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Euclid's Elements 9. 14 and the Fundamental Theorem of Arithmetic

C. M. Taisbak

in Science and Mathematics in Ancient Greek Culture

Published in print:
2002
Published Online:
February 2010
ISBN:
9780198152484
eISBN:
9780191710049
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198152484.003.0013
Subject:
Classical Studies, European History: BCE to 500CE

This chapter clarifies some unfamiliar concepts of Euclidean number theory and examines the bricks, constituents, and formative elements of numbers. It also considers three famous propositions from ... More


Be contradictory, because of the infinitude of primes

Susan D'Agostino

in How to Free Your Inner Mathematician: Notes on Mathematics and Life

Published in print:
2020
Published Online:
April 2020
ISBN:
9780198843597
eISBN:
9780191879388
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198843597.003.0029
Subject:
Mathematics, Educational Mathematics, Applied Mathematics

“Be contradictory, because of the infinitude of primes” offers encouragement and practice with the “proof-by-contradiction” method of mathematical proof. Any mathematician will tell you that the ... More


Prime numbers: The DNA of mathematics

Marcel Danesi

in Pythagoras' Legacy: Mathematics in Ten Great Ideas

Published in print:
2020
Published Online:
January 2020
ISBN:
9780198852247
eISBN:
9780191886959
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198852247.003.0002
Subject:
Mathematics, History of Mathematics, Educational Mathematics

The Pythagoreans developed many of the ideas related to numbers that have become so familiar to us, including even and odd numbers, square numbers, triangular numbers, and so on. They also discovered ... More


The Hardest Problems in NP

Lance Fortnow

in The Golden Ticket: P, NP, and the Search for the Impossible

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175782
eISBN:
9781400846610
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175782.003.0004
Subject:
Computer Science, Programming Languages

This chapter looks at some of the hardest problems in NP. Most of the NP problems that people considered in the mid-1970s either turned out to be NP-complete or people found efficient algorithms ... More


Mental Pictures

Joseph Mazur

in Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691173375
eISBN:
9781400850112
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691173375.003.0023
Subject:
Mathematics, History of Mathematics

This chapter considers the mental pictures of thought and images in relation to algebraic symbols. According to Ludwig Wittgenstein, “We make to ourselves pictures of facts.” For Wittgenstein, the ... More


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