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Georg Cantor (1845-1918) Educreations Sample Lesson: Enhanced Set Theory |
----- Plato ----- Philosophers generally agree that contemplation of Reality is the highest form of happiness that humans can have. The study of Reality is called Metamathematics. The most interesting problem in metamathematics that I know is called Continuum Hypothesis. Do you know that you do not need a high-sounding logical axiom to derive continuum hypothesis? You can derive it, if you assume a simple equation. See Derivation of the Continuum Hypothesis from Axiom of Combinatorial Sets Many mathematicians believe in pantheism, the idea that the only part of Reality that we can reasonably investigate is the enormously complex working of the nature around us. Thus, the rational study of the laws of nature is considered part of mathematics. The most interesting problem that I know in mathematics is called Riemann Hypothesis. An important idea that is used in the current information revolution is the concept of a communication channel. Do you know that there is a connexion between Riemann's zeta function and Shannon's communication channel? See Information-Theoretic Equivalent of Riemann Hypothesis You do not have to be a mathematician to understand and appreciate Goldbach Conjecture, which states that every even number greater than 4 can be expressed as the sum of two odd primes. If you like to see a statement of Goldbach Conjecture in terms of geometry, see the presentation Geometrical Equivalent of Goldbach Conjecture It is time that humans got accustomed to the idea that that there are distant parts of this universe which even theoretically they cannot reach, and that there are visualizable points in the space around them which they cannot even touch. Not convinced? Have you ever looked at a clear night sky and wondered what lies beyond all those stars? The answer is Black Whole. See the presentation The Mathematical Universe in a Nutshell Did you think that Principia Mathematica type proof can be written only for 1+1=2? See Metamath Proof Explorer for the proof of 2^aleph_alpha = aleph_alpha \choose aleph_alpha In fact, you can get even a musical version of the proof. (Courtesy: Norm Megill) Welcome to my eAtheneum Page K. Kannan Nambiar See the left frame for my Publications Contents
Former Dean and Professor
Key responsibilities http://www.e-atheneum.net/
Standardization of definitions in graph theory.
B.S. from University of Madras Tennis These are fogged mirror sites: http://www.ece.rutgers.edu/~knambiar ... end of the page ... |