Preface xv
centuries and not recognized as rightly belonging to mathematics.
In this book, I argue that this is a characteristic property of “math-
ematical” memes:
If a meme has the intrinsic property that it increases the
precision of reproduction and error correction of the meme
complexes it belongs to and if it does that without resorting
to external social or cultural restraints, then it is likely to
be an object or construction of mathematics.
So far research efforts in mathematical cognition have been
concentrated mostly on brain processes during quantification and
counting (I refer the reader to the book The Number Sense: How
the Mind Creates Mathematics by Stanislas Dehaene [171] for a
first-hand account of the study of number sense and numerosity).
Important as they are, these activities occupy a very low level
in the hierarchy of mathematics. Not surprisingly, the remark-
able achievements of cognitive scientists and neurophysiologists
are mostly ignored by the mathematical community. This situation
may change fairly soon, since conclusions drawn from neurophysi-
ological research could be very attractive to policymakers in math-
ematics education, especially since neurophysiologists themselves
do not shy away from making direct recommendations. I believe
that hi-tech “brain scan” cognitive psychology and neurophysiology
will more and more influence policies in mathematics education. If
mathematicians do not pay attention now, it may very soon be too
late; we need a dialogue with the neurophysiological community.
Cognitive psychology and neurophysi-
ology will more and more influence poli-
cies in mathematics education. If math-
ematicians do not pay attention now,
it may very soon be too late; we need
a dialogue with the neurophysiological
The development of neurophysiol-
ogy and cognitive psychology has
reached the point where mathemati-
cians should start some initial dis-
cussion of the issues involved. Fur-
thermore, the already impressive
body of literature on mathematical
cognition might benefit from a criti-
cal assessment by mathematicians.
Second, the Davis–Hersh thesis
puts the underlying cognitive mech-
anisms of mathematics into the focus
of the study.
Finally, the Davis–Hersh thesis is useful for understanding the
mechanisms of learning and teaching mathematics: it forces us to
analyze the underlying processes of interiorization and reproduc-
tion of the mental objects of mathematics.
In my book, I try to respond to the sudden surge of interest in
mathematics education which can be seen in the mathematical re-
search community. It appears that it has finally dawned on us that
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