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

community.

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