New Discovery in Number Theory

People have been interested in a prime number since the ancient times. Euclid proved that an amount of prime numbers is infinite around 300 BC. Eratosthenes used his algorithm to quickly find huge prime numbers around 240 BC.
One of the most important mathematical discoveries that happened in recent years was likewise related to prime numbers. Yitang Zhang, professor at University of New Hampshire, discovered the maximum difference between two consecutive prime numbers in 2013. He found that the interval cannot be more than 70 million. In his proof he used previous works of Goldston, Pintz and Yıldırım. They proved that there exists some finite gap between primes in 2005. However, they could not identify its value.

Statistical analysis for predicting election results

Recently, I read an article about the bookies prediction on Scottish independence referendum (Link). Purpose of referendum was to identify whether Scots want to be independent. There were two options: yes or no. Article stated that according to bookmakers` statistics, about 75% of the voters would choose “No”, while approximately 25% would choose “Yes”.
After some research, I found another article in the news that supports the bookmakers` view (Link). Professor Bell, who is professor at University of Stirling, got the similar results during his analysis  of prediction markets. It showed that the probability of Scots answering negatively is 70%. Pr. Bell`s analysis was presented four months before the actual referendum. According to Scottish Parliament Information Centre, the results were 44.7% and 55.3% for and against Scottish independence, respectively. Consequently, the prediction of bookmakers was correct.

How to evaluate infinite area?

Welcome to my blog about mathematics. My name is Daniyar Omarov. I am studying at Nazarbayev University and majoring in Mathematics.  Also, I am a member of the local mathematics club, where we solve interesting questions and conduct seminars on various topics.  Mathematics fascinates me because one can accomplish extraordinary and amazing things using various theorems and facts.

Have you ever thought how to evaluate infinite area? In my first post I will explain the technique of improper integral, which mathematicians use to estimate areas that go to infinity. To make explanation clearer, I will start by clarifying what is definite integral.