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.

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 July 26, 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 July 26, 2014).

Share This




More Computers & Math News

Saturday, July 26, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Mobile App Gives Tour of Battle of Atlanta Sites

Mobile App Gives Tour of Battle of Atlanta Sites

AP (July 25, 2014) Emory University's Center for Digital Scholarship has launched a self-guided mobile tour app to coincide with the 150th anniversary of the Civil War's Battle of Atlanta. (July 25) Video provided by AP
Powered by NewsLook.com
Bill Gates: Health, Agriculture Key to Africa's Development

Bill Gates: Health, Agriculture Key to Africa's Development

AFP (July 24, 2014) Health and agriculture development are key if African countries are to overcome poverty and grow, US software billionaire Bill Gates said Thursday, as he received an honourary degree in Ethiopia. Duration: 00:36 Video provided by AFP
Powered by NewsLook.com
Creative Makeovers for Ugly Cellphone Towers

Creative Makeovers for Ugly Cellphone Towers

AP (July 24, 2014) Mobile phone companies and communities across the country are going to new lengths to disguise those unsightly cellphone towers. From a church bell tower to a flagpole, even a pencil, some towers are trying to make a point. (July 24) Video provided by AP
Powered by NewsLook.com
Robot Parking Valet Creates Stress-Free Travel

Robot Parking Valet Creates Stress-Free Travel

AP (July 23, 2014) 'Ray' the robotic parking valet at Dusseldorf Airport in Germany lets travelers to avoid the hassle of finding a parking spot before heading to the check-in desk. (July 23) 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:
from the past week

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