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 geniusthe problem solver. However,
brilliant mathematicians can be divided into two basic categoriesthe
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
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