``Brain's Math Machine Traced to 2 Circuits.'' This was the New York Times's take (Sandra Blakeslee, May 11) on a report in the May 7 Science by S. Dehaene, E. Spelke, P. Pinel, R. Stanescu, and S. Tsivkin.
The report, ``Sources of Mathematical Thinking: Behavioral and BrainImaging Evidence'', demonstrates that there are at least two different loci in the brain involved in arithmetic and that the two loci do different things.
These two loci are also associated with other mental activities:
The report concludes with a discussion of the evolutionary difference between exact calculation and approximate.
Dehaene goes deeper into the philosophical, humanistic, and pedagogical implications of his research in an Edge piece: ``What Are Numbers, Really? A Cerebral Basis for Number Sense''.
Multiple Intelligences. From the point of view of teaching and learning mathematics, it is interesting to situate this research in the context of ``multiple intelligences''. This is a circle of ideas developed by Howard Gardner in a series of books starting with Frames of Mind : The Theory of Multiple Intelligences in 1983. (Gardner also is featured in an Edge piece: ``Truth, Beauty, and Goodness: Education for All Human Beings: A Talk with Howard Gardner''.) His classification is based on an empirical effort to understand all human mental abilities. The seven intelligences he proposed

are each ``a capacity, with its component processes, that is geared to a specific content in the world (such as musical sounds or spatial patterns)''. This quote is from his Reflections on Multiple Intelligences: Myths and Messages, where he also mentions that ten years later he proposes adding to the list an eighth intelligence, that of the naturalist.
The experimental results of Deheane, Spelke, and their collaborators strongly suggest that mathematical ability must involve at least three of Gardner's intelligences: the logicalmathematical (by definition), the spatial, and the linguistic.
The concept of multiple mathematical intelligences was put forth, almost at the same time, in a work called Math for Smarty Pants by Marilyn Burns (Little, Brown & Co., 1982). She remarks, ``Being smart in math can mean several things, and different things.

When I came across Burns's book I was very pleased to see explicitly written out, for the first time, what I had felt as a mathematician for many years: there are different kinds of mathematical minds. Besides helping me make sense of a career spent in departments with logicians, analysts, and algebraists, it made me very receptive to the ``rule of three'' as propounded by the members of the Harvard Calculus Consortium, which has become the Rule of Four in the second edition of their Calculus: ``Where appropriate, topics should be presented geometrically, numerically, analytically and verbally.'' It makes sense to access as many intelligences as are available.
...and Multiple Mathematical Personalities? One aspect of the phenomenon that neither Gardner nor the DehaeneSpelke team seem to have gone into is the correlation between the various intelligences and personality traits. In a department of research mathematicians where the mathematical intelligences, at least, can be assumed to be present in their most extreme form, there is considerable evidence of a correlation, which may not be noticeable in the general population, with various personality types. Without going into too many specifics, let me tell the story of a mathematician, a male, who changed fields early in his career. When his wife was asked at a cocktail party what her husband did (this probably dates the story), she said: ``He's a logician. But,'' she quickly added, ``he used to be a topologist.''
Tony Phillips