Featured Research

from universities, journals, and other organizations

Supercomputing for a superproblem: A computational journey into pure mathematics

Date:
November 6, 2012
Source:
University of Leicester
Summary:
In 1900, twenty-three unsolved mathematical problems, known as Hilbert's Problems, were compiled as a definitive list by mathematician David Hilbert. A century later, the seven most important unsolved mathematical problems to date, known as the 'Millennium Problems', were listed by the Clay Mathematics Institute. Solving one of these Millennium Problems has a reward of US $1,000,000, and so far only one has been resolved, namely the famous Poincare Conjecture, which only recently was verified. Now a negative solution to one of Hilbert's problems has been found. Mathematicians are working on the more challenging of maths problems -- and the only one that appears on both lists -- Riemann's zeta function hypothesis.

A world-famous mathematician responsible for solving one of the subject's most challenging problems has published his latest work as a University of Leicester research report.

Related Articles


This follows the visit that famed mathematician Yuri Matiyasevich made to the Department of Mathematics where he talked about his pioneering work. He visited UK by invitation of the Isaac Newton Institute for Mathematical Sciences.

In 1900, twenty-three unsolved mathematical problems, known as Hilbert's Problems, were compiled as a definitive list by mathematician David Hilbert.

A century later, the seven most important unsolved mathematical problems to date, known as the 'Millennium Problems', were listed by the Clay Mathematics Institute. Solving one of these Millennium Problems has a reward of US $1,000,000, and so far only one has been resolved, namely the famous Poincare Conjecture, which only recently was verified by G. Perelman.

Yuri Matiyasevich found a negative solution to one of Hilbert's problems. Now, he's working on the more challenging of maths problems -- and the only one that appears on both lists -- Riemann's zeta function hypothesis.

In his presentation at the University, Matiyasevich discussed Riemann's hypothesis, a conjecture so important and so difficult to prove that even Hilbert himself commented: "If I were to awaken after having slept for a thousand years, my first question would be: has the Riemann hypothesis been proven?"

Professor Alexander Gorban, from the University of Leicester, said: "His visit was a great event for our mathematics and computer science departments.

"Matiyasevich has now published a paper through the University that regards the zeros of Riemann Zeta Function (RZF). This is a mathematical function which has been studied for over a hundred years.

"The goal of this paper is to present numerical evidence for a new method for revealing all divisors of all natural numbers from the zeroes of the RZF. This approach required supercomputing power.

"There is previous evidence of famous pure mathematical problems using massive computations. Unfortunately, the Riemann hypothesis is not reduced to a finite problem and, therefore, the computations can disprove but cannot prove it. Computations here provide the tools for guessing and disproving the guesses only."

Report: http://www2.le.ac.uk/departments/mathematics/research/research-reports-2/reports-2012/MA12_03Matiyasevich.pdf


Story Source:

The above story is based on materials provided by University of Leicester. Note: Materials may be edited for content and length.


Cite This Page:

University of Leicester. "Supercomputing for a superproblem: A computational journey into pure mathematics." ScienceDaily. ScienceDaily, 6 November 2012. <www.sciencedaily.com/releases/2012/11/121106125558.htm>.
University of Leicester. (2012, November 6). Supercomputing for a superproblem: A computational journey into pure mathematics. ScienceDaily. Retrieved November 23, 2014 from www.sciencedaily.com/releases/2012/11/121106125558.htm
University of Leicester. "Supercomputing for a superproblem: A computational journey into pure mathematics." ScienceDaily. www.sciencedaily.com/releases/2012/11/121106125558.htm (accessed November 23, 2014).

Share This


More From ScienceDaily



More Computers & Math News

Sunday, November 23, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

European Parliament Might Call For Google's Break-Up

European Parliament Might Call For Google's Break-Up

Newsy (Nov. 22, 2014) This is the latest development in an antitrust investigation accusing Google of unfairly prioritizing own products and services in search results. Video provided by Newsy
Powered by NewsLook.com
Google Announces Improvements To Balloon-Borne Wi-Fi Project

Google Announces Improvements To Balloon-Borne Wi-Fi Project

Newsy (Nov. 21, 2014) In a blog post, Google said its balloons have traveled 3 million kilometers since the start of Project Loon. Video provided by Newsy
Powered by NewsLook.com
Is Nintendo Making A Comeback With 'Super Smash Bros.'?

Is Nintendo Making A Comeback With 'Super Smash Bros.'?

Newsy (Nov. 21, 2014) Nintendo released new "Super Smash Bros." Friday, and it's getting great reviews. Could this mean a comeback for the gaming company? Video provided by Newsy
Powered by NewsLook.com
NSA Director: China Can Damage US Power Grid

NSA Director: China Can Damage US Power Grid

AP (Nov. 20, 2014) China and "one or two" other countries are capable of mounting cyberattacks that would shut down the electric grid and other critical systems in parts of the United States, according to Adm. Michael Rogers, director of the National Security Agency and hea Video provided by AP
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:

Breaking News:

Strange & Offbeat Stories


Space & Time

Matter & Energy

Computers & Math

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile: iPhone Android Web
Follow: Facebook Twitter Google+
Subscribe: RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins