Some years ago, at a conference that brought together mathematicians and science writers to discuss ways to inform the public more effectively about mathematics and discoveries in mathematics, a prominent mathematician presented a talk on exciting new findings linking the Riemann Hypothesis, quantum physics, and random matrix models.
Though carefully prepared and relying on little more than basic calculus and linear algebra, the presentation missed its mark. A model of mathematical exposition, it would have worked well with an audience of mathematicians. It did not work for an audience of science writers.
The talk contained too little of the grand ideas underlying the mathematics and too much of the mechanics of presenting these ideas mathematically. Indeed, by neglecting to define prime numbers or even dip into the lore and lure of primes, the speaker failed to connect with his audience from the beginning.
In the discussion that followed the presentation, one science writer likened the talk to the way she had felt at a party with some German friends. Her friends would try to speak English for a while but would inevitably lapse into German. She could understand very little of the ensuing conversation.
Speakers also tend to overestimate how much new information their audiences can absorb in one sitting. To reach the "new and exciting" part of his talk, the conference speaker had to describe the Prime Number Theorem, the Riemann zeta function, the Riemann Hypothesis, quantization and linear operator matrices (along with eigenvalues), random matrix theory and unitary symmetry, Poissonian statistics, and quantum chaos. That was a heavy burden for any audience, even more so for listeners not already attuned to these topics.
Some time later, mathematician Dan Rockmore wrote an article about the conference presentation for an online publication called CHANCE News. His commentary filled in some of the details that had been missing from the original talk, including telling glimpses of the mysteries of the primes and their distribution—and what this distribution has to do with the Riemann Hypothesis. Several years later, Rockmore wrote a successful, nontechnical book on the subject titled Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers.
Authors of written material have an advantage over speakers. Readers who lose the thread of an argument can reread a difficult passage, return to earlier sections to recall a definition or key point, or even go to an outside source to obtain the necessary knowledge to proceed. Listeners typically can't do that.
At the same time, authors cannot count on readers being willing to put in a lot of extra effort just to get to the end of an article. Many readers would (and do) give up.
This article is part of a contribution by I. Peterson to the Proceedings, International Congress of Mathematicians, Hyderabad, India, Aug. 25, 2010.
Peterson, I. 1991. Searching for new mathematics. SIAM Review 13(March):37-42.