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.
Math Problem: Squaring a CircleIt 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

What are prime gaps and who is Yitang Zhang?

You have probably read a news about one professor proving The Prime Gap conjecture. In this post, I will give you an overview of what the excitement is all about in the mathematics community.

Prof. Yitan Zhang (courtesy of UNH via Slate.com)

This post is written for the high school students and those who are interested in mathematics that are non mathematics majors.

What are Prime Numbers?

Most of us are familiar with prime numbers. A prime number is a positive integer that is divisible only by 1 and itself.  The number 5 is a prime number, while 8 is not prime because 8 is divisible by 2 and 4. If we examine the 10 positive integers, it is easy to see that only four are prime numbers: 2, 3, 5 and 7. In the figure below, shown are the prime numbers less than 100. » Read more