statisticsstatistics,
science of collecting and classifying a group of facts according to their relative number and determining certain values that represent characteristics of the group.
..... Click the link for more information. are often considered parts of applied mathematics. The distinction between pure and applied mathematics is now becoming less significant.
Development of Mathematics
The earliest records of mathematics show it arising in response to practical needs in agriculture, business, and industry. In Egypt and Mesopotamia, where evidence dates from the 2d and 3d millennia B.C., it was used for surveying and mensuration; estimates of the value of π (pipi,
in mathematics, the ratio of the circumference of a circle to its diameter. The symbol for pi is π. The ratio is the same for all circles and is approximately 3.1416.
..... Click the link for more information. ) are found in both locations. There is some evidence of similar developments in India and China during this same period, but few records have survived. This early mathematics is generally empirical, arrived at by trial and error as the best available means for obtaining results, with no proofs given. However, it is now known that the Babylonians were aware of the necessity of proofs prior to the Greeks, who had been presumed the originators of this important step.
A profound change occurred in the nature and approach to mathematics with the contributions of the Greeks. The earlier (Hellenic) period is represented by ThalesThales
, c.636–c.546 B.C., pre-Socratic Greek philosopher of Miletus and reputed founder of the Milesian school of philosophy. He is the first recorded Western philosopher. Thales taught that everything in nature is composed of one basic stuff, which he thought to be water.
..... Click the link for more information. (6th cent. B.C.), PythagorasPythagoras
, c.582–c.507 B.C., pre-Socratic Greek philosopher, founder of the Pythagorean school. He migrated from his native Samos to Crotona and established a secret religious society or order similar to, and possibly influenced by, the earlier Orphic cult.
..... Click the link for more information. , PlatoPlato
, 427?–347 B.C., Greek philosopher. Plato's teachings have been among the most influential in the history of Western civilization. Life
After pursuing the liberal studies of his day, he became in 407 B.C. a pupil and friend of Socrates. From about 388 B.
..... Click the link for more information. , and AristotleAristotle
, 384–322 B.C., Greek philosopher, b. Stagira. He is sometimes called the Stagirite. Life
Aristotle's father, Nicomachus, was a noted physician. Aristotle studied (367–347 B.C.
..... Click the link for more information. , and by the schools associated with them. The Pythagorean theorem, known earlier in Mesopotamia, was discovered by the Greeks during this period.
During the Golden Age (5th cent. B.C.), Hippocrates of Chios made the beginnings of an axiomatic approach to geometry and Zeno of EleaZeno of Elea
, c.490–c.430 B.C., Greek philosopher of the Eleatic school. He undertook to support in his only known work, fragments of which are extant, the doctrine of Parmenides by demonstrating that motion and multiplicity are logically impossible.
..... Click the link for more information. proposed his famous paradoxes concerning the infinite and the infinitesimal, raising questions about the nature of and relationships among points, lines, and numbers. The discovery through geometry of irrational numbers, such as √2, also dates from this period. Eudoxus of CnidusEudoxus of Cnidus
, 408?–355? B.C., Greek astronomer, mathematician, and physician. From the accounts of various ancient writers, he appears to have studied with Plato in Athens, spent some time in Heliopolis, Egypt, founded a school in Cyzicus, and spent his later years
..... Click the link for more information. (4th cent. B.C.) resolved certain of the problems by proposing alternative methods to those involving infinitesimals; he is known for his work on geometric proportions and for his exhaustion theory for