveries have been driven by recent advances in artificial intelligence. These almost all result from training flexible algorithms to solve difficult optimization problems specified in advance by teams of…
We argue that it is neither necessary nor sufficient for a mathematical proof to have epistemic value that it be "correct", in the sense of formalizable in a formal proof system. We then present a view on the relationship between…
The Turing test may or may not be a valid test of machine intelligence. But in an age of generative AI, the test describes the positions we humans occupy. Judging whether or not something is human or machine produced is an everyday…
This book provides a comprehensive and accessible introduction to the emerging field of AI for mathematics. It covers the core principles and diverse applications of using artificial intelligence to advance mathematical research. Through…
As the real-world impact of Artificial Intelligence (AI) systems has been steadily growing, so too have these systems come under increasing scrutiny. In response, the study of AI fairness has rapidly developed into a rich field of research…
Automated decision systems are increasingly used for consequential decision making -- for a variety of reasons. These systems often rely on sophisticated yet opaque models, which do not (or hardly) allow for understanding how or why a given…
Verified artificial intelligence (AI) is the goal of designing AI-based systems that that have strong, ideally provable, assurances of correctness with respect to mathematically-specified requirements. This paper considers Verified AI from…
Artificial Intelligence (AI) increasingly shows its potential to outperform predicate logic algorithms and human control alike. In automatically deriving a system model, AI algorithms learn relations in data that are not detectable for…
A new generation of AI models generates step-by-step reasoning text before producing an answer. This text appears to offer a human-readable window into their computation process, and is increasingly relied upon for transparency and…
The opaqueness of many complex machine learning algorithms is often mentioned as one of the main obstacles to the ethical development of artificial intelligence (AI). But what does it mean for an algorithm to be opaque? Highly complex…
Scientific discovery is a complex cognitive process that has driven human knowledge and technological progress for centuries. While artificial intelligence (AI) has made significant advances in automating aspects of scientific reasoning,…