Related papers: Is Mathematics Obsolete?
A core challenge for both physics and artificial intellicence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of…
We describe AI agents as stochastic dynamical systems and frame the problem of learning to reason as in transductive inference: Rather than approximating the distribution of past data as in classical induction, the objective is to capture…
The remarkable advancements in artificial intelligence (AI), primarily driven by deep neural networks, have significantly impacted various aspects of our lives. However, the current challenges surrounding unsustainable computational…
We propose that symbols are first and foremost external communication tools used between intelligent agents that allow knowledge to be transferred in a more efficient and effective manner than having to experience the world directly. But,…
Rationality has been an intriguing topic for several decades. Even the scope of definition of rationality across different subjects varies. Several theories (e.g., game theory) initially evolved on the basis that agents (e.g., humans) are…
Artificial intelligence (AI) has become a part of everyday conversation and our lives. It is considered as the new electricity that is revolutionizing the world. AI is heavily invested in both industry and academy. However, there is also a…
The ability to use symbols is the pinnacle of human intelligence, but has yet to be fully replicated in machines. Here we argue that the path towards symbolically fluent artificial intelligence (AI) begins with a reinterpretation of what…
It is inconceivable how chaotic the world would look to humans, faced with innumerable decisions a day to be made under uncertainty, had they been lacking the capacity to distinguish the relevant from the irrelevant---a capacity which…
We introduce the AI co-mathematician, a workbench for mathematicians to interactively leverage AI agents to pursue open-ended research. The AI co-mathematician is optimized to provide holistic support for the exploratory and iterative…
Mathematical maturity is a key concept for the professional life of a mathematician. This paper is not only a brief discussion of the importance of mathematical maturity but also presents some unusual ways we can use the concept to help our…
This paper provides an overview of the intricate relationship between social dynamics, technological advancements, and pioneering figures in the fields of cybernetics and artificial intelligence. It explores the impact of collaboration and…
We paraphrase Descartes' famous dictum in the area of AI ethics where the "I doubt and therefore I am" is suggested as a necessary aspect of morality. Therefore AI, which cannot doubt itself, cannot possess moral agency. Of course, this is…
Reasoning is central to human intelligence, enabling structured problem-solving across diverse tasks. Recent advances in large language models (LLMs) have greatly enhanced their reasoning abilities in arithmetic, commonsense, and symbolic…
Mathematics has long been conveyed through natural language, primarily for human understanding. With the rise of mechanized mathematics and proof assistants, there is a growing need to understand informal mathematical text, yet most…
Mathematical research is often motivated by the desire to reach a beautiful result or to prove it in an elegant way. Mathematician's work is thus strongly influenced by his aesthetic judgments. However, the criteria these judgments are…
AI is a magnificent field that directly and profoundly touches on numerous disciplines ranging from philosophy, computer science, engineering, mathematics, decision and data science and economics, to cognitive science, neuroscience and…
We integrate foundational theories of meaning with a mathematical formalism of artificial general intelligence (AGI) to offer a comprehensive mechanistic explanation of meaning, communication, and symbol emergence. This synthesis holds…
"Is math useful?" might sound as a trick question. And it is. Of course math is useful, we live in a data-filled world and every aspect of life is totally entwined with math applications, both trivial and subtle applications, of both basic…
This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…
The paper discusses relationships between aesthetics theory and mathematical models of mind. Mathematical theory describes abilities for concepts, emotions, instincts, imagination, adaptation, learning, cognition, language, approximate…