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

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