The Mathematical Career of Pierre de Fermat 1601-1665

1996 ◽  
Vol 80 (489) ◽  
pp. 628
Author(s):  
Chris Pritchard ◽  
M. S. Mahoney
Keyword(s):  
Mathematical Career

The Mathematical Work of S.C.Kleene

1995 ◽  
Vol 1 (1) ◽  
pp. 9-43 ◽  
Author(s):  
J.R. Shoenfield
Keyword(s):  
Recursion Theory ◽  
Mathematical Work ◽  
Church’S Thesis ◽  
Recursive Functions ◽  
Close Relationship ◽  
Church's Thesis ◽  
Mathematical Career ◽  
Definable Functions ◽  
Class Of Functions ◽  
Computable Functions

§1. The origins of recursion theory. In dedicating a book to Steve Kleene, I referred to him as the person who made recursion theory into a theory. Recursion theory was begun by Kleene's teacher at Princeton, Alonzo Church, who first defined the class of recursive functions; first maintained that this class was the class of computable functions (a claim which has come to be known as Church's Thesis); and first used this fact to solve negatively some classical problems on the existence of algorithms. However, it was Kleene who, in his thesis and in his subsequent attempts to convince himself of Church's Thesis, developed a general theory of the behavior of the recursive functions. He continued to develop this theory and extend it to new situations throughout his mathematical career. Indeed, all of the research which he did had a close relationship to recursive functions.Church's Thesis arose in an accidental way. In his investigations of a system of logic which he had invented, Church became interested in a class of functions which he called the λ-definable functions. Initially, Church knew that the successor function and the addition function were λ-definable, but not much else. During 1932, Kleene gradually showed1 that this class of functions was quite extensive; and these results became an important part of his thesis 1935a (completed in June of 1933).

A Better Use of Tests in Mathematics

1924 ◽  
Vol 17 (3) ◽  
pp. 140-147
Author(s):  
W. D. Reeve
Keyword(s):  
Diagnostic Tests ◽  
Mathematical Work ◽  
Prognostic Tests ◽  
Mathematical Career ◽  
Innate Ability

Tests in mathematics may be classified under two main heads, namely, prognostic tests, and achievement or diagnostic tests. Prognostic tests are those which may be given by the teacher early in the pupil's mathematical career the results of which are supposed to measure innate ability to do mathematical work. By their use one is supposed to be able to predict how the pupil will probably perform in his later mathematical work. These tests must, in the nature of things, be more comprehensive than any which have been devised for particular fields.

Public Honors for Mathematical Contributions

1923 ◽  
Vol 16 (6) ◽  
pp. 335-339
Author(s):  
G. A. Miller
Keyword(s):  
High Order ◽  
The Public ◽  
Mathematical Career

The student who is considering the question of preparing himself for a mathematical career is naturally interested in the possible public honors for important contributions along this line. He is probably aware that the Ph.D. degree is supposed to imply such contributions, but he may not have heard much about the public honors which normally follow this degree in ease a man continues to make contributions of high order. It is evident that society should be so organized as to encourage such contributions for after the start has been made under the inspiration of the Ph.D. degree still better results may normally be expected from the more mature later efforts if they are sufficiently strenuous and prolonged.

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