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Scientists through the ages have noted, often with some astonishment, not only the remarkable success of mathematics in describing the natural world, but also the fact that the best mathematical formulations are usually those that are the most beautiful. And almost all research mathematicians pepper their description of important mathematical work with terms like “unexpected,” “elegance,” “simplicity” and “beauty.”
Some selected opinions
British Mathematician G. H. Hardy (1877–1947), pictured below, expressed in his autobiographical book A Mathematician’s Apology what most working mathematicians experience: “Beauty is the first test; there is no permanent place in the world for ugly mathematics.”
Continue reading Why mathematics is beautiful and why that matters
Physicist Max Tegmark has just published an interesting new book entitled Our Mathematical Universe: My Quest for the Ultimate Nature of Reality. In this very lucidly written book, Tegmark takes the reader on a tour of modern physics and then introduces his theory of the ultimate nature of the universe.
Tegmark starts out by exploring a list of questions, such as “How big is space?,” “Where did our solar system come from?” and “Where did our big bang come from?.” He then examines some of the difficulties with current theories, including both the successes and failures of the “inflation”
Continue reading Max Tegmark’s “Our Mathematical Universe”
Numerous studies have been done trying to assess the degree to which mathematical ability is inborn or learned. Especially since the era of brain imaging made neurological enquiry realistic.
For example, in a 2011 study, Melissa Libertus, a psychologist at Johns Hopkins University, displayed briefly flashing groups of blue and yellow dots on a computer screen to 200 four-year-old children. The children had to estimate which group of dots was larger (in number). They also were given a standard test of early mathematical ability that measures numbering skills (counting items on a page), numeral literacy (reading numbers), and elementary calculation
Continue reading Are our brains hard-wired for numbers?
Material on this site is provided for purposes of academic research, and does not necessarily reflect views of the bloggers’ employers, funding agencies or any other organization. Also, inclusion of material (articles, quotations, excerpts) on this website does not necessarily indicate that the bloggers endorse that material. Where articles have other authors indicated, those authors are themselves responsible for the contents. All material on this blog and website is copyrighted by David H. Bailey (c) 2024.
[Editor’s note: This is reprinted from The Conversation, 18 Dec 2013. The original article is authored by Michael Rose and Jonathan Borwein.]
The warmth on your face, the scenic view outside — such delights are delivered to you by countless photons from the sun. But believe it or not, these photons move in much the same way as an inebriated person wandering home from the pub, or the initial whiff of coffee as you open a bag of beans.
Let me explain.
Travelling at the fastest speed known to physics, these photons crossed from the sun to the Earth in
Continue reading Tipsy tottering, sunlight and the smell of coffee: it’s all random
In July 2012, Russian billionaire Yuri Milner startled the world of physics by establishing the Fundamental Physics Prize, with awards of $3,000,000 each to nine physicists, including well-known cosmologists Alan Guth, Andrei Linde, Juan Maldacena and Edward Witten, among others. These physicists now constitute a committee to select future awardees. The 2013 awardee was Alexander Polyakov for his work in quantum field theory and string theory. In December 2013, the 2014 awardees were announced, which are John Schwarz of Caltech and Michael Green of Cambridge.
In 2013, Milner, in partnership with Google founder Sergey Brin, Facebook CEO Mark Zuckerberg and
Continue reading Yuri Milner to award $3M prizes to mathematicians
The 2012 edition of the Programme for International Student Assessment (PISA) are in, and once Asia leads the way, with China, Singapore, Taiwan, Korea and Japan scoring very well, while many first-world nations, such as Australia, the U.K. and the U.S., lag behind.
In Canada, which placed 13th overall in mathematics, “alarm bells went off” as
[m]ath scores, the focus of 2012 PISA tests whose results have just been released, declined 14 points in nine years in Canada. And the country produced fewer students who were high achievers – 16 per cent were at Level 5 or
Continue reading PISA international test scores show Australia, Canada, UK, USA lagging
In the latest issue (December 2013) of the Notices of the American Society, noted mathematician Doron Zeilberger has published an Opinion piece on the state of pure mathematics, and then contrasts this with experimental mathematics. His article, entitled “[Contemporary Pure] Math Is Far Less Than the Sum of Its [Too Numerous] Parts,” is available here.
Doron Zeilberger is perhaps best known for his work with Herbert Wilf in developing the Wilf-Zeilberger method for computer-based proving of combinatorial identities, a problem that mathematician-computer scientist Donald Knuth once rated as “50” (meaning of the greatest difficulty) in his book The Art of
Continue reading Doron Zeilberger comments on experimental mathematics in AMS Notices
Homer contemplates pi
Mathematics in the Simpsons
In a newly published book, Simon Singh presents a too little-known back story about the Simpsons TV show: underlying much of the clever screenplay are numerous references to somewhat sophisticated mathematics both in the Simpsons and in the follow-up Futurama.
Simon Singh is no stranger to either mathematics or show business. He directed an award–winning BBC documentary on Fermat’s Last Theorem and authored the best-selling book Fermat’s Enigma on the same topic. He is a physicist by training, with a Ph.D. from Cambridge and is engaged in a host of science
Continue reading Pi in the Simpsons
Fundamental, wide-ranging and curious research is the basis of a country’s development. Cuts to CSIRO won’t help. CarbonNYC/Flickr
Like many scientists, I was apprehensive in advance about the Abbott government’s approach to science policy. Would it be pragmatic but fact-based or would it be ideological and politically driven?
Sadly it has only taken two months to discover that it is the latter.
As a relatively recent immigrant (2008), who has chaired the precursor to Compute Canada (the national high performance computing organisation), NATO’s Physical Sciences and Engineering Technology Panel, and the National Research Council of Canada information institute (CISTI)
Continue reading Australia needs fundamental research to build a great country
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