The Mathematician Who Refused 1 Million Dollars

One of the greatest mathematicians of our time is Grigori Perelman.  Perelman solved one of the most difficult problems in mathematics that has puzzled mathematicians for a hundred years, the Poincaré Conjecture.

The Poincaré Conjecture was posted by Henri Poincaré in 1904. It was one of the seven Millenium Prize Problems, the most difficult mathematics problems selected by the Clay Mathematics Institute. A correct solution to any of the unsolved problems can earn the author 1 million dollars. As of this writing, the remaining six problems are still unsolved. » Read more

Where does the Metric System come from?

The beginning

If any one man can be credited with being the creator of the Metric System it would be the French vicar, Gabriel Mouton. As far back as 1670 his method of measurement, based on the decimal system, was discussed. He based the ideas for this upon the measurement of what would later become a nautical mile: one minute of the the arc of the Earth’s circle. His measurement ideas that he had, including a unit of length based upon a pendulum swing of one beat per second, were all later elaborated on by French scientists, bringing us closer to the current Metric system.

metric system

During the French Revolution these ideas were carried one step further by Talleyrand (the Bishop of Autun). The revolution encouraged many changes and reforms, amongst them the need to reform the way that things were measured and weighed. Talleyrand’s political indulgence and guidance allowed the French Academy to begin research into a new French system for measures and weights. One of the ideas carried forward used the length based on a decimal fraction of the distance between the North Pole and the equator, the move towards decimalization was underway. » Read more

Mersenne Primes Under the Microscope

What are Mersenne Primes?

The recent discovery of the largest known prime number which is 17 million digits highlighted the importance of Mersenne primes.  This newest prime number and the thirteen largest primes are all Mersenne primes. But what are Mersenne primes really and why are they important in finding the largest prime numbers?

If a prime number can be expressed in the form 2^n - 1, n an integer, then it is said to be a Mersenne prime. The name came from Marin Mersenne who studied them, a French monk and well-known mathematician in the 17th century.

mersenneprimes

Many early mathematicians saw and conjectured that if n is a prime number, 2^n - 1 is prime.  For instance, in the figure above, for n = 2, 3, 5, 7 which are prime numbers, their corresponding 2^n - 1 values are also prime numbers. However, this is not true in general since 2^{11} - 1 = 2047 = (23)(89) is not prime.  » Read more

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