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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?
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?
[Note: A condensed and revised version of this article was published here in The Conversation, an online forum of academic research headquartered in Melbourne, Australia.]
Introduction
Monumental inventions of history can be grouped into three categories: (a) those whose origin is well known and well appreciated; (b) those whose origin is completely lost to history; and (c) those who origin may be known, at least in general terms, but which are not very well appreciated in modern society. Among those in the first category are efficient steam engines (by James Watt in 1765), movable-type printing (by the Chinese inventor Bi
Continue reading What if base-10 arithmetic had been discovered earlier?
The Conversation is a recently established web journal dedicated to making academic and related policy issues accessible to an informed public. The editors write:
The Conversation is an independent source of information, analysis and commentary from the university and research sector – written by acknowledged experts and delivered directly to the public. As professional journalists, we aim to make this wealth of knowledge and expertise accessible to all.
So far this has been done in a most lively and stimulating fashion; it is garnering readers within and without the academy from across the world let us hope it can be
Continue reading Turning IBM’s Watson into a maths genius
Acronyms have been used lately to describe various groups of world nations. Readers may be familiar with “PIIGS”, namely Portugal, Italy, Ireland, Greece and Spain, which are the nations now teetering on default after years of lax fiscal policies, and unrealistic expectations for the Euro. Readers may also have heard of “BRIC”, namely Brazil, Russia, India and China, which many observers now believe constitute a powerhouse of large, upwardly mobile nations that very likely will dominate the economy and political structure of the 21st century world. All except Russia inarguably have show extraordinary economic growth since the millennium.
We would
Continue reading PIIGS, BRICs and STRAW
A new book, co-authored by one of the present bloggers is now available: An Introduction to Modern Mathematical Computing: With Maple, authored by Jonathan M. Borwein and Matthew P. Skerritt, published by Springer, 2011. Here is a brief synopsis:
Thirty years ago, mathematical computation was difficult to perform and thus used sparingly. However, mathematical computation has become far more accessible due to the emergence of the personal computer, the discovery of fiber-optics and the consequent development of the modern internet, and the creation of Maple, Mathematica, and Matlab.
An Introduction to Modern Mathematical Computing: With Maple looks beyond teaching the
Continue reading An Introduction to Modern Mathematical Computing
In a previous blog post, we addressed the perplexing phenomenon that whereas the scientific community years ago reached a strong consensus regarding the fact of global warming and the very likely human contribution to global warming, the public continues to believe that there is significant uncertainty and disagreement in the scientific community.
For example, in a recent poll, only 56% of Americans agreed that there is solid evidence of warming, and only 32% agreed that this warming can mostly be attributed to human actions. Similar results were found in 2009. For details, see 2010 Pew poll; 2009 Pew poll. Similarly,
Continue reading Merchants of Doubt
As we have argued in an earlier blog, our modern system of positional decimal notation with zero, together with efficient algorithms for computation, which were discovered in India some time prior to 500 CE, certainly must rank among the most significant achievements of all time. As Pierre-Simon Laplace explained:
Its very simplicity and the great ease which it has lent to all computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two
Continue reading Ancient Indian square roots
The proliferation of the Internet and the pressure to make headlines has led to a number of recent self announcements of impressive-looking new mathematical results, often noted in press reports and blogs. This phenomenon is neither entirely new nor always without merit. Some genuine breakthroughs have been announced this way — one example is the discovery in August 2002 of what is now known as the Agrawal–Kayal–Saxena primality test, discovered by three researchers of these names at the Indian institute of Technology in Kanpur, India.
However, there are many other examples of mathematical results touted in press announcements that have
Continue reading Quick tests for checking whether a new math result is plausible
In 1937, Lothar Collatz proposed the following conjecture: Start with a positive integer n, then repeatedly iterate the following: If n is even, divide it by 2; if n is odd, compute 3*n+1. Collatz conjectured that for every starting value n, the result will invariably return to 1.
The Collatz conjecture has been studied by thousands of mathematicians and computer scientists. Portuguese mathematician Tomas Oliveira e Silva has verified the conjecture for all integers up to 5.76 x 10^18. But no proof has yet been found. Well-known mathematician Paul Erdos once characterized the Collatz conjecture as “Mathematics is not yet
Continue reading Has the 3n+1 conjecture been proved?
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