Related papers: Meta Math! The Quest for Omega
Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…
This book provides a thorough survey of the important questions at the interface between theoretical particle physics and cosmology. After discussing the theoretical and experimental physics revolution that led to the rise of the Standard…
A brief description and results of A.M. Mathai's research programme on statistics and probability, initiated in the 1970s, and its relation to physics is given.
The paper is partly a survey with historical background and references, partly provides the opportunity to put in print some unpublished early work, and partly has new results. A special case of relative categoricity is identified (almost…
Remarks on mathematical proof and the practice of mathematics.
Mathematical aspects of contemporary classical and quantum gauge theory are sketched.
Metaphor is widely used in human communication. The cohort of scholars studying metaphor in various fields is continuously growing, but very few work has been done in bibliographical analysis of metaphor research. This paper examines the…
These notes were written from a series of lectures given in March 2010 at the Universidad Complutense of Madrid and then in Barcelona for the centennial anniversary of the Spanish Mathematical Society (RSME). Our aim is to give an…
Did time begin at a Big Bang? Will the present expansion of the universe last for a finite or infinite time? These questions sound philosophical but are becoming, now in the twenty-first century, central to the scientific study of…
The research in the subfield of analytic number theory around error term of summation of sigma functions possesses a history which can be dated back to the mid-19th century when Dirichlet provided an $O(\sqrt{n})$ estimation of error term…
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…
This paper gives a concise introduction into the basic theory of {\omega}-automata (as of March 2014). The starting point are the different types of recurrence conditions, modes of operation (deterministic, nondeterministic, alternating…
This is a tract on the art and practice of mathematical writing. Not only does the book cover basic principles of grammar, syntax, and usage, but it takes into account developments of the last twenty years that have been inspired by the…
The odds theorem and the corresponding solution algorithm (odds algorithm) are tools to solve a wide range of optimal stopping problems. Its generality and tractability have caught much attention. (Google for instance "Bruss odds" to obtain…
Inspired by the recent 90th anniversary of the Scottish Book we present some reflections about its impact. First we discuss new areas of mathematics it helped launch. Then we argue that it was actively used in stimulating the interests and…
This book chapter attempts to counter anxieties in the humanities and social science about the role of big data in research by focusing on approaches which, by being firmly grounded in the traditional values of disciplines, enhance existing…
Quantum cosmology from the late sixties into the early twenty-first century is reviewed and appraised in the form of a debate, set up by two presentations on mainly the Wheeler-DeWitt quantization and on loop quantum cosmology,…
We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the same. This view of mathematics as…
Meta-analysis is a systematic approach for understanding a phenomenon by analyzing the results of many previously published experimental studies. It is central to deriving conclusions about the summary effect of treatments and interventions…
A review of Jaynes' posthumous book "Probability Theory--The Logic of Science." I use scientific and personality elements gathered from other papers by Jaynes to help throw light on the origins of Jaynes' life quest.