Concept
Algebra
Overview
part of mathematics in which letters and other symbols are used to represent numbers and quantities in formulae and equations
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
In the original texts
Passages from public-domain books where Algebra is discussed.
C. 1600) gave room for a development which had already been faintly anticipated in later Greek mathematics. Algebra now came upon the scene, and algebra is a generalisation of arithmetic. In the same way as the notion of number abstracted from reference to any one particular set of entities, so in algebra abstraction is made from the notion of any particular numbers. Just as the number ‘5’ refers impartially to any…
Alfred North Whitehead, Science and the modern world
names the idea; states what it is; author linked in the graph
But all that is an evasion of our real question, and I merely state it in order to avoid being misunderstood in my answer. Quadratic equations are part of algebra, and algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world. There is no getting out of it. Through and through the world is infected with quantity. To talk sense, is to talk in quantities…
Alfred North Whitehead, The organisation of thought, educational and scientific
states what it is; names the idea; author linked in the graph
Thought is in fact a kind of Algebra, as Berkeley long ago said, "in which, though a particular quantity be marked by each letter, yet to proceed right, it is not requisite that in every step each letter suggest to your thoughts that particular quantity it was appointed to stand for." Mr. Lewes has developed this algebra-analogy so well that I must quote his words: "The leading characteristic of algebra is that of…
William James, The Principles of Psychology, Volume 1
names the idea; states what it is; opens on it
But mathematics does not confine itself to the construction of quantities (quanta), as in the case of geometry; it occupies itself with pure quantity also (quantitas), as in the case of algebra, where complete abstraction is made of the properties of the object indicated by the conception of quantity. In algebra, a certain method of notation by signs is adopted, and these indicate the different possible…
Immanuel Kant, The Critique of Pure Reason
names the idea; opens on it
Just as arithmetic deals with the common properties of lines, areas, bulks, forces, periods; so does algebra deal with the common properties of the numbers which arithmetic presents; so does transcendental analysis deal with the common properties of the equations exhibited by algebra. Thus, the generality of the higher branches of the calculus, when compared with the lower, is the same kind of generality as that of…
Herbert Spencer, Illustrations of Universal Progress
names the idea; opens on it
Philosophers who discussed Algebra
- Avicenna
- Gottfried Wilhelm Leibniz
- John Stuart Mill
- René Descartes
- George Boole
- Hypatia
- Paul Feyerabend
- Islam
- Charles Sanders Peirce
- Penelope Maddy
- Grigore Moisil
- Józef Maria Hoene-Wroński
Related ideas
- Artificial intelligence
- Garrett Birkhoff
- Outline of ancient India
- Gerolamo Cardano
- Integer
- Truth value
- Foundations of mathematics
- Latin
- Fibonacci
- Propositional logic
- Function (mathematics)
- Mathematics
- Geography
- Geometry
- Mathematical object
- Model theory
- Real number
- Number theory
- Physics
- Pythagoras
- Euclid's Elements
- Scientific law
- Quantum mechanics
- René Descartes
Place in the tradition
Part of First-order logic.