MATHS WEEK:THE 19TH century was a golden age for the advance of mathematical research. But it would take many years to demonstrate the value of what was discovered, a leading mathematician will argue in a lecture this evening.
A key area of development, particularly during the early to mid-1800s, was in new kinds of algebra, says Prof Efim Zelmanov, the Atkinson professor of mathematics at the University of California, San Diego.
Prof Zelmanov will this evening deliver the annual Hamilton lecture, Noncommutative Algebra: from Hamilton to our Time. He will trace the development of novel "abstract algebras" during the 19th century, which at the time they were devised were suited to no particular application.
Since then, however, many of these mathematical forms have become very important in a range of areas, including data communications and finance, Prof Zelmanov said.
“It started with the work of [Évariste] Galois, [Joseph-Louis] Lagrange and [William Rowan] Hamilton and it has become widely applied today,” Prof Zelmanov said. “For all this time, it was considered to be the most abstract and pure mathematics without any chance to be applied. But it has all changed in the last 30 years because of the development of communications.”
These abstract algebras help run bank ATMs, deliver music and film from CDs and DVDs and have been applied in the development of computer-to-computer communications.
Dublin-born Hamilton was central to this advance, developing a novel mathematical form called quaternions.
He later described how on October 16th, 1843, a flash of inspiration caused him to create quaternions. The annual Hamilton lecture takes place on October 16th to celebrate that day. The lecture is organised by the Royal Irish Academy and The Irish Times and is sponsored by Invest Northern Ireland.
Each year brings a leading mathematician to Dublin to deliver a talk on the subject of their choice. Many are winners of the world’s leading prize for mathematics, the Fields Medal, as is the case with Prof Zelmanov. The Fields is often described as the Nobel Prize for maths given the Nobel does not make an award for this subject.
Prof Zelmanov stressed the importance of Hamilton’s contribution. “He is the father of noncommutative algebra,” he said, a reference to a particular form of algebra where A times B does not always equal B times A.
“His work was the foundation. Quaternions affected the whole of mathematics. It was the first time when he broke that one important rule, commutativity.”
Hamilton was among “a whole group of young geniuses who made huge contributions”, Prof Zelmanov added. “Since then mathematics has never been the same.”
Prof Zelmanov does not fear for the future of mathematical discovery, given there will always be people studying the subject.
“During the last 2,000 years, this business has been amazingly stable so we have good reason to believe it will stay so. There are sufficient students who have special abilities and the urge to do mathematics.”
Prof Zelmanov’s talk takes place at 7.30pm this evening in the Burke Lecture Theatre, Trinity College Dublin. It is free and open to the public.
TODAY’S PUZZLE
If these shapes were four cut out pieces of paper, which of them will not fold up in three dimensions to form a cube? An array of squares that will fold into a cube is called a net of a cube.
Answer to yesterday's puzzle:
1980. If you were born in 1980 you will be 45 in 2025, a number which is the square of 45.
This will next happen for people born in 2070, who will celebrate their 46th birthdays in 2116.
