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
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
Semiotic fiddling while a digital Rome burns
“So to summarise, according to the citation count, in order of descent, the authors are listening to themselves, dead philosophers, other specialists in semiotic work in mathematics education research, other mathematics education research researchers and then just occasionally to social scientists but almost never to other education researchers, including mathematics teacher education researchers, school teachers and teacher educators. The engagement with Peirce is being understood primarily through personal engagements with the original material rather than as a result of working through the filters of history, including those evidenced within mathematics education
Continue reading Semiotic fiddling while a digital Rome burns
[Earlier version posted 6 Feb 2010]
Introduction
Question: What mathematical discovery more than 1500 years ago:
Is one of the greatest, if not the greatest, single discovery in the field of mathematics? Involved three subtle ideas that evaded the greatest minds of antiquity, even including geniuses such as Archimedes? Was fiercely resisted in Europe for hundreds of years after its discovery? Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source?
Answer: Our modern system of positional decimal arithmetic with zero, which was discovered in India in the fourth
Continue reading The Greatest Mathematical Discovery?
In honor of Pi Day — 3.14.2011 — we offer a brief history of Pi and of its computation.
By David H. Bailey and Jonathan M. Borwein
I. A brief history of Pi
The mathematical constant we now know as Pi = 3.14159… has fascinated mathematicians for millennia. Archimedes of Syracuse (~250 BCE) rigorously showed that the area of a circle is Pi times the square of the radius. He then presented an approximation scheme, based on inscribed and circumscribed polygons, which enabled one to compute Pi to any desired accuracy. He himself found, with laborious and ingenious computation, that
Continue reading Pi goes on forever
What is the real significance of the recent victory by the IBM “Watson” computer system on the quiz show Jeopardy!? It certainly wasn’t a profitable undertaking: IBM’s $1 million winnings, which will be given to charity, pale in comparison to the estimated $1 billion price tag of the project. A somewhat more tangible benefit to IBM is that the project has reportedly done wonders in burnishing IBM’s image as a leading-edge technology company, especially among students (see FINS article). It has also already led to various co-development contracts in the health and commerce sectors.
The real significance is IBM’s demonstration
Continue reading What does Watson’s victory really mean?
At the dawn of the computer age in the 1950s and 1960s, researchers in the emerging field of artificial intelligence (AI) confidently predicted a new wave of discoveries that would revolutionize technology and society. For example, Herbert Simon predicted that “machines will be capable, within twenty years, of doing any work a man can do,” and Marvin Minsky wrote that “within a generation … the problem of creating ‘artificial intelligence’ will substantially be solved” [Crevier1993]. Needless to say, in spite of advances in computer hardware vastly exceeding even the most optimistic predictions at the time, many of the exuberant goals
Continue reading Can machines teach themselves?
Two developments, one in the U.K. and one in the U.S., presage serious difficulties for science funding and indeed the future of scientific research worldwide.
In the U.K., Business Secretary Vince Cable announced this week that he wants to “ration” British science. The proposal is to eliminate the 46% of U.K. research that is not defined as “world class.” Numerous political analysts, not to mention research scientists, are dumbfounded at this development. The announcement appears to suggest that Cable, and others in his ministry, are unaware of the extent to which U.K. research projects are already sifted by a very
Continue reading Political threats to science funding
I am a great fan of the intelligent use of technology. Indeed, I like David Bailey have spent a great deal of my career advocating just such use. The story below is an unexaggerated description of one of the most frustrating encounters I have ever had with a major company. I am left wondering whether Telstra has ever learned what it means to be a private company; to offer genuine service, honest quality assurance, and knowledgeable assistance; to use modern databases or train competent assistants. There again, when the main competition in Oz is Optus what choice does a consumer
Continue reading Why I love my Telco
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