Ancient Indian square roots

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

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June 14th, 2011 | Category: Essays | Comments are closed

Quick tests for checking whether a new math result is plausible

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

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June 8th, 2011 | Category: Essays | Comments are closed

Has the 3n+1 conjecture been proved?

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

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June 3rd, 2011 | Category: News | Comments are closed