Computers essential to advances in research
THAT'S MATHS:A supercomputer can do in an hour what it would take 10 billion people 10 years to calculate
Will computers ever be able to do mathematical research? Computers have amazing power to analyse huge data-bases and carry out extensive searches far beyond human capabilities. They can assist mathematicians in checking cases and evaluating functions at lightning speed, and they have been essential in producing proofs that depend on exhaustive searches.
The four-colour theorem, which states that four colours suffice for a map with neighbouring regions having distinct colours, was first proposed in 1852. It resisted all attempts at proof until 1989, when it became the first major theorem to be proven with substantial computer assistance.
Automatic Theorem Proving (ATP) is a developing branch of computer science. With the blistering pace of technological advances, the goal of generating proofs using computers looks increasingly realistic. In 1950, the early computer called ENIAC (Electronic Numerical Integrator and Computer) was five orders of magnitude faster than a human: that is, it could calculate as fast as 100,000 people.
Today, supercomputer speeds are measured in Petaflops - one thousand million million calculations per second. That is five orders of magnitude faster than Earth's entire human population. These supercomputers can do in one hour what would take 10 billion people, calculating day and night, about 10 years.
But computers have another vital role in science: the simulation of physical systems ranging from sub-atomic to cosmic scales. Many fields now require complex simulations and calculations that are feasible only with high-performance computers. Irish researchers working on climate prediction, modelling the birth of stars, fluid dynamics, chemical engineering, biomedical modelling and nuclear physics are using supercomputers for their work.
Access to supercomputers allows researchers to run complex simulations and calculations. The Irish Centre for High-End Computing (ichec.ie) is Ireland's national high-performance computer-service provider.
Many researchers in Irish academic institutions are benefiting from computational time at ICHEC, producing significant scientific breakthroughs and articles in leading journals. Met Éireann's weather forecasts are also run on ICHEC computers.
But some research requires computer power greater than anything available in Ireland. ICHEC is a member of Prace, the Partnership for Advanced Computing in Europe (prace-ri.eu), and Irish researchers are gaining benefits from Prace through access to Europe's fastest computers. This is enabling them to carry out world-class science and engineering research.
The applications of supercomputing are almost boundless and will only increase in the future. Ireland's participation in Prace means that Irish scientists will have access to emerging computer technology. This week, Prace held a council meeting in Dublin to plan the next phase of the partnership.
What about pure mathematics? Although computer proofs are scorned by some mathematicians, it seems to me that they will ultimately be better than humans at generating and solving mathematics problems. Progress in automatic theorem-proving software over recent decades has been impressive.
Although mathematics involves drawing logical conclusions from stated axioms, which can be mechanised, aesthetics plays a central and indeed essential role. Mathematicians are motivated by curiosity and seek results that are interesting, elegant and beautiful. How will computers do this? Watch this space.