Related papers: Desperately seeking mathematical truth
Some relations between physics and finitary and infinitary mathematics are explored in the context of a many-minds interpretation of quantum theory. The analogy between mathematical ``existence'' and physical ``existence'' is considered…
These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathematics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
This article presents a source list to support departments in creating more equitable, diverse, and inclusive mathematics classrooms. Included are relevant general-interest books, as well as articles and books presenting research results…
We explore the rational, formal and non-formal criteria of consistency, non-triviality and redundancy in the mathematical research now a days. We develop a paradigmatic discussion by analysing the different conceptions of those criteria,…
This essay, originally published in the Sept 1990 Notices of the AMS, discusses problems of our mathematical education system that often stem from widespread misconceptions by well-meaning people of the process of learning mathematics. The…
Epistemology is the branch of philosophy that deals with gaining knowledge. It is closely related to ontology. The branch that deals with questions like "What is real?" and "What do we know?" as it provides these components. When using…
The goal of this paper is twofold. First, we present a unified way of formulating numerical integration problems from both approximation theory and discrepancy theory. Second, we show how techniques, developed in approximation theory, work…
This article analyzes the emerging ethical turn in mathematics education, arguing that it is a nuanced extension of the sociopolitical turn. While sociopolitical studies of mathematics have highlighted systemic issues and group concerns…
This article looks at philosophical aspects and questions that modern astrophysical research gives rise to. Other than cosmology, astrophysics particularly deals with understanding phenomena and processes operating at "intermediate" cosmic…
In the past two decades, teaching and outreach have come to hold an expected place in more missions of mathematics departments and organizations. Still, there is more to do as a mathematical sciences community for mathematics education and…
This thesis investigates on measure theoretic aspects of fluctuations of error terms appearing in various asymptotic formulas.
Mathematics enters the period of change unprecedented in its history, perhaps even a revolution: a switch to use of computers as assistants and checkers in production of proofs. This requires rethinking traditional approaches to mathematics…
Several thoughts are presented on the long ongoing difficulties both students and academics face related to Calculus 101. Some of these thoughts may have a more general interest.
Development of several alternative mathematical models for the biological system in question and discrimination between such models using experimental data is the best way to robust conclusions. Models which challenge existing theories are…
The issue of asymmetric uncertainties resulting from fits, nonlinear propagation and systematic effects is reviewed. It is shown that, in all cases, whenever a published result is given with asymmetric uncertainties, the value of the…
We describe in dialogue form a possible way of discovering and investigating 10-adic numbers starting from the naive question about a `largest natural number'. Among the topics we pursue are possibilities of extensions to transfinite…
This paper examines the processes involved in attempting to capture the subtlest aspects of nature by the scientific method and argues on this basis that nature is fundamentally elusive and may resist grasping by the methods of science. If…