Mathematics Is Physics

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 primitives that lead to unambiguous nontrivial theorems. Indian (and of Indian origin) mathematicians have continued to do seminal work till present times, culminating in Manjul Bhargava receiving the Fields Medal last year. In such fabulous tim...

A perplexing problem in understanding physical reality is why the universe seems comprehensible, and correspondingly why there should exist physical systems capable of comprehending it. In this essay I explore the possibility that rather than being an odd coincidence arising due to our strange position as passive (and even more strangely, conscious) observers in the cosmos, these two problems might be related and could be explainable in terms of fundamental physics. The persp...

A sketch of some of the fundamental notions related to the nature of knowledge is offered, with special focus on the role of mathematics and my own opinions. No single idea exposed here is entirely original; indeed, this topic has been explored by legions of philosophers, mathematicians, and scientists throughout history -- I listed a few related books among the references. I look forward to observations and criticisms that may serve to improve this exposition.

The role of mathematics in physical sciences is discussed, particularly how higher mathematics found applications in empirical problems. Several examples are given to illustrate this role.

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 "pure" and "applied" mathematics is artificial. The criterion of creativity and applicability outside of the original context is used as a litmus test. It is emphasized that great societies and cultural environments produce great mathematics ...

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 modelling and scientific computing. We discuss mathematics as a martial art and a key to paradigm changes.

This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of mathematics and a paradigm for education, namely Learn to structure.

There is no mysterious link between mathematics and physics, because both of them are human inventions designed to study the world.

This paper traces the seminal roles that physicists and mathematicians have played in the conceptual development of the biological sciences in the past, and especially in the 19th and 20th centuries.

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 of the human brain privileges concept naming and short formulations. This leads to organizing mathematical knowledge structurally. We consider briefly the problem of non-mathematical sciences.