Search

The article presents an encyclopedia entry for the term "probability." As a mathematical discipline, probability dates back to the seventeenth century. Probability lies between the problem of induction and the field of statistics and it is founded in a solution to the former and depends for its applications on the latter.

Friedrich Ludwig Gottlob Frege (pronounced "FRAY-guh") was born in 1848 as the son of Alexander Frege, the principal of a girls' high school, and Auguste Bialloblotzky. His home environment was typically Prussian, a political and social influence that Frege was not to shake for the rest of his life. Frege attended the Gymnasium (high school) in Wismar and then entered the University of Jena. He studied at the University of Göttingen, taking courses in areas ranging from mathematics and philosophy to chemistry and physics. His dissertation dealt with geometrical representations of imaginary structures in the plane. Imaginary numbers arise from allowing the square root of -1 into one's arithmetic. One of the major arguments for their use is that they can be represented geometrically in the two-dimensional Cartesian plane. Following his dissertation, Frege needed to produce another major piece of research to earn teaching privileges at the university. He did so back at Jena, where he would spend the rest of his academic career. Frege's thesis was in the forefront of group theory, a relatively new field. A group is a collection of objects that is closed under various operations, and Frege's work dealt with a group composed of functions. INSET: Gottlob Frege.

Charles Lutwidge Dodgson, creator of the Alice books under the name "Lewis Carroll," was born in the parish where his father was rector. Dodgson grew up in a crowded household that mixed recreation with religion. His lifelong membership in the Church of England reflected this atmosphere. Dodgson wrote and performed plays for his family and edited a household comic newspaper. He was less happy when he entered Rugby School, although his academic record was impressive. When he arrived at Christ Church College, Oxford University, he was glad to have escaped the schoolboy atmosphere of Rugby School and remained in residence at Christ Church until his death. In 1854, he distinguished himself on the final examinations in mathematics and became a lecturer at Christ Church the next year. Dodgson found himself ill at ease in society. This demeanor carried over to the lecture hall, where he was afflicted with a stammer. The combination of stammer and shyness ensured that Dodgson would never be a popular lecturer, although he did not seem to miss that distinction. In 1855, renowned scholar Henry George Liddell came to Christ Church to take the position of dean. He is best known to the academic world as the compiler of a Greek lexicon. To the reading world, however, he is the father of Alice Liddell, to whom Dodgson narrated the stories that became the much-loved volumes Alice's Adventures in Wonderland (1865) and Through the Looking-Glass and What Alice Found There (1871). In the presence of Alice, her sisters, and other young female friends, Dodgson lost his stammer. His friends did not remain young, however, and he drifted away from them. His pseudonym, "Lewis Carroll," came from Latin versions of his middle and first names, and had been used for verses before he composed the Alice books. INSET: Charles Lutwidge Dodgson.

Little is known of the early life of Johannes Stark (pronounced "shtahrk"), the son of a farmer. He attended local schools in Bayreuth and Regensburg, Germany, and entered the University of Munich in 1894, receiving his doctoral degree in physics in 1897. After passing a couple of examinations required for teaching mathematics, he began work in 1897 at Munich. Three years later, he became an assistant to Eduard Riecke at the University of Göttingen. Even at this early stage of his career, Stark's strengths and weaknesses were already visible. His colleagues observed that his experimental skills were remarkable but that he was lacking in the area of translating physical situations into mathematical models. Stark's first book, on the electric conduction of gases, appeared in 1902. By the first few years of the twentieth century, Stark was one of the researchers most familiar with the details of particle physics. One of the initial successes of his career was the discovery of an optical equivalent of the Doppler effect (a shift in frequency dependent on the motion of the source) in canal rays, a beam of positive particles. Even while he was achieving this distinction, however, Stark was liable to errors of interpretation and frequently lost theoretical arguments in physics journals. INSET: Johannes Stark.

Charles Scott Sherrington was the son of James Norton and Anne Brookes Sherrington of Great Yarmouth, England. He went to Ipswich Grammar School, where he was deeply influenced by one of the masters, a poet. His father died when Sherrington was quite young, and the home of his stepfather in Ipswich was a gathering place for good conversationalists. After an impressive academic and athletic career at school, Sherrington proceeded to Gonville and Caius College at Cambridge University. While there, he played rugby for his college and continued his academic success. At Cambridge, Sherrington was singled out by the physiologist Sir Michael Foster to help with his research. His first publication was read to the Royal Society of London while he was still an undergraduate. He received a first-class degree on the natural science tripos (examination for honors) and subsequently received both bachelor's and doctor's degrees in medicine from Cambridge. After his graduation, he conducted studies in Germany and France, studying cholera at first hand in Spain and Italy. INSET: Sir Charles Scott Sherrington.