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 . . . → Read More: Is mathematics invented or discovered?
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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 . . . → Read More: 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, . . . → Read More: 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, . . . → Read More: 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 . . . → Read More: 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 . . . → Read More: 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 . . . → Read More: 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 . . . → Read More: 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 . . . → Read More: Has the 3n+1 conjecture been proved? 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 . . . → Read More: Semiotic fiddling while a digital Rome burns |
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