Page 36 - 10-21-2019 Final English Edition, the Book with Ch. 46 Added by James H Hong. (1)

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.