Related papers: Interview with Hyman Bass
While the consequences of mathematically-based software, algorithms and strategies have become ever wider and better appreciated, ethical reflection on mathematics has remained primitive. We review the somewhat disconnected suggestions of…
Questions concerning origin of mathematical knowledge and roles of language and intuition (imagery) in mathematical thoughts are long standing and widely debated. By introspection, mathematicians usually have some beliefs regarding these…
Access to mathematical knowledge has changed dramatically in recent years, therefore changing mathematical search practices. Our aim with this study is to scrutinize professional mathematicians' search behavior. With this understanding we…
A brief overview and history of the American Mathematics Competitions.
Metaphysics is the science of being and asks the question ``What really exists?'' The answer to this question has been sought for by mankind since the beginning of recorded time. In the past 2500 years there have been many answers to this…
Mathematics is changing. Computers are verifying proofs, checking calculations, and exploring complex structures that would overwhelm human effort. Yet curiosity-driven research is where tomorrow's breakthroughs are quietly prepared. In…
We spell two conundrums, one of physical and another of mathematical nature, and explain why one helps to elucidate the other
The Bayesian statistical paradigm uses the language of probability to express uncertainty about the phenomena that generate observed data. Probability distributions thus characterize Bayesian analysis, with the rules of probability used to…
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.
I published an interview of Leo Breiman in Statistical Science [Olshen (2001)], and also the solution to a problem concerning almost sure convergence of binary tree-structured estimators in regression [Olshen (2007)]. The former summarized…
This is a discussion of some themes in Max Tegmark's recent book, Our Mathematical Universe. It was written as a review for Plus Magazine, the online magazine of the UK's national mathematics education and outreach project, the Mathematics…
This article provides a survey on some main results and recent developments in the mathematical theory of water waves. More precisely, we briefly discuss the mathematical modeling of water waves and then we give an overview of local and…
This talk traces the history of RHIC over the last two decades, reviewing the scientific motivations underlying its design, and the challenges and opportunities the machine presents.
People who by training end up dealing with probabilities ("statisticians") roughly fall into one of two camps. One is either a frequentist or a Bayesian. To a scientist, who needs to use probabilities to make sense of the real world, this…
This book invites readers to see mathematics not just as formulas and rules, but as the deepest expression of human thought. It begins by exploring the timeless idea of mathematics as a universal language, contrasting its precision with the…
The primary aim of this chapter is, commemorating the 150th anniversary of Riemann's death, to explain how the idea of {\it Riemann sum} is linked to other branches of mathematics. The materials I treat are more or less classical and…
Courses in mathematical methods for physics students are not known for including too much in the way of mathematical rigour and, in some ways, understandably so. However, the conditions under which some quite commonly used mathematical…
The 175th anniversary of the ASA provides an opportunity to look back into the past and peer into the future. What led our forebears to found the association? What commonalities do we still see? What insights might we glean from their…
How cells maintain a stable size has fascinated scientists since the beginning of modern biology, but has remained largely mysterious. Recently, however, the ability to analyze single bacteria in real time has provided new, important…
This paper seeks to provide a thorough account of the ubiquitous nature of the Bayesian paradigm in modern statistics, data science and artificial intelligence. Once maligned, on the one hand by those who philosophically hated the very idea…