Magic numbers

The Conversation, an online forum from the Australian academic research community and aimed at the interested public, has featured an essay written by the present bloggers. Entitled “Magic numbers: the beauty of decimal notation,” it is available here: Conversation article.

This piece briefly mentions the history of positional decimal arithmetic, from its original discovery by unknown Indian mathematicians approximately 2000 years ago, to its modern incarnation (at least in binary) in computers. The article then speculates how history may have changed if either arithmetic had been discovered earlier, or it had been communicated to Greek mathematicians such as Archimedes.

It

Continue reading Magic numbers

August 23rd, 2011 | Category: Essays, News | Comments are closed

Is math ability inborn or developed?

The “nature versus nurture” debate refers to discussions of the relative importance of a person’s innate qualities (“nature”) versus the importance of upbringing and experience (“nurture”). Such debates have been ongoing for centuries. Shakespeare even referred to such a debate in his play The Tempest (4:1). The phrase “nature versus nurture” in the current sense was first used by Francis Galton in the 19th century, in commentary on the work of Darwin, his cousin. Along this line, philosopher John Locke coined the term “tabula rasa” (“blank slate”) to refer to the “nurture” view that all or almost all human behavior

Continue reading Is math ability inborn or developed?

August 14th, 2011 | Category: Essays | Comments are closed

Is mathematics invented or discovered?

One of the most fascinating aspects of modern mathematics is the extent to which developments in “pure” mathematics are subsequently, and often quite unexpectedly, found to have direct relevance to the physical world. Albert Einstein asked, “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” [Jammer1921, pg. 124].

One source that is often cited in this context is Eugene Wigner’s 1960 essay “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” [Wigner1960]. He cites numerous examples:

Newton’s laws and planetary motion. Wigner notes that Newton’s

Continue reading Is mathematics invented or discovered?

August 7th, 2011 | Category: Essays | Comments are closed