Analysis is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development.
- The terms synthesis and analysis are used in mathematics in a more special sense than in logic. In ancient mathematics they had a different meaning from what they now have. The oldest definition of mathematical analysis as opposed to synthesis is that given in Euclid, XIII. 5, which in all probability was framed by Eudoxus: "Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth; synthesis is the obtaining of the thing sought by reasoning up to the inference and proof of it."
- The idea that God may be approached and understood through intellectual analysis is uniquely Christian. ...It is probably not an accident that modern science grew explosively in Christian Europe and left the rest of the world behind.
- Freeman Dyson, The Scientist As Rebel (2006)
- Philosophers hasten too much from the analytic to the synthetic method ; that is, they draw general conclusions from too small a number of particular observations and experiments.
- Lord Bolingbroke, reported in Austin Allibone ed. Prose Quotations from Socrates to Macaulay. (1903), p. 34
- Analysis and synthesis, though commonly treated as two different methods, are, if properly understood, only the two necessary parts of the same method. Each is the relative and correlative of the other.
- Sir W. Hamilton, reported in Austin Allibone ed. Prose Quotations from Socrates to Macaulay. (1903), p. 34
- Fortunately analysis is not the only way to resolve inner conflicts. Life itself still remains a very effective therapist... The therapy effected by life itself is not, however, within one's control. Neither hardships nor friendships nor religious experience can be arranged to meet the needs of the particular individual. Life as a therapist is ruthless; circumstances that are helpful to one neurotic may entirely crush another.
- Karen Horney Our Inner Conflicts (1945)
- Analysis and natural philosophy owe their most important discoveries to this fruitful means, which is called induction. Newton was indebted to it for his theorem of the binomial and the principle of universal gravity.
- Laplace, A Philosophical Essay on Probabilities, [Truscott and Emory] (New York 1902), p. 176.
- Government, in the last analysis, is organized opinion. Where there is little or no public opinion, there is likely to be bad government, which sooner or later becomes autocratic government.
- William Lyon Mackenzie King, Message of the Carillon (1927)
- By this way of Analysis we may proceed from Compounds to Ingredients, and from Motions to the Forces producing them; and in general, from Effects to their Causes, and from particular Causes to more general ones, till the Argument end in the most general. This is the Method of Analysis: and the Synthesis consists in assuming the Causes discover'd, and establish'd as Principles, and by them explaining the Phænomena proceeding from them, and proving the Explanations.
- The investigation of difficult things by the method of analysis ought ever to precede the method of composition.
- Isaac Newton, reported in Austin Allibone ed. Prose Quotations from Socrates to Macaulay. (1903), p. 34
- The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists in the analysis of Symbolic Logic itself.
- Bertrand Russell, Principles of Mathematics (1903), Ch. I: Definition of Pure Mathematics, p. 5
- The word Analysis signifies the general and particular heads of a discourse, with their mutual connections, both co-ordinate and subordinate, drawn out into one or more tables.
- Isaac Watts, reported in Austin Allibone ed. Prose Quotations from Socrates to Macaulay. (1903), p. 34