Dr. Laurens Gunnarsen’s talk was incorrectly advertised as Gifted Children, for which we apologize. However, the subject matter with which Dr. Gunnarsen dealt was even more interesting than the two previous talks he gave on the advertised topic. At the end of his presentation, he did indeed provide a concise update on the progress of the children with whom he has been working.
Dr. Gunnarsen started by emphasizing that mathematics is an art. He then dealt with the question of recognizing mathematical genius and, consistent with his work with children, recognizing it early.
One of the problems, he said, is that standardized intelligence tests recognize only one category of mathematical genius--the problem solver. However, brilliant mathematicians can be divided into two basic categories--the problem solvers and the theory builders, with the latter devising the very language in which the former think and write.
Dr. Gunnarsen provided a very interesting example of how the two groups differ perceptually. No problem solver would mistake 57 for a prime number. However, the person many consider to be the greatest contemporary mathematical theoretician, Alexander Grothendieck, did just that. In a discussion with other mathematicians in which he needed an example of a prime number, he cited the number 57. Not only did he not recognize it as the product of 3 and 19, but the matter was of no interest to him.
Theory builders don't set out to solve problems; rather, they set out to find the right way of thinking about the whole domain of ideas to which the problems belong. Theory builders believe that once you find that right way of thinking, the problems will become trivial. And they know that the right way of thinking is the one that makes the whole domain of ideas as beautiful as it can be. So what distinguishes great mathematical theory builders is their sense of what is beautiful in this art. For this reason, Dr. Gunnarsen is designing variants of the traditional tests, in which those being tested are asked, not only to find patterns (e.g., in number series), but to state which ones they find beautiful and which they find merely mundane. He provided the audience with three examples, one of which was particularly fascinating and, in a mathematical sense, esthetically pleasing.
Dr. Gunnarsen allowed questions, of which there were quite a few, during his presentation. In his review of the gifted children with whom he works, he cited both successes and disappointments.
Report prepared by Bill Potts