Related papers: Artificial Intelligence and the Structure of Mathe…
We employ techniques of machine-learning, exemplified by support vector machines and neural classifiers, to initiate the study of whether AI can "learn" algebraic structures. Using finite groups and finite rings as a concrete playground, we…
The growing ubiquity of artificial intelligence (AI), in particular large language models (LLMs), has profoundly altered the way in which learners gain knowledge and interact with learning material, with many claiming that AI positively…
The evolution of AI systems toward agentic operation and context-aware retrieval necessitates transforming unstructured text into structured formats like tables, knowledge graphs, and charts. While such conversions enable critical…
The article analyses foundational principles relevant to the creation of artificial general intelligence (AGI). Intelligence is understood as the ability to create novel skills that allow to achieve goals under previously unknown…
This paper demonstrates that artificial intelligence can accelerate mathematical discovery by autonomously solving an open problem in theoretical physics. We present a neuro-symbolic system, combining the Gemini Deep Think large language…
The classical platonist / formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: \emph{Is new mathematics discovered or invented? Using examples from my own mathematical work during the…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
This talk presents foundations of mathematics as a historically variable set of principles appealing to various modes of human intuition and devoid of any prescriptive/prohibitive power. At each turn of history, foundations crystallize the…
In conceptual modeling (CM), humans apply abstraction to represent excerpts of reality for means of understanding and communication, and processing by machines. Artificial Intelligence (AI) is applied to vast amounts of data to…
Artificial intelligence (AI) systems, such as machine learning algorithms, have allowed scientists, marketers and governments to shed light on correlations that remained invisible until now. Beforehand, the dots that we had to connect in…
Artificial intelligence (AI) is transforming scientific research, including proteomics. Advances in mass spectrometry (MS)-based proteomics data quality, diversity, and scale, combined with groundbreaking AI techniques, are unlocking new…
Materials are the foundation of modern society, underpinning advancements in energy, electronics, healthcare, transportation, and infrastructure. The ability to discover and design new materials with tailored properties is critical to…
Specialized intelligent systems can be found everywhere: finger print, handwriting, speech, and face recognition, spam filtering, chess and other game programs, robots, et al. This decade the first presumably complete mathematical theory of…
Symmetries play a central role in physics, organizing dynamics, constraining interactions, and determining the effective number of physical degrees of freedom. In parallel, modern artificial intelligence methods have demonstrated a…
Artificial intelligence (AI) in its various forms finds more and more its way into complex distributed systems. For instance, it is used locally, as part of a sensor system, on the edge for low-latency high-performance inference, or in the…
The overarching problem in artificial intelligence (AI) is that we do not understand the intelligence process well enough to enable the development of adequate computational models. Much work has been done in AI over the years at lower…
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…
Recent advances in computing have changed not only the nature of mathematical computation, but mathematical proof and inquiry itself. While artificial intelligence and formalized mathematics have been the major topics of this conversation,…
Artificial intelligence (AI) is an extensive scientific discipline which enables computer systems to solve problems by emulating complex biological processes such as learning, reasoning and self-correction. This paper presents a…
The evolution of artificial intelligence (AI) has rendered the boundary between humanity and computational machinery increasingly ambiguous. In the presence of more interwoven relationships within human-machine symbiosis, the very notion of…