Related papers: Is Mathematics Obsolete?
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…
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…
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…
Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
Combining machine learning with logic-based expert systems in order to get the best of both worlds are becoming increasingly popular. However, to what extent machine learning can already learn to reason over rule-based knowledge is still an…
With the rapid advancement of Artificial Intelligence (AI), Large Language Models (LLMs) have significantly impacted a wide array of domains, including healthcare, engineering, science, education, and mathematical reasoning. Among these,…
The proliferation of Artificial Intelligence (AI) in workplaces stands to change the way humans work, with job satisfaction intrinsically linked to work life. Existing research on human-AI collaboration tends to prioritize performance over…
The rapid adoption of generative AI (GenAI) in design has sparked discussions about its benefits and unintended consequences. While AI is often framed as a tool for enhancing productivity by automating routine tasks, historical research on…
Artificial Intelligence (AI) is a powerful new language of science as evidenced by recent Nobel Prizes in chemistry and physics that recognized contributions to AI applied to those areas. Yet, this new language lacks semantics, which makes…
Recent advancements in large language models (LLMs) have led to significant breakthroughs in mathematical reasoning capabilities. However, existing benchmarks like GSM8K or MATH are now being solved with high accuracy (e.g., OpenAI o1…
In the words of the esteemed mathematician Paul Erd\"os, the mathematician's task is to \emph{prove and conjecture}. These two processes form the bedrock of all mathematical endeavours, and in the recent years, the mathematical community…
Automated reasoning is a key technology in the young but rapidly growing field of Explainable Artificial Intelligence (XAI). Explanability helps build trust in artificial intelligence systems beyond their mere predictive accuracy and…
Grading assessments is time-consuming and prone to human bias. Students may experience delays in receiving feedback that may not be tailored to their expectations or needs. Harnessing AI in education can be effective for grading…
For being potentially destructive, in practice incomprehensible and for the most unintelligible, contemporary technology is setting high challenges on our society. New conception methods are urgently required. Reorganizing ideas and…
Mathematics enters the period of change unprecedented in its history, perhaps even a revolution: a switch to use of computers as assistants and checkers in production of proofs. This requires rethinking traditional approaches to mathematics…
This paper discusses digital online mathematics examinations -- a discussion ranging from high school to university level examinations. In particular, we consider the nature of mathematical writing, what is distinctive about mathematical…
In this expository article we highlight the relevance of explanations for artificial intelligence, in general, and for the newer developments in {\em explainable AI}, referring to origins and connections of and among different approaches.…
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…
Artificial Intelligence (AI) is one of today's most relevant emergent technologies. In view thereof, this paper proposes that more attention should be paid to the philosophical aspects of AI technology and its use. It is argued that this…