Mathematics Magazine for Grades 1-12
4/2003
Math
Info
At a meeting of the American
Mathematical Society in Los Angeles "Mathematical Challenges of
the 21st Century" were proposed. Unlike "Hilbert's
problems" from 100 years earlier, these were given by a team of
30 leading mathematicians of whom eight were Fields Medal winners. Fields Medal Fields Medals are given every four
years to the most distinguished mathematicians aged 40 or under. In
the absence of a Nobel prize in mathematics, they are regarded as the
highest professional honour a mathematician can attain. I the year
2000 a prize of seven million dollars is put up for the
solution of seven famous mathematical problems. Called the Millennium
Prize Problems they are: P versus NP; The
"Hodge Conjecture"; The Poincaré Conjecture; The Riemann
Hypothesis; "Yang-Mills Existence and Mass Gap"; "Navier-Stokes
Existence and Smoothness"; and The "Birch and Swinnerton-Dyer
Conjecture". Poincaré conjecture In 1904 Poincaré conjectured that
any closed 3-dimensional manifold which is homotopy equivalent to the
3-sphere must be the 3-sphere. Although higher-dimensional analogues
of this conjecture have been proved, the original conjecture remains
open Riemann hypothesis The Riemann hypothesis
states that the nontrivial roots of the Riemann zeta function defined
on the complex plane C all have real part 1/2 . zeta function The Riemann zeta function
is the sum of the infinite series prime number theorem The Prime Number Theorem
states that prime number A prime number is an integer > 1 is prime if it is divisible only by itself and 1. The number 1 is not considered prime. Every positive integer can be written as a product of prime numbers in a unique way (up to the order of the factors). |
(s)
=
(1/ns)
n
tends to
as
fast as n/loge n.