In the Middle Ages, one person who worked quietly and tirelessly at bringing together scientists and mathematicians from all across Western Europe was Marin Mersenne. I've put up his portrait at the left. I find him a great source of inspiration.
Father Marin Mersenne (1588-1648) was a French mathematician, philosopher, and theologian whose greatest contribution to the development and growth of mathematics was not the discovery of any particular result (though he did do a lot of work on the Mersenne numbers - more on that some other day) but rather his work in bringing together the leading mathematicians and scientists of his day into contact with one another.
He lived at a time when the tradition of publication of results had yet to be established, and when discoveries were jealously guarded, and he sought to establish links in the world of science and mathematics. So he maintained regular contact with individuals such as Rene Descartes, Girard Desargues, Pierre de Fermat, Blaise Pascal and Galileo.
It was said of him that "to inform Mersenne of a discovery meant to publish it throughout the whole of Europe".
Surely everyone knows of Fermat's Last Theorem - the statement that there are no solutions to the equation
if x, y, z, n are positive integers with n greater 2.
It remained as a conjecture for more than three and a half centuries, and was finally proved by Andrew Wiles about fifteen years back, in 1993-94.
But not many know of another such conjecture which is still waiting to be proved:
"Suppose that A, B, C, x, y, z are positive integers, with x, y, z all greater than 2, and
Then the bases A, B, C share a common factor greater than 1."
For example we have
and the bases (3, 6, 3) have a common factor, namely, 3, which exceeds 1.
Another example:
Yet again, the three bases (27, 162, 9) have a common factor, namely, 9, which exceeds 1.
This is called Beal's Conjecture, and there is a huge prize waiting for the first person who proves it!
Hi, my name is Shailesh Shirali, and I head a Community Math Center based in Rishi Valley School (located in Rishi Valley, near Madanapalle, Andhra Pradesh, India).
I have been involved for many years now in mathematics teaching and mathematics olympiads, but am getting more and more into math teacher education. This blog will be my attempt to keep in touch with the many teachers and students I meet in my workshops. I will post articles and problems on a regular interval here, and I look forward to hearing comments about them from readers.
