Analysis
Analysis is the process of breaking a complex topic or substance into smaller parts in order 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.
Culture
Culture () is the social behavior and norms found in human societies. Culture is considered a central concept in anthropology, encompassing the range of phenomena that are transmitted through social learning in human societies. Some aspects of human behavior, social practices such as culture, expressive forms such as art, music, dance, ritual, religion, and technologies such as tool usage, cooking, shelter, and clothing are said to be cultural universals, found in all human societies. The concept of material culture covers the physical expressions of culture, such as technology, architecture and art, whereas the immaterial aspects of culture such as principles of social organization (including practices of political organization and social institutions), mythology, philosophy, literature (both written and oral), and science comprise the intangible cultural heritage of a society.
Analysis
[A]t the close of the Middle Ages, when the so-called Arabic figures became established throughout Europe with the symbol 0 and the principle of local value, immediate progress was made in the art of reckoning. The problems... led up to the general solutions of equations of the third and fourth degree by the Italian mathematicians of the sixteenth century. Yet even these discoveries were made in somewhat the same manner as problems in mental arithmetic are now solved in common schools; for the present signs of plus, minus, and equality, the radical and exponential signs, and especially the systematic use of letters for denoting general quantities in algebra, had not yet become universal. The last step was definitively due to... Vieta... and the mighty advancement of analysis resulting therefrom can hardly be measured or imagined.
Thomas J. McCormack, "Joseph Louis Lagrange. Biographical Sketch" (1898) in his translation of Joseph Louis Lagrange, Lectures on Elementary Mathematics (1898); 2nd edition (1901) p. viii.
Analysis
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
