Mathematical Science & Technologies » Mathematics-Phenomenology

A Course in the Philosophy and Foundations of Mathematics

Assad Ebrahim — Thu, 15 Apr 2010 16:36:30 +0000

An examination of mathematical methods and the search for mathematical meaning.

During your studies of mathematics, physics and engineering, you may find yourself distracted or troubled by meta questions about mathematics — questions that fall outside the syllabi of most of the coursework that you’ll take.

For those for whom this itch is persistent, what [...]

Why Zero Raised to the Zero Power IS One

Assad Ebrahim — Thu, 25 Feb 2010 13:56:16 +0000

The question of what value 0^0 should evaluate to has been discussed since the time of Euler (1700s). There are three candidate choices: 1,0, or “indeterminate” (i.e., throw an error).

In this article, I argue that the only reasonable choice (for discrete mathematics) is 0^0=1 (), and I’ll give a tangible, feel-the-grit-in-your-palms reason [...]

Good mathematical technique and the case for mathematical insight

Assad Ebrahim — Sun, 31 Jan 2010 19:16:14 +0000

Good mathematical technique can bring the solution to certain mathematical questions within reach. By a proper formulation (one that is both tractable and that generalizes readily) and the use of mechanical techniques, one can often pass from a single insight to the solution of a family of problems, and in some cases, to the [...]

Catalysts in the Development of Mathematics

Assad Ebrahim — Fri, 15 Jan 2010 13:57:04 +0000

The development of mathematics has had many encouraging forces: societal, technological, cultural. These have served to accelerate mathematics and have been accelerated in turn, in many cases the pair becoming locked into a mutually beneficial resonance that has dramatically energized both.

In this article, I look at some of the significant catalysts, from the rise [...]

The Development of Mathematics

Assad Ebrahim — Sun, 03 Jan 2010 17:23:48 +0000

… in a nutshell

The development of mathematics is intimately interwoven with the progress of civilization, influencing the course of history through its application to science and technology.

But mathematics has changed. Even the mathematics of the 1800s can seem quite strange now, so greatly has mathematics evolved in the past 100 years and [...]

Characteristics of Modern Mathematics

Assad Ebrahim — Sat, 02 Jan 2010 14:17:25 +0000

What are the characteristics of mathematics, especially contemporary mathematics?

I’ll consider five groups of characteristics:

Applicability and Effectiveness, Abstraction and Generality, Simplicity, Logical Derivation, Axiomatic Arrangement, Precision, Correctness, Evolution through Dialectic…

Characteristics of Modern Mathematics

In the article What is Mathematics?, I have posited that Mathematics arises from Man’s attempt to summarize the variety of empirical phenomena that [...]

What is Mathematics?

Assad Ebrahim — Wed, 30 Dec 2009 14:34:25 +0000

Can a definition be given that captures the meaning of Mathematics across the millennia of its recorded history? What unites the practice of mathematics throughout its history and into the present time?

In this article, I will try for a short answer by proceeding iteratively — convergence will be reached in two iterations….

What is Mathematics?

Though [...]

Mathematics in Pre-History

Assad Ebrahim — Tue, 29 Dec 2009 14:28:02 +0000

…Taking into account early human evolution, and in particular, the development of speech, it is likely that the understanding of counting and keeping time far pre-dates the discovered fossil evidence of Homo Sapiens from 30,000 years ago, and reaches back at least as far as 250,000 years ago, coincident with speech, fire, and cooperative hunting, [...]