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Mathematics without ApologiesPortrait of a Problematic Vocation$
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Michael Harris

Print publication date: 2017

Print ISBN-13: 9780691175836

Published to Princeton Scholarship Online: May 2018

DOI: 10.23943/princeton/9780691175836.001.0001

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The Habit of Clinging to an Ultimate Ground1

The Habit of Clinging to an Ultimate Ground1

(p.181) Chapter 7 The Habit of Clinging to an Ultimate Ground1
Mathematics without Apologies

Michael Harris

Princeton University Press

This chapter suggests that notions of real interest to mathematicians are not on the printed page but lurk behind the doors of conception. It is believed that they will someday emerge and shed so much light on earlier concepts that the latter will disintegrate into marginalia. By their very nature, they elude precise definition, so that on the conventional account they are scarcely mathematical at all. Coming to grips with them is not to be compared with attempting to solve an intractable problem. Instead, it harbors a more fundamental obscurity. One cannot even formulate a problem, much less attempt to solve it; the items (notions, concepts) in terms of which the problem would be formulated have yet to be invented. How then can we talk to one another, or to ourselves, about the mathematics we were born too soon to understand?

Keywords:   mathematicians, mathematical concepts, mathematical problems

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