Chemists and mathematicians from New Zealand, like their colleagues in physics, often found that moving overseas greatly enhanced their ability to carry out creative research work. The universities and research centres in countries such as Britain and the US gave more scope for theoretical work, while their chemistry laboratories were often far better equipped than their New Zealand equivalents.

### The music of maths

Mathematician Alexander Aitken was also an accomplished musician. He once explained his approach to solving mathematical problems as dividing numbers into sets of five and then applying German waltz time to them.

### Mathematicians

#### Alexander Aitken

Alexander Aitken, a mathematician from Otago, was renowned as one of the greatest of his era. Aitken had a traumatic time in the New Zealand Expeditionary Force during the First World War, fighting at Gallipoli and in the battle of the Somme. He then taught at the University of Edinburgh for most of his career. Aitken was a master of mental arithmetic, specialising in performing difficult calculations without even the use of pencil and paper.

### Solving the impossible

Roy Kerr commented on the ‘Kerr solution’: ‘I solved Einstein’s equations and found this rotating black hole solution and quite a lot of other stuff as well … It had actually been proven that what I was doing was impossible just a few months before.’^{1}

#### Roy Kerr

Roy Kerr, originally from Canterbury, spent many years based at Cambridge University, England, and then the University of Texas at Austin. He finally returned to New Zealand in 1971. In 1963 Kerr was the first to find a set of solutions to Einstein’s equations of general relativity. Through this Kerr described the astronomical phenomena of rotating black holes. His calculations had earlier become stuck after he tried various novel mathematical approaches to the problem. Kerr then read a paper by physicist Ezra ‘Teddy’ Newman, arguing that the solution Kerr was seeking could not exist. Kerr came to the opposite conclusion from reading the paper, got back to work and in a few weeks produced the ‘Kerr solution’.

#### Vaughan Jones

Mathematician Vaughan Jones, born in Gisborne, solved an important mathematical problem in a fever of late-night inspiration. Jones, who studied in New Zealand and Switzerland, established a career in algebra, topology and mathematical physics in the United States. He came up with a formula now known as the Jones Polynomial. The formula allows a user to tell whether or not two knots are different, and can sometimes be used to deduce that two knots are the same. Jones had been working on a related problem for years, then one night, he said, ‘everything crystallised. I sat up in the middle of the night, ran downstairs, did a few calculations and it seemed to work. This was one of those rare occasions where it was still true the next morning.’^{2} Jones’s formula** **won him the Fields Medal – the top mathematics prize for a researcher under 40 – in 1990.

### Chemists

#### Joseph Mellor

Joseph Mellor, a chemist who trained at Otago University, was later based in Staffordshire, the heart of the English pottery industry. Mellor’s experimental work in the early 20th century transformed the production of ceramics in Britain.

#### Richard Barrer

Richard Maling Barrer, originally from the Wairarapa, is regarded as the founding father of the study of zeolites, porous aluminosilicate crystals with a wide range of industrial uses. Based at Cambridge, England, and then at the University of London. Barrer worked on zeolites from the late 1930s until his death in 1996, discovering many of their properties. In 1948 he was the first to make synthetic zeolites not seen in nature. Barrer attributed his passion for zeolites to inspiration from James McBain’s book *Sorption of gases by solids*.