The work of the french mathematician Nicoloas Bourbaki influenced the change in thinking about the structure of mathematics from 1940 on.  One of the Bourbaki publications, Part 1 of the Fundamental Structures of Analysis, was directly used to develop later curriculum.  It influenced the curriculums in the areas of set theory, algebra, general topology, fuctions of a real variable, topological vector space, and integration.  Nicolas bourbaki, a Greek name, was actually a pseudonym, or nom de plum, that a group of French mathematicians used to publish under.  The members of the group writing under this name, did not stay consistent, but in general, most of them were from the University at Nancy, and many of them had appointments at American universities.  The number of mathematicians publishing under this name usually was around 12 at a time; the most ever in the group at any one time was 20.  Four well-known members of the group were C. Chevalley, J. Delsarte, J. Dieudonne, and A. Weil.  The only rule of the group was that they most retire from the group at 50 years of age.

The work of Bourbaki influenced a change in thinking about math to the degree that a "new math" curriculum was developed to try to address the issues that Bourbaki brought to the surface of mathematical education.  His publishings began in 1939.  The influential publishings were a general surbey of math.  They were trying to develop all of math from a few broad axioms, giving complete proofs for all of mathematics.  Set theory was being used to axiomatisize, in a system of first order logic, building on the Axiom of Global Choice.  He, or they, developed properties of a lot of "key math structures," like topological spaces and groups.  One easy way to understand Bourbaki's work is to see that "the Bourbaki system is a ‘big theory' rather than a mosaic of ‘little theories.'"

OTHER MATHEMATICIANS WHO WERE BORN OR DIED IN 1939:

DICKSTEIN, was 88 and died.  He helped found the Warsaw Scientific Society and the Polish Mathematical society.  He worked in the fields of Algebra and the history of math.

LINDEMANN, was 87 and died.  He was the first to prove pi was transcendental.  He worked in non-Euclidian line geometry.

GRAVE was 76 and died.  He worked on methods for the 3-body problem and map projections

EPSTEIN was 68 and died.  He worked in number theory, specifically on the zeta function, as well as on the history of mathematics.

LESHNIEWISKI was 53 and died.  His field was math logic.

HARTLEY was born this year.  His field was group theory.

ALAN BAKER was born.  He won the Fields medal for work with diophantine equations.

KINGMAN was born this year.  He later went on to author Introduction to Measures and Probability and The Algebra of Queries.

Author: Maggie Cooper

References:
Encyclopedia.com, Concise Columbia electronic encyclopedia, 3rd ed., "Bourbaki", <<http://encyclopedia.com/articles/01742.html>>, Columbia University Press of Inso Corp, 1998.

Eves, Howard, "An Introduction to the History of Mathematics", 6th ed., Saunders College Publishing, San Diego, 1988, p641-2.

Harrison, John, "Bouraki", <<http://www.pip.com.pl/MathUniversalis/2/harrison/jrh0105.html>>, 96/2/22.

<<http://www.groups.dcs.st-and.ac.uk/~history/Chronology/WhoWasThere.html.

Moon, Bob, "The 'New Maths' Curriculum Controversy; An International Story", The Falmer Press, 1986, p5-6.

Alan Baker was born on August 19, 1939 in London, England, during the outbreak of the second World War.  After surviving the German bombings as a small child, he went on to attend University College London, where he received his B.Sc., and Trinity College Cambridge, where he received both his M.A. and his doctorate.  Upon receiving his doctorate in 1964, he was elected a Fellow of Trinity College.

Baker received the distinguished Fields Medal in 1970 at the International Congress at Nice for his work on diophantine equations.  Building upon the previous work of Thue, Siegel, and Klaus Roth, Baker "produced results which, at least in principle, could lead to a complete solution of" diophantine equations of the form f(x, y) = m where m is an integer and f is an irreducible homogeneous binary form of degree at least three with integer coefficients.

Baker has also made contributions to research on transcendental number theory, including Hilbert's seventh problem, which asked whether or not a^q was transcendental when a and q are algebraic.  His work on transcendental numbers led him to generate a large a category of previously unidentified transcendental numbers, and he showed how the theory underlying his research could be used to solve a wide range of Diophantine problems.

He has published several books on number theory and transcendental numbers, including Transcendental Number Theory (1975).  Transcendental Number Theory contains a considerable amount of work on transcendental numbers by earlier mathematicians.  Baker includes work by Liouville; Cantor; Hermite; Hilbert; Thue, Siegel, and Roth; and several other twentieth century mathematicians and their advances in transcendental number theory.  Of course, his book also contains a substantial amount of his own work in the field.

Author: Tony Brinsko

References:
Baker, Alan. Transcendental Number Theory. Cambridge:  Cambridge University Press, 1975.

http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Baker_Alan.html