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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

1499.0. "The GREATEST Maths Theorems" by STAR::ABBASI () Sun Oct 06 1991 05:08

    this is summary of the greatest theorems of mathematics, the reference
    is "journey through genius" by william dunham, great book, i recommend
    it for every math person, it goes through the proves in detailes, well
    written, although i think the list can be longer than it is.
    
    strange, why no Gauss stuff on the list ?

    well, here it is, the *Greatest* Theorms of Mathematics ..
/nasser
    

-----------------------------------------------------------------------
1. Hippocrates, 440 B.C.
   The areas of two circles (or semicircles) are to each other as the squares
   of their diameters.

2. Euclid 300 B.C.
   the Pythagorean theorem

3. Euclid 300 B.C.
   infinity of primes

4. Archimedes 225 B.C.
   circumference to diameter is Pie (the area of circle equation)

5. Heron 75 A.D.
   triangle formula     -----------------
   area of triangle = \/ s(s-a)(s-b)(s-c)
   where s = a+b+c
             -----
              2

    where  a,b,c are the lengths of the sides of the triangles

6. Carano  1545
   solution of cubic equation

7. Newton  late 1660s
   newton's approximation to Pie

8. John Bernoullis  1689
   harmonic series 1+ 1/2 + 1/3 + ...+ 1/k + ...  is infinite (divergent)


9 Euler  1734
   evaluate 1+ 1/4 + 1/9 + 1/16 + .. + 1/k^2 + ....
   (if you dont want to see what this equal to, then hit CR twice, close
    you eyes before)
    
    
       2
   = Pi
     --
      6
    
    
    
    

                                                       n
10. Leonhard Euler 1736                               2
   refuted fermat claim that all primes are of form 2     + 1
   (p.s. he did this by looking at 4,294,967,297 and factoring it , in an
    ingenious way . to prove the formula is wrong)


11. Cantor 1874
    proved that the interval of all real numbers between 0 and 1 is not
    denumerable

12  Cantor 1891
    if A is any set, then cardinality of A is less than cardinality of
    power set of A.

T.R	Title	User	Personal Name	Date	Lines
1499.1	Rather Perish than Publish	CORREO::BELDIN_R	Pull us together, not apart	`Mon Oct 07 1991 18:10`	12
	My theory is that Gauss is not on the list for the following reason. He was more concerned with private knowledge than publication. We have anecdotal evidence that he polished his work over long periods of time, long enough to let others get priority. There is also evidence that suggest that he was disturbed by the acrimony of the Newton - Leibniz controversy and avoided any appearance of anxiety over priority. IMHO, Dick
1499.2	another one for the list ..	STAR::ABBASI		`Tue Oct 08 1991 04:53`	7
	Gauss theorem that every polynomial equation f(z)=0, where z is complex number, has at least one root, either real or complex. this is called the fundamental theorem of algebra. this was Gauss PhD thesis. he showed that earlier attempts by Euler, d'Alembert and Lagrange were as he put it "unsatisfactory and illusory" . well, who can argue with him.. /Nasser
1499.3	Who says pedantry is dead?	ELIS::GARSON	V+F = E+2	`Tue Oct 08 1991 09:16`	17
	re .0 >6. Carano 1545 > solution of cubic equation I think the guy's name was Cardano. (And, yes, I liked the derivation of this solution when I first came upon it.) > n >10. Leonhard Euler 1736 2 > refuted fermat claim that all primes are of form 2 + 1 This is obviously false as stated. I presume you mean that he refuted the claim that all numbers of the given form are prime. Personally speaking, I think V+F=E+2 should be on the list.
1499.4		ALLVAX::JROTH	I know he moves along the piers	`Tue Oct 08 1991 10:10`	13
	<<< Note 1499.3 by ELIS::GARSON "V+F = E+2" >>> -< Who says pedantry is dead? >- > Personally speaking, I think V+F=E+2 should be on the list. The Euler-Poincare characteristic is more elegantly expressed as an alternating sum of k-faces: F - E + V = 2 because it generalizes to higher dimensions and genus in this form. - Jim
1499.5	Law of Quadratic Reciprocity	CIVAGE::LYNN	Lynn Yarbrough @WNP DTN 427-5663	`Tue Oct 08 1991 14:28`	10
	Although Gauss didn't discover it, he was the first to prove the "Golden Theorem" ascribed to Legendre, the Law of Quadratic Reciprocity. Gauss found seven different proofs, and at least 50 different proofs have been found since his first! Chapter six of Beiler's "Recreations in the Theory of Numbers" is devoted to it. However, not very many people know about this law, which forms part of the foundation of what we know about factoring large numbers, so maybe it's not great in terms of popularity and accessibility. Still, it's pretty neat stuff.