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3 - Warning Signs of a Possible Collapse of Contemporary Mathematics

Published online by Cambridge University Press:  07 June 2011

Edward Nelson
Affiliation:
Princeton University (New Jersey), United States
Michael Heller
Affiliation:
Pontifical University of John Paul II
W. Hugh Woodin
Affiliation:
University of California, Berkeley
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Summary

I rejoice that we live in a world of boundless, infinite possibilities, one in which, with Blake, we can see a world in a grain of sand and a heaven in a wildflower, hold infinity in the palm of our hand and eternity in an hour. I rejoice that the sacred scriptures of our faith portray a God who listens to prayer, who loves us and longs to lead us. I rejoice that my chosen line of work, mathematics, has enabled me to bring into being new things that did not exist before and to greet with wonder and awe many amazing inventions of my fellow workers. I rejoice that daily we live immersed in infinity, that we have the freedom not only to make choices but at times to be the agent, by will or by grace, to sing to the Lord a new song.

Is infinity real? For example, are there infinitely many numbers? Yes indeed. When my granddaughter was a preschooler, she asked for a problem to solve. I gave her two seventeen-digit numbers, chosen arbitrarily except that no carrying would be involved in finding the sum. When she summed the two numbers correctly, she was overjoyed to hear that she had solved a mathematical problem that no one had ever solved before.

The celebration of infinity is the celebration of life, of newness, of becoming, of the wonder of possibilities that cannot be listed in a finished, static rubric.

Type
Chapter
Information
Infinity
New Research Frontiers
, pp. 76 - 86
Publisher: Cambridge University Press
Print publication year: 2011

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