If mathematicians can make up a complex problem then why can't they solve it?

I'm looking at some very complex problems


mind boggling...





So, how did they put together this problem


and why is it so difficult to solve?If mathematicians can make up a complex problem then why can't they solve it?
Why should being able to come up with a complex problem have anything to do with being able to solve it? It's easy to come up with questions that are difficult, if not impossible to answer. Why do you think philosophers struggle with questions concerning the meaning of life or the existence of God? They are easy questions to ask, but impossible to answer fully.





Math is no different. There a tons of unsolved problems out there, but those problems are responsible for the development of new kinds of mathematics. When mathematicians have attacked a problem from all possible angles and still can't come up with an answer, they often decide that the tools needed to solve it aren't currently known. Entire branches of math have sprung up simply to solve a single problem. For example, mathematicians had long suspected that there was no formula to solve a general polynomial of degree 5 or greater (such as the quadratic formula for second degree polynomials). Galois theory emerged as a result of this problem, and was ultimately used to prove that such formulas were indeed impossible. Since then, Galois theory has expanded into a huge subject with many other uses.





To demonstrate the ease with which someone can come up with a mathematical problem which is extremely difficult to prove, consider the Goldbach conjecture. It states that every even integer greater than 2 can be written as the sum of two primes. The question is so simple, a fifth grader can understand it. However, it has never been proven, despite having been around for over 250 years.If mathematicians can make up a complex problem then why can't they solve it?
They have found ways to *describe* certain very complex problems, which is a good start -- if you can't even characterize something, you can't understand it -- but the methods of solution are not always apparent. They're putting some very high-powered brains into figuring things out, though, believe me.
Because the solution may not be known currently. That's what theoretical mathematics really is, finding solutions to problems we don't know the solutions to. If we already know the answer to the problem, it is no longer a ';problem';, is it?
Because real things in the world are not trivial rudimentary exercises like you are given in school. You might get a more useful answer if you gave an example or two of what you are referring to.
Where are the problems? :O Link them here so everyone can look and try to solve them.