Related papers: Mathematics discovered, invented, and inherited
Wigner's famous and influential claim that mathematics is "unreasonably effective" in physics is founded on unreasonable assumptions about the nature of mathematics and its independence of physics. Here I argue that what is surprising is…
Information is everywhere in nature which is very uncertain and unpredictable. But information, in itself, is a very ambiguous term. In this cursory write-up, we attempt to understand the formal meaning of information by quantifying…
The human mind is endowed with innate primordial perceptions such as space, distance, motion, change, flow of time, matter. The field of cognitive science argues that the abstract concepts of mathematics are not Platonic, but are built in…
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…
According to the philosopher Kant, Mathematics is an "a priori cognition". Kant's assumption, together with the unsolvability of Hilbert's 10th problem, implies an astonishing result.
This is the transcript of a lecture given at UMass-Lowell in which I compare and contrast the work of Godel and of Turing and my own work on incompleteness. I also discuss randomness in physics vs randomness in pure mathematics.
Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the…
Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are…
Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…
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,…
The development of a mathematics for living systems is one of the most challenging prospects of this century. The search began with the pioneering contribution of Ilia Prigogine, who developed methods from statistical physics to describe…
Mathematics is probably the only subject that can be classified both as art as well as science - former, because it is not constrained by the real world and latter because it is a logical system with precisely defined rules as well as…
This is a short historical note concerning the evolution of Wetzel's problem and Erdos' solution.
The fundamental role of mathematics as an inspiration for artists, but also as a tool for art creation, is presented in this paper following different art fields, like architecture, sculpture, painting, photography, literature and poetry,…
Causality is one of the most fundamental -- and yet elusive -- concepts in physics. From its intuitive role in everyday experience to its formal and often implicit role in scientific theories, causality has challenged philosophers and…
Math is widely considered as a powerful tool and its strong appeal depends on the high level of abstraction it allows in modelling a huge number of heterogeneous phenomena and problems, spanning from the static of buildings to the flight of…
Several aspects of mathematical astrobiology are discussed. It is argued that around the time of the origin of life the handedness of biomolecules must have established itself through an instability. Possible pathways of producing a certain…
There are important problems in physics related to the concept of probability. One of these problems is related to negative probabilities used in physics from 1930s. In spite of many demonstrations of usefulness of negative probabilities,…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
Quantum mechanics has enjoyed a multitude of successes since its formulation in the early twentieth century. At the same time, it has generated puzzles that persist to this day. These puzzles have inspired a large literature in physics and…