![]() However, the prime numbers are not distributed evenly. In the millennia since, we have learnt that 2 is the first prime 1, 3 is the second prime, 5 is the third prime, 7 is the fourth prime, 11 is the fifth prime and so forth. The Greek mathematician Euclid found long ago that there are infinitely many prime numbers. If you can create a periodic table of prime numbers, you will have a way to understand all numbers. Think of prime numbers as what atoms are to matter, or what alphabets are to a language. Prime numbers are the basic building blocks of natural numbers. ![]() And Yitang Zhang has claimed that he has taken a big step towards solving it. The Riemann hypothesis is often considered the most important unsolved problem in pure mathematics today. It expressed an idea about a function he had discovered, called the Riemann zeta function, and its ability to estimate the number of prime numbers up to a particular point on the number line. In 1859, the German mathematician Bernhard Riemann came close to answering the question when he formulated the Riemann hypothesis. While mathematicians pursuing a resolution to the hypothesis may be motivated by their quest for knowledge alone, many others – including physicists – are interested because the answer has tantalising connections to many concepts in modern physics. It’s a simple question but it has only complicated answers. The conjecture is that there are solutions to the zeta function that don’t assume the form prescribed by the Riemann hypothesis.Įarlier this October, Chinese websites claimed that the Chinese-American mathematician Yitang Zhang had solved the Landau-Seigel zeros conjecture – an important open problem in number theory related to cracking a bigger problem: is there a pattern to the way prime numbers are distributed on the number line?.Yitang Zhang has claimed that he has disproved a weaker version of the Landau-Siegel zeroes conjecture, an important problem related to the hypothesis.The hypothesis is about the form that solutions to the Riemann zeta function, which could estimate the number of prime numbers between two numbers, are allowed to take.The Riemann hypothesis makes an important statement about their distribution, offering to remove the seeming arbitrariness with which they turn up and impose order.However, they are not distributed evenly: they become less common as they become larger. Euclid found long ago that there are infinitely many prime numbers.Plot: Nschlow/Wikimedia Commons, CC BY-SA 4.0 The Re(½ ) line passes vertically through the middle. A part of a visualisation of the Riemann zeta function in the complex plane.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |