Related papers: The Universal Language of Mathematics (Introductio…
A unified theory of language combines a Bayesian cognitive linguistic model of language processing, with the proposal that language evolved by sexual selection for the display of intelligence. The theory accounts for the major facts of…
There is a problem with the foundations of classical mathematics, and potentially even with the foundations of computer science, that mathematicians have by-and-large ignored. This essay is a call for practicing mathematicians who have been…
A number of elite thinkers in Europe during the 16th and 17th centuries pursued an agenda which historian Paolo Rossi calls the "quest for a universal language," a quest which was deeply interwoven with the emergence of the scientific…
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…
Trying to be effective (no matter who exactly and in what field) a person face the problem which inevitably destroys all our attempts to easily get to a desired goal. The problem is the existence of some insuperable barriers for our mind,…
The unique and beautiful character of certain mathematical results and proofs is often considered one of the most gratifying aspects of engaging with mathematics. We study whether this perception of mathematical arguments having an…
The Price equation describes the change in populations. Change concerns some value, such as biological fitness, information or physical work. The Price equation reveals universal aspects for the nature of change, independently of the…
In this paper, I present a critical discussion of mathematical arguments employed in the philosophy of event of Alain Badiou. On the basis of "Being and Event" as well as his other writings, I analyze the main notions of his philosophy such…
This paper establishes grounds for deeper exploration into the question of dual nature of mathematics as an abstract discipline and as a concrete science. It is argued, as one of the consequences of the discussion, that the division into…
We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyze. In particular the functioning…
Do we have two kinds of reality: physical and mathematical? What is the role of mathematics in physics? These fundamental questions have intrigued original and brilliant minds since ancient times. A recent article (Aharonov, Cohen and…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
We re-examine the old question to what extent mathematics may be compared with a game. Mainly inspired by Hilbert and Wittgenstein, our answer is that mathematics is something like a rhododendron of language games, where the rules are…
In a previous work, "pure data" is proposed as an axiomatic foundation for mathematics and computing, based on "finite sequence" as the foundational concept rather than based on logic or type. Within this framework, objects with…
A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the…
Objects are a centerpiece of the mathematical realm and our interaction with and reasoning about it, just as they are of the physical one (if not more). And humans' mathematical reasoning must ultimately be grounded in our general…
Can mathematics help us find our way through all the wonders and mysteries of the universe? When physicists describe the laws governing the physical world, mathematics is always involved. Is this due to the fact that the universe is, at…
Recent progress in artificial intelligence (AI) is unlocking transformative capabilities for mathematics. There is great hope that AI will help solve major open problems and autonomously discover new mathematical concepts. In this essay, we…
There are different meanings of foundation of mathematics: philosophical, logical, and mathematical. Here foundations are considered as a theory that provides means (concepts, structures, methods etc.) for the development of whole…
Understanding and creating mathematics using natural mathematical language - the mixture of symbolic and natural language used by humans - is a challenging and important problem for driving progress in machine learning. As a step in this…