Related papers: A Survey on Wild Mathematics
From classical mechanics to quantum field theory, the physical facts at one point in space are held to be independent of those at other points in space. I propose that we can usefully challenge this orthodoxy in order to explain otherwise…
We prove that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild. We also prove that any deformation of a derived tame algebra is derived tame.
The lectures review the state of affairs in modern branch of mathematical physics called probabilistic topology. In particular we consider the following problems: (i) We estimate the probability of a trivial knot formation on the lattice…
Ecology studies biodiversity in its variety and complexity. It describes how species distribute and perform in response to environmental changes. Ecological processes and structures are highly complex and adaptive. In order to quantify…
Our conventional understanding of space-time, as well as our notion of geometry, break down once we attempt to describe the very early stages of the evolution of our universe. The extreme physical conditions near the Big Bang necessitate an…
Magic squares have been well explored here on Earth [1], but there appears to have been little-to-no examination of $\textit{lunar}$ magic squares. Some kinds of magic squares exist on the moon (i.e. under lunar arithmetic) but not on Earth…
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…
Sets in R^n in which every pair of elements x, y can be connected by a path in the set of length bounded by a constant multiple of the distance between x and y are considered.
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
This paper collects some problems that I have encountered during the years, have puzzled me and which, to the best of my knowledge, are still open. Most of them are well-known and have been first stated by other authors. In this sad season…
I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of…
The world appears to be well described by gauge theories; why? I suggest that gauge is more than mathematical redundancy. Gauge-dependent quantities can not be predicted, but there is a sense in which they can be measured. They describe…
If there is a "platonic world" M of mathematical facts, what does M contain precisely? I observe that if M is too large, it is uninteresting, because the value is in the selection, not in the totality; if it is smaller and interesting, it…
Nature's many varied complex systems (including galaxies, stars, planets, life, and society) are islands of order within the increasingly disordered universe. All organized systems are subject to physical, biological or cultural evolution,…
We discuss the nature of reality in the ontological context of Penrose's math-matter-mind triangle. The triangle suggests the circularity of the widespread view that math arises from the mind, the mind arises out of matter, and that matter…
Physicists study a wide variety of phenomena creating new interdisciplinary research fields by applying theories and methods originally developed in physics in order to solve problems in economics, social science, biology, medicine,…
We prove that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild. The proof is based on the technique of matrix problems (boxes and reduction algorithm). It implies, in particular,…
I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the…
Using methods of descriptive theory it is shown that the classification problem for wild knots is strictly harder than that for countable structures.
Active feedback between geometry and physics is woven throughout the study of Nature at its fundamental level, and is of key importance in string theory. Methods of complex algebraic geometry in particular have brought about an unrivaled…