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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
Richard C. Brown, Are Science and Mathematics Socially Constructed?: A Mathematician Encounters Postmodern Interpretations of Science, World Scientific, 2009.
In this book, Brown recounts the rise of what is now known as the “postmodern interpretations of science” (PIS) or “sociology of scientific knowledge” (SSK) movement. In addition to pioneers Karl Popper and Thomas Kuhn (the latter of whom Brown personally knew), the author describes the contributions of Berkeley philosopher Paul Feyerabend; Harry Collins and Trevor Pinch at Bath University; Steve Woolgar at Brunel; Michel Callon and Bruno Latour in Paris; a group of scholars at the University of Edinburgh; and
Continue reading Are science and mathematics socially constructed?
Prof. Jonathan M. Borwein of the University of Newcastle in Australia (one of the present bloggers) will participate in a panel discussion at the World Science Festival, to be held on 3 Jun 2011 7:00pm in the Tishman Auditorium at the New School, 66 W 12th Street, New York City, USA. Other panelists are Keith Devlin (the “Math Guy” on National Public Radio and author of 30 books), Marcus du Sautoy (mathematician, author and BBC commentator) and Simon Singh (physicist, author and BBC TV producer). Tickets and other information are available at WSF website.
Here is a synopsis of the
Continue reading Borwein to participate in World Science Festival panel
[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?
Two IBM researchers, with the assistance of the present bloggers (Bailey and Borwein), have calculated binary digits of pi-squared beginning at the 60 trillionth binary digit. In addition, they calculated ternary (base-3) digits of pi-squared, beginning at the 60 trillionth digit, and binary digits of Catalan’s constant, beginning at the 120 trillionth digit. Other researchers have previously calculated binary digits of pi itself, beginning at the two quadrillionth binary digit.
These calculations would have taken a single computer processor unit (CPU) 1,500 years to calculate, but the researchers managed to complete this work in just a few months on IBM’s
Continue reading Researchers compute 60 trillionth binary digit of pi-squared
A Museum of Mathematics is slated to open in New York City in the fall of 2012.
This organization was formed in 2009 by Glen Whitney, formerly the algorithm manager for the $15 billion hedge fund firm Renaissance Technologies. Renaissance was founded by James Simons, who, like Whitney, was previously a professor of mathematics at the University of Michigan. As of April 2011, the museum has raised $22 million from various donors, including $2 million from Google.
When it opens, the “MoMath” museum will feature exhibits that “stimulate inquiry, spark curiosity, and reveal the wonders of mathematics,” according to
Continue reading Museum of Mathematics to be opened in NYC
John Milnor, the American mathematician known for his discovery of exotic hyperspheres, has been awarded the 2011 Abel Prize by the Norwegian Academy of Science and Letters. The Abel Prize, which is accompanied by a cash award of USD$1 million, is generally regarded as the equivalent of the Nobel Prize in the field of mathematics.
Milnor’s principal field of study is the field of differential topology. One of Milnor’s discoveries was an exotic hypersphere in seven dimensions. Milnor showed that the solution of a problem such the propagation of waves or heat on this manifold could not be smoothly translated
Continue reading Milnor wins 2011 Abel prize
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?
It’s official: IBM’s “Watson” computer system has defeated two of the brightest minds that our species could put forward for battle, namely legendary Jeopardy! champs Ken Jennings and Brad Rutter. Ken Jennings, recognizing that Watson had an insurmountable lead heading into Final Jeopardy (the final question of the match), summed up the situation by writing on his computer slate below his final bid, “I for one welcome our new computer overlords.”
Unlike Tuesday’s round, at least Wednesday’s contest was not a runaway. Watson started out strong, but then stumbled on a variety of subjects. For example, Watson incorrectly answered “What
Continue reading IBM’s “Watson” victorious: Our new computer overlords?
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