Unsolved problems in mathematics

Unsolved mathematical problems are those which have either exceeded the intellect of every living mathematician so far in history, or are just plain impossible, or no one has really cared to bother with it much, as of yet.
==== The problem of the unsolved problems ====
Finding solutions to unsolved problems is becoming an increasing problem, due to the decreasing numeracy of an increasingly calculator-dependent population, who have lost any number sense. Kids these days can't even recognise the equation below is actually a limerick from 1980 by Leigh Mercer:
\frac{12 + 144 + 20 + 3\sqrt{4}}{7} + 5 \times 11 = 9^2 + 0
The Millennium Prize Problems are too much for most of the population, who wouldn't even recognize imaginary numbers such as twiddly-two or eleventy-eight. The unsolved problems in math which should challenge the general population ought to be of a humbler nature, and less intellectually dense. What follows are some examples.
== Unsolved Math Problems for the Common Man ==
Examples of unsolvable mathematical problems include, but are by no means limited to, the following:
==== The unequal equality problem ====
1 = 2
The solution to 1 = 2 has driven many a mathematician to drink, especially when they are asked to solve for the unknown. Most people take the easy way out and say that the statement 1 = 2 is false. But that's just lazy.
==== The two or more unknowns problem ====
x + y = 99
Solving a single equation with more than one unknown has also caused many a mathematician to weep openly.
==== The problem of the square root of bugger all times six ====
\sqrt{bugger\ all} \times 6
There needs to be a more elegant solution to the problem than just "bugger all". An alternate solution is needed, because that would imply that "bugger all" is its own square root.
==== The redefinition of the numerical properties of the number zero ====
While we are on the topic, the properties of zero need to be cleaned up. According to the proceedings of the 2008 AMS Conference, zero is at the heart of computer failure, affecting everything from recording instruments to guided missile systems. This is due to zero's unruly nature ascribed to it by humans. When we say that division by zero lacks definition, it is because we have not bothered. Mankind invented the number system, it is a construct of our own perceptions and ideas. Surely we can invent a zero that does not cause so much mayhem when you divide by it accidentally in a computer program. But for now mankind is the zero's bitch. Zero pwns mankind and the world, and the madness has got to stop.
==== The Inconvenience of Indeterminate Forms ====
Indeterminate forms are problems which face us that have no actual defined value. Division by zero, as shown above, leads to undefined behaviour. But there are other problems which the common man can understand, and hopefully offer a solution. L'Hôpital's Rule was made to take care of many cases of undefined behaviour in algebra by cancelling like terms in a rational function, and so on. But there are many other cases where indeterminate forms can't be avoided. The rewards for solving most of these problems are immense, and can result in fame, fortune, and a place in history.
===== The problem of \frac{0}{0} =====
What about the problem of evaluating \frac{0}{0}? If you cancel them out, do you really get 1? If you could, we could definitely get something for nothing and our economic problems would vanish the world over.
===== The problem of \frac{\infty}{\infty} =====
What about \frac{\infty}{\infty}? Since the properties of infinity are such that \sqrt{\infty} = \infty, we are given to believe that \frac{\sqrt{\infty}}{\infty} = \frac{\infty}{\infty}. What utter hogwash! If that's true, that means we can't cancel the infinities to make 1! What number behaves like that? It looks like we need to tame infinity also.
===== The problem of 0^0 =====
Your math teacher told you that anything to the power zero equals 1, but what about 0^0? If it can equal 1, then you can get something for nothing again. So this remains an expression which is without definition. This is also up for grabs. If you can define it so that my calculator doesn't give me an error, there is either a Field's Medal or a Nobel Prize in it for you, and a place in history. Get to work!
==== Opaque story problems ====
A bus drives along its daily route. At the first stop, two guys get on. At the next stop, three guys get on and one guy gets off. At the third stop, three guys get off and four guys get on. At the fourth stop, eight people get on and six guys get off. What is the name of the driver?
Now, they say there is no solution to this kind of math problem. But that is only that no one has worked at it enough yet.
==== Billy's unfinished math problems ====
Billy is a kid in grade eight who had a homework assignment to hand in to his teacher today and he didn't finish it. There is a whole sheet of unsolved math problems that were left blank because he wanted to play FIFA on his PS/3 with his buddies and watch Avatar on Blu-Ray for the rest of the evening. Billy is a lazy bum who text messages his friends while in math class and frequently asks to "go to the bathroom" (he has no medical problems). He is mathematically illiterate due to a litany of his own avoidance behavior. Sucks to be Billy.
==See also==
*The World's Hardest Maths Problems
Category:Science
Category:Mathematics
Category:Technology
Category:TAW Entry 2010