THE MILLENIUM PRIZE PROBLEMS.

According to many, mathematical aptitude is an outcome of hard work and practice. You may have heard your teachers say : "Just try hard, and there is no problem on the earth that can not be solved." But the statement is far from reality. There are several problems in mathematics and physics that have puzzled the greatest of the mathematicians since centuries, and still continue to do so. Clay mathematics institute stated some such problems way back in 2000 and declare a prize of one million dollars to the one who correctly solves any one of the problem. Following the list of problems:

The "P vs NP" problem- a famous problem of computer science, proposed by Stephen Cook.
Hodge conjecture - a problem of algebra.
Poincare conjecture- a problem of topology. (proved by Grigori Yakovlevich Perelmann)
The Riemann Hypothesis (my favorite!!) - A proof or disproof of this would have far reaching implications in number theory, especially in distribution of prime numbers.
Yang-Mills existence and mass gap - A problem of electromagnetism
Navier-Stokes existence and smoothness- These equations describe the motion of fluids but still lack a rigorous mathematical version.
The Birch and Swinnerton-Dyer conjecture- A problem dealing with certain equations defining elliptical curves over rational numbers.

A more detailed discussion on the topic is welcome....!!!!

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Math

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Remember to wrap math in $ ... $ or \[ ... \] to ensure proper formatting.

2 \times 3

2 \times 3

2^{34}

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a_{i-1}

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\frac{2}{3}

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Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Is there an equivalent problem to the Hodge conjecture that is not so difficult ?

Prof. pseudo-expert - 6 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$