## 10 Math Problems That Look Easy But Immensely Difficult to Solve

There are thousands of math problems that are difficult for a common person to understand even though mathematicians may find them easy to solve.  On the other hand, there are math problems that look really easy that even a middle student would understand the way they are stated, but their solution or proof is immensely difficult. Yes, such math problems exist and below are the some of the most well known.

1. Squaring the Circle
Squaring the circle is one of the classic math problems proposed by Geometers.
It was a challenge to use compass and straightedge to construct  a square with the same area as a given circle in a finite number of steps. Although the circle to square approximation was known since the time of the ancient Babylonian mathematicians, it was Anaxagoras (c. 510 – 428 BC) who was the first to be recorded in history to work on the problem.

In 1882, Ferdinand von Lindemann proved that $\pi$ was transcendental. The consequence of this is the impossibility of squaring the circle.  » Read more

## Understanding the Fermat’s Last Theorem

The Fermat’s Last Theorem is one of the hardest problems in the history of mathematics.  The problem was written by Pierre de Fermat in 1637, and it was only solved more than 300 years later —  in 1995 by Professor Andrew Wiles.

But what is exactly the Fermat’s Last Theorem?

The Fermat’s Last Theorem is an extension of the Pythagorean Theorem.  Recall that the Pythagorean Theorem states that given a right triangle whose side lengths are $x, y$ and hypotenuse $z$, $x^2 + y^2 = z^2$ is satisfied. For example, a right triangle with side lengths $2$, and $3$ has hypotenuse $\sqrt{13}$.

There are some interesting things that we can see if we examine the side lengths of right triangles.  For instance, if we let the triples $(x,y,z)$ be the side lengths of a right triangle, where $z$ is the hypotenuse, we can find triples such that all lengths are integers. The triples  $(3, 4, 5)$, $(5,12,13)$, $(8,15,17)$ are integer triples, and they satisfy the Pythagorean Theorem. These triples are called Pythagorean Triples. It is not also difficult to see that there are infinitely many Pythagorean Triples (Can you see why?). » Read more