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 October 22, 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 October 22, 2014).

Share This



More Computers & Math News

Wednesday, October 22, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Chameleon Camouflage to Give Tanks Cloaking Capabilities

Chameleon Camouflage to Give Tanks Cloaking Capabilities

Reuters - Innovations Video Online (Oct. 22, 2014) — Inspired by the way a chameleon changes its colour to disguise itself; scientists in Poland want to replace traditional camouflage paint with thousands of electrochromic plates that will continuously change colour to blend with its surroundings. The first PL-01 concept tank prototype will be tested within a few years, with scientists predicting that a similar technology could even be woven into the fabric of a soldiers' clothing making them virtually invisible to the naked eye. Matthew Stock reports. Video provided by Reuters
Powered by NewsLook.com
Internet of Things Aims to Smarten Your Life

Internet of Things Aims to Smarten Your Life

AP (Oct. 22, 2014) — As more and more Bluetooth-enabled devices are reaching consumers, developers are busy connecting them together as part of the Internet of Things. (Oct. 22) Video provided by AP
Powered by NewsLook.com
Free Math App Is A Teacher's Worst Nightmare

Free Math App Is A Teacher's Worst Nightmare

Newsy (Oct. 22, 2014) — New photo-recognition software from MicroBlink, called PhotoMath, solves linear equations and simple math problems with step-by-step results. Video provided by Newsy
Powered by NewsLook.com
Rate Hike Worries Down on Inflation Data

Rate Hike Worries Down on Inflation Data

Reuters - Business Video Online (Oct. 22, 2014) — Inflation remains well under control according to the latest consumer price index, giving the Federal Reserve more room to keep interest rates low for awhile. Bobbi Rebell reports. Video provided by Reuters
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