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I present a somewhat selective review of microlensing theory, covering five major areas: 1) the derivation of the basic formulae, 2) the relation between the observables and the fundamental physical parameters, 3) binaries, 4) astrometric…

This is a completely reformulated presentation of a previous paper with the same title; this time with a much stronger emphasis on conceptual aspects of string theory and a detailed review of its already more than four decades lasting…

We give a short non-technical introduction to the Ising model, and review some successes as well as challenges which have emerged from its study in probability and mathematical physics. This includes the infinite-volume theory of phase…

Baroque questions of set-theoretic foundations are widely assumed to be irrelevant to physics. In this article, I demonstrate that this assumption is incorrect. I show that the fundamental physical question of whether a theory is…

We present a method for using standard techniques from satisfiability checking to automatically verify and discover theorems in an area of economic theory known as ranking sets of objects. The key question in this area, which has important…

A family of cosmological solutions with $(n+1)$ Ricci-flat spaces in the theory with several scalar fields and multiple exponential potential is obtained when coupling vectors in exponents obey certain relations. Two subclasses of solutions…

We are pleased to present a Special Section on Statistics and Astronomy in this issue of the The Annals of Applied Statistics. Astronomy is an observational rather than experimental science; as a result, astronomical data sets both small…

We have found that proposals addressing the old cosmological constant problem come in various categories. The aim of this paper is to identify as many different, credible mechanisms as possible and to provide them with a code for future…

The quantum reality problem is that of finding a mathematically precise definition of a sample space of configurations of beables, events, histories, paths, or other mathematical objects, and a corresponding probability distribution, for…

This paper describes a large set of related theorem proving problems obtained by translating theorems from the HOL4 standard library into multiple logical formalisms. The formalisms are in higher-order logic (with and without type…

The conformal thin sandwich (CTS) equations are a set of four of the Einstein equations, which generalize the Laplace-Poisson equation of Newton's theory. We examine numerically solutions of the CTS equations describing perturbed Minkowski…

We provide bounds on the compression size of the solutions to 22 problems in computer science. For each problem, we show that solutions exist with high probability, for some simple probability measure. Once this is proven, derandomization…

With our current level of understanding, the problem of making string theory predictions is not one of "solving" the theory, but rather of trying to determine whether there are any generic expectations. Within this context, we discuss what…

Large language models (LLMs) are now widely accessible, reaching learners at all educational levels. This development has raised concerns that their use may circumvent essential learning processes and compromise the integrity of established…

We consider cosmological solutions to general relativity with a single barotropic fluid, where the pressure is a general function of the density, $p = f(\rho)$. We derive conditions for static and oscillating solutions and provide examples,…

These notes present a brief introduction to `naturalness' problems in cosmology, and to the Cosmological Constant Problem in particular. The main focus is the `old' cosmological constant problem, though the more recent variants are also…

Big Bang models of the Universe predict rapid domination by curvature, a paradox known as the flatness problem. Solutions to this problem usually leave the Universe exactly flat for every practical purpose. Explaining a nearly but not…

We discuss the obstacles for defining a set of observable quantities analogous to an S-matrix which are needed to formulate string theory in an accelerating universe. We show that the quintessence models with the equations of state $-1 < w…

This essay presents a critical evaluation of the concepts of string theory and its impact on particle physics. The point of departure is a historical review of four decades of string theory within the broader context of six decades of…

There is a persistent confusion about determinism and predictability. In spite of the opinions of some eminent philosophers (e.g., Popper), it is possible to understand that the two concepts are completely unrelated. In few words we can say…