Professor Ranjan Roy of Beloit College spoke on "How many prime numbers are there less than any given number?". A
prime number is an integer greater than one which cannot be evenly divided only by one and itself.  Euclid proved that there are
an infinite number of primes.  The more difficult problem of the distribution of primes was not considered until the 18th century
when Euler, Gauss and Legendre independently suggested an approximate formula for the number of primes less than a given
integer.  It took mathematicians a hundred years to prove this result.  It is, however, still an open problem to decide how good
this formula is.  In fact, this is one of the most famous and important problems in mathematics and the conjectured answer is
known as the Riemann Hypothesis.

Professor Ranjan Roy has Ph.D. from SUNY at Stony Brook and has been at Beloit College since 1982. His research
interests are complex analysis and discontinuous groups, differential equations in the complex domain, special functions, fluid
mechanics and nonlinear waves, the history of mathematics, and number theory. He has published numerous research articles, a
text on special functions (with R. Askey and G. Andrews), and is preparing a new text, "Glimpses into the History of
Mathematics". This was Professor Ranjan Roy's second presentation at MATC.
 

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