There is a quiet, but very real drama attached to this problem. Because it is one of the most sought after gems of pure mathematics, many prominent mathematicians have tried to find a proof. While a few have contributed bits and pieces, most have failed. Some, to their eventual embarrassment, have announced a solution, only to find that their argument was incomplete in some essential way.

As we indicated in an earlier posting, the Riemann Hypothesis (RH) is a highly educated guess about the zeros of the zeta function. The zeta function is defined on the complex numbers, and among its zeros are the so-called "trivial" ones, which occur at each of the negative even whole numbers. The other complex zeros are the ones that RH is all about. The RH states that the nontrivial zeros all lie on what in this subject is called the "critical line". This is the line parallel to the imaginary axis passing through the point 1/2 on the real axis.

It has long been known that all these zeros lie inside the "critical strip" which is the set of points that lie within a distance of 1/2 from the critical line. In other words, all the nontrivial zeros are complex numbers x+iy whose real part x satisfies 0 < x < 1. Just knowing this much enables one to prove a famous result called the Prime Number Theorem. (This theorem, first enunciated by the great mathematician C. F. Gauss, says that the number of primes between 0 and N is approximately N/log(N).) If we knew the truth of RH, we could give an even better description of how the primes are distributed.

Among the human interest stories of the quest for a proof of RH is that of Norman Levinson, a quiet, modest, highly respected professor of mathematics at M.I.T.

Levinson was one of many who believe that mathematicians do all their great work when they are quite young. Ironically, he was an excellent living proof that this need not be so.

He also regarded certain problems as being too risky for a young person to attempt since failure was highly likely and might end up wasting the energy and time of a young mathematician. For example, he would have admonished Charlie to stay away from the P vs. NP problem. He might have seen Charlie's obsession with it as a kind of professional death wish (which would actually have been consistent with the role this problem played in Charlie's life).

RH was another such "death wish" problem, although perhaps not as hopeless as P vs. NP. Levinson worked on it because he felt it was the kind of work only an older mathematician could afford to do.

In NUMB3RS, the dramatic image of a great mathematician is presented in terms of lightning insight. For example, Charlie barely glances at a piece of work and declares it brilliant, but soon he is able to spot a flaw in the argument its "seriously brilliant" creator has overlooked after years of work.

The reality of mathematical work is rarely that abrupt. More often, long hours of intense, single-minded attention to the problem accounts for the important breakthroughs. At least that is what happened in Levinson's case. He had given some though to RH in his youth (he wrote one paper on the subject in 1940 at the age of 28 and another in 1956) but it was not his principal interest at that time. It was not until he was in his late 50's that he returned to the problem, but then he immersed himself in it, and gradually made headway.

His work was painstaking and intricate. It was not the sort of thing that another mathematician could glance at and pronounce brilliant, as Charlie did. Until one digests what is being said, it might equally well be delusional nonsense. Levinson himself, while sure of what he had so far accomplished, was not always confident about the final outcome. In a memorable remark, he said that "the impenetrability of the critical strip is ominous."

But against his own misgivings, he persisted, digging deeper, cutting into the core of the problem, publishing a series of ground-breaking results through the early to mid 1970's and he achieved what was up to that time (and remained for years after) the best result achieved toward a proof that all the nontrivial zeros were on the critical line by showing that at least a third of them were.

Then, when he was hot on the trail, and was armed with a unique set of insights that might well have taken him the distance, he learned that he had a lethal brain tumor.

Try to imagine the impact of this news on a man who lived largely in his mind. A few years earlier he had been diagnosed with a different cancer. It had been treated effectively and he seemed to be in remission, but at the time he had instructed his doctors to do anything they thought medically appropriate, so long as it didn't affect his mind.

Moreover, had he been inclined to cherish a place in history as the solver of RH, this was to be a fatal blow to that hope. Indeed, he ceased all work on the problem. When it was suggested to him that had he been spared he might have found the proof, and with it a measure of immortality, he brushed aside the suggestion, saying that in mathematics we never know we have a proof until it is written down.

So one mathematical story ended, but the human story did not quite end there. During his life he had made many friends. He was a great teacher and colleague, and was well loved by his many students and professional associates. The news that he had a fatal disease came as a shock to many, and they came to see him, wishing to say something affirming, but deeply saddened by this turn of events. Levinson directed his energies to cheering up his visitors, in a display of selfless courage as moving as any battlefield act of heroism.

There are, of course, many stereotypes of mathematicians, not all of them flattering. Charlie is one type. The truth is that mathematicians are people, much like other people, not much more likely to be kind or indifferent, sensitive or insensitive than anyone else. But a person may be judged to some extent by his or her heros, and for some of us, one of our heros was Norman Levinson.