Related papers: Post-human mathematics
While Artificial Intelligence has successfully outperformed humans in complex combinatorial games (such as chess and checkers), humans have retained their supremacy in social interactions that require intuition and adaptation, such as…
Hypercomputation is a relatively new branch of computer science that emerged from the idea that the Church--Turing Thesis, which is supposed to describe what is computable and what is noncomputable, cannot possible be true. Because of its…
In recent years we observed rapid and significant advancements in artificial intelligence (A.I.). So much so that many wonder how close humanity is to developing an A.I. model that can achieve human level of intelligence, also known as…
Formal grammars are extensively used in Computer Science and related fields to study the rules which govern production of a language. The use of these grammars can be extended beyond mere language production. One possibility is to view…
Approaching limitations of digital computing technologies have spurred research in neuromorphic and other unconventional approaches to computing. Here we argue that if we want to systematically engineer computing systems that are based on…
Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…
Recent advancements in artificial intelligence (AI) and its sub-branch machine learning (ML) promise machines that go beyond the boundaries of automation and behave autonomously. Applications of these machines in creative practices such as…
The purpose of this note is to raise two different questions, which are rarely if ever considered, and to which, it seems, we lack convincing, systematic answers. These questions can be posed as: - Why do we compute? - What do we compute?…
The ability to read, write, and speak mathematics is critical to students becoming comfortable with statistical models and skills. Faster development of those skills may act as encouragement to further engage with the discipline. Vocabulary…
The ubiquitous presence of computer simulations in all kinds of research areas evidence their role as the new driving force for the advancement of science and engineering research. Nothing seems to escape the image of success that computer…
In this paper the author presents some non-conventional thoughts on the complexity of the Universe and the algorithmic reproducibility of the human brain, essentially sparked off by the notion of algorithmic complexity. We must warn that…
This essay examines how automation has reconfigured mathematical proof and labor, and what might happen in the future. It discusses practical standards of proof, distinguishes between prominent forms of automation in research, provides…
Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice…
The way we work is no longer hybrid -- it is blended with AI co-workers, automated decisions, and virtual presence reshaping human roles, agency, and expertise. We now work through AI, with our outputs shaped by invisible algorithms. AI's…
The recent advances of AI technology, particularly in AI-Generated Content (AIGC), have enabled everyone to easily generate beautiful paintings with simple text description. With the stunning quality of AI paintings, it is widely questioned…
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…
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…
Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum…
If we take the subjective character of consciousness seriously, consciousness becomes a matter of "being" rather than "doing". Because "doing" can be dissociated from "being", functional criteria alone are insufficient to decide whether a…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…