James A. Maynard - Patterns in the primes скачать в хорошем качестве

James A. Maynard - Patterns in the primes

The inaugural lecture of the Pittsburgh Mathematical Horizons Lecture Series was given by James A. Maynard (Oxford). How often do two prime numbers differ by exactly 2? This simple (and famous) question is unsolved despite mathematicians working on it for over 100 years. Moreover, basic questions like this about prime numbers turn out to lie at the heart of many important real-world questions. For example, it turns out that the security of internet communication (which we rely on whenever we buy something online) is related to basic questions about patterns in prime numbers which we don't know how to solve! I'll talk about why prime numbers are so special to mathematicians, how important questions in both pure mathematics and the real world turn out to be connected to primes, and how we are making progress towards solving these famous problems which have been studied for hundreds of years. https://www.mathematics.pitt.edu/abou...