P versus NP

Main article: Complexity classes P and NP

The question is whether, for all problems for which a computer can verify a given solution quickly (that is, in polynomial time), it can also find that solution quickly. This is generally considered the most important open question in theoretical computer science.

The official statement of the problem was given by Stephen Cook.

The Hodge conjecture

Main article: Hodge conjecture

The Hodge conjecture is that for projective algebraic varieties, Hodge cycles are rational linear combinations of algebraic cycles.

The official statement of the problem was given by Pierre Deligne.

The Poincaré conjecture

Main article: Poincaré conjecture

In topology, a sphere with a two-dimensional surface is essentially characterized by the fact that it is simply connected. It is also true that every 2-dimensional surface which is both compact and simply connected is topologically a sphere. The Poincaré conjecture is that this is also true for spheres with three-dimensional surfaces. The question had long been solved for all dimensions above three. Solving it for three is central to the problem of classifying 3-manifolds. A proof of this conjecture was given by Grigori Perelman in 2003; its review was completed in August 2006, and Perelman was awarded the Fields Medal for his solution. Perelman declined the award.^[1]

The official statement of the problem was given by John Milnor.

The Riemann hypothesis

Main article: Riemann hypothesis

The Riemann hypothesis is that all nontrivial zeros of the Riemann zeta function have a real part of 1/2. A proof or disproof of this would have far-reaching implications in number theory, especially for the distribution of prime numbers. This was Hilbert's eighth problem, and is still considered an important open problem a century later.

The official statement of the problem was given by Enrico Bombieri.

Yang-Mills existence and mass gap

Main article: Yang-Mills existence and mass gap

In physics, classical Yang-Mills theory is a generalization of the Maxwell theory of electromagnetism where the chromo-electromagnetic field itself carries charges. As a classical field theory it has solutions which travel at the speed of light so that its quantum version should describe massless particles (gluons). However, the deictic phenomenon of color confinement permits only bound states of gluons, forming massive particles. This is the mass gap. Another aspect of confinement is asymptotic freedom which makes it conceivable that quantum Yang-Mills theory exists without restriction to low energy scales. The problem is to establish rigorously the existence of the quantum Yang-Mills theory and a mass gap.

The official statement of the problem was given by Arthur Jaffe and Edward Witten.

Navier-Stokes existence and smoothness

Main article: Navier-Stokes existence and smoothness

The Navier-Stokes equations describe the movement of liquids and gases. Although they were found in the 19th century, they still are not well understood. The problem is to make progress toward a mathematical theory that will give us insight into these equations.

The official statement of the problem was given by Charles Fefferman.

The Birch and Swinnerton-Dyer conjecture

Main article: Birch and Swinnerton-Dyer conjecture

The Birch and Swinnerton-Dyer conjecture deals with a certain type of equation, those defining elliptic curves over the rational numbers. The conjecture is that there is a simple way to tell whether such equations have a finite or infinite number of rational solutions. Hilbert's tenth problem dealt with a more general type of equation, and in that case it was proven that there is no way to decide whether a given equation even has any solutions.

The official statement of the problem was given by Andrew Wiles.

#include <cstdlib>
#include <iostream>

using namespace std;

void convert(long x){
     long a[30000] = {0};
     long n = 0; 
     while (x != 0){
          a[n] = x % 3;
          x = (x/3) * 2;
          n++;
     }
    
     n--;
     while (n != -1){
          cout << a[n];
          n--;
          }
}

int main(int argc, char *argv[])
{
    long start, end;
    cout << "Convert decimal number to 3-2 system!\nYou can print value in range!\n";
    cout << "Start printing value from?";
    cin >> start;
    cout << "End printing value at?";
    cin >> end;
    for (long i = start; i <= end; i++){
        cout << i << " -> ";
        convert(i);
        cout << "\n";
        }
    system("PAUSE");
    return EXIT_SUCCESS;
}

#include <cstdlib>
#include <iostream>

using namespace std;

bool even(int a){
     return ((a%2) == 0);
}

long even_function(long &a){
       a = a/2;
       cout << a << "\n";
       return a;
}

long odd_function(long &a){
       a = ((a+a+a) + 1);
       cout << a << "\n";
       return a;
}

void output_generator(long &a, long y){
       if (even(a))
          even_function(a);
       else
          odd_function(a);
}          

int main(int argc, char *argv[])
{
    long x;
    long limit;
    long y = 0;
    cout << "limit? ";
    cin >> limit;
    cout << "Calculate...\n";
    x =limit;
    while ( x > 1 ){
      y++;   
      output_generator(x,y);
    }
    cout << "success\n";
    system("PAUSE");
    return EXIT_SUCCESS;
}

一天, 某黑幫的一個頭頭 收到一封由老大寄來的信 ,內容如下 :

   TelL MuM and dad thAt maXI lOVe mARy anD JeSS oK ? WiSH UR FD LiVE bAD    (文法可能有錯,但不礙事)

他收到信後不明所以, " 說什麼東東呀?"

他發現信中付著一首詩, 加以解讀後發現了一些東西

某人將會被殺

------------------------------------------------------------------------

the poet

Mr. little looks like a LINE , Mr. Capital looks like a DOT

They have a race

The referee is Mr. MORSE

After the race they EXCHANGE with their OPPOSING MEMBERS

----------------------------Answer-------------------------------

TelL MuM and dad thAt maXI lOVe mARy anD JeSS oK ? WiSH UR FD LiVE bAD

大階代表點, 細階代表線, 經轉換後成為以下:

.--. .-. --- --- --.- --.. -..- .--. --. .-.. -. .-.. .. .. .-.. -..

以上為摩斯密碼, 轉換成為英文字母後為:

PROOQZXPGLNLIILD

英文字母順序倒轉置換:

a -> z
b -> y
c -> x
d -> w
e -> v
f -> u
g -> t
h -> s
i -> r
j -> q
k -> p
l -> o
m -> n
n -> m
o -> l
p -> k
q -> j
r -> i
s -> h
t -> g
u -> f
v -> e
w -> d
x -> c
y -> b
z -> a

prooqzxpglnliild -> killjacktomorrow

jack將會被殺!

[ 本帖最後由 hks_sing 於 2007-8-26 07:52 編輯 ]