Related papers: In whose mind is Mathematics an "a priori cognitio…
Mathematics is one of the ways our species makes sense of this world and I believe that it is inherent in our thinking machinery. The mathematics we do in turn is dependent on the way we view our universe and ourselves. Lakoff and Nunez…
Kant's Critique of Pure Reason, a major contribution to the history of epistemology, proposes a table of categories to elucidate the structure of the a priori principles underlying human judgment. Artificial intelligence (AI) technology,…
In part one of the Critique of Judgment, Immanuel Kant wrote that "the judgment of taste...is not a cognitive judgment, and so not logical, but is aesthetic."\cite{Kant} While the condition of aesthetic discernment has long been the subject…
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…
Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then…
We explore in the framework of Quantum Computation the notion of computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm that exploits the quantum adiabatic processes is considered…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
Some reflections on the role in the development of Mathematics of our unconscious perception of the world and just as unconscious organizing pulsions for those perceptions.
This paper is concerned with a dialogue between Rabindranath Tagore and Albert Einstein, where Tagore argued that our knowledge is essentially human, while Einstein maintained that some kinds of knowledge are more objective. Arguments by…
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
The information-theoretic point of view proposed by Leibniz in 1686 and developed by algorithmic information theory (AIT) suggests that mathematics and physics are not that different. This will be a first-person account of some doubts and…
Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer arithmetics into either a problem involving a set of infinitely coupled differential equations or a problem involving a Shr\"odinger propagator…
We show that quantum mechanics is the first theory in human history that violates the basic a priori principles that have shaped human thought since immemorial times. Therefore although it is more contrary to magic than any body of…
The Riemann hypothesis is one of the most famous unresolved problems in modern mathematics. The discussion here will present an overview of past methods that prove the Riemann hypothesis is a $\Pi_1^0$ sentence. We also end with some…
We discuss views about whether the universe can be rationally comprehended, starting with Plato, then Leibniz, and then the views of some distinguished scientists of the previous century. Based on this, we defend the thesis that…
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…
Einstein initially objected to the probabilistic aspect of quantum mechanics - the idea that God is playing at dice. Later he changed his ground, and focussed instead on the point that the Copenhagen Interpretation leads to what Einstein…
We consider a definition of mathematics as the art of thinking in terms of formalized systems, and the science of relations, structures and algorithms. We also touch upon the relation of mathematics to other sciences, in particular through…
The classical platonist/formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: is new mathematics discovered or invented? Using an example from my own mathematical life, I argue that…
Mathematics cannot anymore be assimilated to a linguistic game, where formal proofs are strongly differentiated with conjectural thinking, without building any category of knowledge to understand the passage (Wittgenstein's gist). Nowadays,…