Page 36 - The 40 Ch. Book by James Hong or 洪祥智
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Chapter 8 Solving Millennium Prize Problems Millennium
                   Challenge (in math).

                   James H Hong To#1 P / NP question I James H Hong: A: Ex:
                   results, so all P are in NP (1 + 1 = 2 is a law. So extending all

                   calculations is made up of law So machine computing is the law,
                   the fact that logic is also a law-based one.) B: But NP is greater

                   than P, as evidenced by Pythagorean theorem (NP). As a result,
                   wisely, all Ps are within the NP, but C: if reverse processing is

                   required, such as x + y = 3 to find x and y, then NP and P are not
                   equal
                   .

                   James H Hong To#2 Hodge guess: I am James H Hong: A. The
                   function gives a line, for example y = x is a straight line. B: For

                   a plane, 3-D, the example is z = x + y and z = x ^ 2 + y ^ 2. C:
                   set x = a + bi and y = c + di ;; and b and d can be zero. D: set Z

                   = x + y and: d / dx f(x) = x and d / dy g (y ) = y insert x and y ;;
                   enter z = x + y ;; z = d / dx f(x) + d / dy g(y) and f(x) = 1 / 2x ^ 2

                   and g(y) = 1 / 2y ^ 2.James H Hong Extra to Hodge conjecture:
                   y = X;; y = x is the area under the line, is Area(y') = 1/2 x(y),
                   and x = y , = 1/2 (x ^ 2), the integral of line is the area;; E: the

                   integral of the area formula = volume: Ex. 4 pi R ^ 2 = 4/3 pi R
                   ^ 3 integral.


                   James H Hong To#3 Riemann hypothesis: Me: A: When
                   applying infinity, the infinity value is infinite, so the real

                   number is not 1/2. B: imaginary number, root 2 of i, i = (-1),
                   does not exist in real life. James H Hong


                   #4或#6 Birch and Swinnerton-Dyer Conjecture: Me: A:

                   ecliptical curve = y ^ {2} = x ^ {3} + ax + b B: when a = 0 b = 0
                   y ^ 2 = x ^ 3 ;; y = x ^(3/2) then y and x have an infinite number

                   of solutions. solved.
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