The seven-bridges-of-Königsberg puzzle was solved by Swiss mathematician Leonhard Euler.
Mathematicians do proof in order to solve Geometry theorems.
Mathematicians study to explore and understand the patterns, structures, and relationships that exist in the world, and to solve complex problems using logic and reasoning.
It enabled mathematicians to apply algebra to solve geometric problems.
Imaginary numbers were discovered when mathematicians tried to solve equations of the form x^2 + 2 = 0
I'll explain the "why" for now. The idea is that mathematicians want to be able to solve as many integration formulae as possible, in an exact way.
A mathematician is a person who studies mathematics or otherwise works with mathematics for a living. Many mathematicians try to come up with new discoveries and creative inventions in mathematics that they think might be useful. These people are research mathematicians. These mathematicians mostly work for universities. Others might work for government agencies doing various things. Still other mathematicians work for big corporations such as General Electric. A person might be called a mathematician even if he doesn't try to invent new math. Some mathematicians spend most of their time solving somewhat routine but complex math problems that most people don't understand how to solve. These people are applied mathematicians.
The invention of algebra traces back to the ancient Babylonians. At the time, Egyptian, Greek, and Chinese mathematicians actually used geometry to solve math problems.
It enabled geometric information to be converted into algebraic form. This meant that the tools of algebra could be applied to solve geometric problems and the tools of geometry to algebraic problems. That greatly increased the ability of mathematicians to solve problems.
Pierre de Fermat. The problem was called Fermat's Last Theorem
True. But thousands of years is a gross exaggeration. However, not being able to solve a problem only means that the problem has not yet been solved, not that it is impossible. Spending years trying to solve problems that turned out to be impossible is only true if a proof is found showing that their is no solution to a problem. An example is Fermat's Last Theorem defined as a problem in 1637. It took until 1995 for a proof to be found after numerous failed attempts by mathematicians and students.
Descartes did not discover geometry - he invented analytical geometry, which enabled mathematicians to use algebra to solve problems in geometry and geometry to solve problems in algebra. The world would be less developed than now, as would be the case with most discoveries.
The concept of negative numbers was first documented by Chinese mathematicians around the 2nd century BC. These numbers were initially used to solve practical problems related to debt and payments.