Related papers: What is Mathematics and What Should it Be

Quantum computing exposes the brilliance of quantum mechanics through computer science and, as such, gives oneself a marvelous and exhilarating journey to go through. This article leads along that journey with a historical and current…

Interview with Hyman Bass, whose mathematical life has spanned seven decades.

Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the…

Data science is an emerging interdisciplinary field that combines elements of mathematics, statistics, computer science, and knowledge in a particular application domain for the purpose of extracting meaningful information from the…

We aim to use the concept of sheaf to establish a link between certain aspects of the set of positive integers numbers, a topic corresponding to the elementary mathematics, and some fundamental ideas of contemporary mathematics. We hope…

We discuss the idea that computers might soon help mathematicians to prove theorems in areas where they have not previously been useful. Furthermore we argue that these same computer tools will also help us in the communication and teaching…

This paper is concerned with a dialogue between Rabindranath Tagore and Albert Einstein, where Tagore argued that our knowledge is essentially human, while Einstein maintained that some kinds of knowledge are more objective. Arguments by…

Logic has its origins in basic questions about the nature of the real world and how we describe it. This article seeks to bring out the physical and epistemological relevance of some of the more recent technical work in logic and…

Wigner's famous and influential claim that mathematics is "unreasonably effective" in physics is founded on unreasonable assumptions about the nature of mathematics and its independence of physics. Here I argue that what is surprising is…

Learning to use math in science is a non-trivial task. It involves many different skills (not usually taught in a math class) that help blend physical knowledge with mathematical symbology. One of these is the idea of quantification: that…

The author recalls general tendencies of the "mathematization" of the sciences and derives challenges and tentative obstructions for a successful merger of mathematics and physics on fancied steps towards "Quantum Gravity". This is an…

Our introductory classes in statistics and data science use too much mathematics. The key causal effect which our students want our classes to have is to improve their future performance and opportunities. The more professional their…

The rapid advances in technology over the last decade have significantly altered the nature of engineering knowledge and skills required in the modern industries. In response to the changing professional requirements, engineering…

This year is the 100th birth anniversary of Richard Philips Feynman. This article commemorates his scientific contributions and lasting legacy.

Steven Weinberg was a giant of late 20th Century physics on whose shoulders we stand while groping for the science of the 21st Century. This article provides a too-brief summary of a selection of his many achievements -- eight decades of…

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as…

Network (as a general notion) is not a mathematical object - there is no even any definition. However, there is a lot of good rigorous mathematics for well-defined classes of networks. In sections 1-3 we give a short overview of classes of…

Here I indulge in wide-ranging speculations on the shape of physics, and technology closely related to physics, over the next one hundred years. Themes include the many faces of unification, the re-imagining of quantum theory, and new forms…

Data science is not a science. It is a research paradigm. Its power, scope, and scale will surpass science, our most powerful research paradigm, to enable knowledge discovery and change our world. We have yet to understand and define it,…

The rapid evolution of information systems managing more and more voluminous data has caused profound paradigm shifts in the job of statistician, becoming successively data miner, bioinformatician and now data scientist. Without the sake of…