Mathematicians dream of proving Riemann's Hypothesis.by Karl Sabbagh / January 20, 2002 / Leave a comment
Over the last century or so, maths became “modern.” It has reached new heights of abstraction and provided tools for the revolution in physics and cosmology that came to the public’s attention with Einstein. Modern mathematics now routinely handles concepts such as infinities of different magnitudes and has invented new numbers which lie nowhere on the line from minus infinity to plus infinity. It has devised closed shapes with finite areas but infinite perimeters. Techniques which at first seem to have no useful function turn out decades later to provide tools for use in the real world. But the essential joy of maths has remained unchanged. When a mathematician proves a hypothesis, he or she has discovered something which is true forever.
Living on a planet that is running out of unexplored territory, the mathematical explorer can never run out of discoveries to savour. And the mathematical world is now at a significant moment: one of its most important unsolved problems may be on the brink of solution.The problem has been around since 1859 and every pure mathematician has longed for it to be resolved. In fact, it may be insoluble, but even knowing that for certain would be a major advance.
This is not a problem that is important in the way that splitting the atom was, or unravelling the genetic code. But last year a US foundation thought the problem merited a prize of $1m to the first person to provide a proof. In fact, the Clay Foundation offered seven prizes of $1m each for proofs of what it considered to be the most significant maths problems. (Some of them sound deceptively easy-“prove that P = NP” for example.) But the most important of these problems, and the most difficult judging by the effort being put into it, is the Riemann Hypothesis.
In 1859, a German mathematician called Bernhard Riemann, a “timid diffident soul with a horror of attracting attention to himself,” published a paper that drew more attention to him than to almost any other mathematician in the 19th century. In it he made an important statement: the non-trivial zeros of the Riemann zeta function all have real part equal to H.
That is the Riemann Hypothesis: 15 words encapsulating a mystery at the heart of our number system. If you read the statement with no mathematical knowledge, you could still ask a meaningful question about…