Concept
Number theory
Overview
branch of pure mathematics devoted primarily to the study of the integers
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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This seems to imply that they regarded matter as consisting of atoms with empty space in between. But if so, they must have thought space could be studied by only paying attention to the atoms, for otherwise it would be hard to account for their arithmetical methods in geometry, or for their statement that "things are numbers." The difficulty which beset the Pythagoreans in their attempts to apply numbers arose…
Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy
Close in meaning to Number theory; the term itself is not named.
In the Pythagorean system numbers seem partly to be themselves allied to categories—that is, to be at once the thought-determinations of unity, of opposition and of the unity of these two moments. In part, the Pythagoreans from the very first gave forth universal ideal determinations of numbers as principles, and recognized, as Aristotle remarks (Metaph. I. 5), as the absolute principles of things, not so much…
Georg Wilhelm Friedrich Hegel, Hegel's Lectures on the History of Philosophy
Close in meaning to Number theory; the term itself is not named.
In the social sciences, however, such examples as the "political" and the "economic" man are signal failures, while, perhaps, the "atom" and the "electron" approach the ideal in physics and chemistry. In mathematics, all further concepts can be defined by collections of these fundamental entities constituted in certain specified ways. And it is worth noting that both factually and logically a collection of entities…
John Dewey, Creative Intelligence
Close in meaning to Number theory; the term itself is not named.
Philosophers who discussed Number theory
Related ideas
- Infinite set
- Integer
- Ibn al-Haytham
- Fibonacci
- Mathematics
- Mathematical object
- Rational number
- Real number
- Euclid's Elements
- Renaissance
- Pythagorean theorem
- Limit (mathematics)
- Set (mathematics)
- Pythagoreanism
- Identity (mathematics)
- United Kingdom
- Computer scientist
- Eudemus of Rhodes
- Octave
- Babylonian mathematics
- Royal Society
- Calculus
- Computer science
- Complex number
Place in the tradition
Part of First-order logic.