Martin E Flashman
Department of Mathematics,
Humboldt State University,
Arcata, CA 955521
The Continuum Hypothesis:
A Look at the History of the Real Numbers in The Second Millennium.
After Cantor first demonstrated that the real numbers
(continuum) were uncountable, the hypothesis arose that the set of the
real numbers was "the smallest" uncountable set. In 1900 David Hilbert
made settling the continuum hypothesis the first problem on his now famous
list of problems for this century. The author will discuss some of the
historical, philosophical, and mathematical developments connected
to this problem proceeding from issues of definition of the real numbers
and proofs of uncountability to issues of consistency and models and proofs
of the independence of this hypothesis and possibly some comments on its
current status. (Received September 14, 2001)
Outline of possible
Discussion (depending on time allowed).
I. "Greek" Views - Control early Second Millenium.
II. Pre-Calculus and Early Calculus Views
III. The Age of Development
Bolzano 1781- 1848 (1817 paper)
IV. The Age of Critical
Awareness and Foundations
Weierstrass: 1815- 1897
V. Cantor 1845-1918: Investigation of discontinuities with Fourier series and Set Theory Beginnings.
VI. The XXth Century:
An Age of Exploration and Discovery.
Cohen: (1934- )
Dana Scott/ Solovay
VII.? The XXIst Century: The Hypothesis is False?
Now onto a slightly more detailed ouline.