‘Profound discoveries’ earn Hector Medal for maths professor

Mathematician Professor Rod Gover won the Hector Medal for his “profound discoveries” and “deep mathematical contributions” to science.

Gover co-invented tractor calculus, a tool used in several areas of mathematics and by theoretical physicists exploring gravitational waves, black holes, spacetime and the edge of the Universe.

It’s part of a field in maths called conformal geometry, which has strong links to angles and shapes while ignoring size.

Gover says he was “thrilled” to receive the award from Royal Society Te Apārangi, which also cited his mentorship of young mathematicians and his role in the New Zealand Mathematics Research Institute.

He is using the occasion to call for New Zealand to increase its investment in fundamental science.

“The big breakthroughs in science and technology almost all have foundations in, or links to, fundamental science. But this is poorly understood at all levels.

“The public understands that we want to have cures for cancer and to be safe in a pandemic. But few understand that most of the science that can enable those outcomes is linked to fundamental science, including mathematics.”

An example of conformal geometry in action is the most commonly seen world map.

Distances and angles can’t both be accurately represented because the world is curved and a map is flat. So size is ignored – making Greenland, for example, ludicrously large – to preserve the accurate angles that allow for successful navigation.

Conformal geometry’s focus on angle-type relationships rather than absolute distances features in:

• Einstein's theory of relativity
• gravitational wave research
• quantum field theory
• string theory
• black hole physics

In four-dimensional spacetime (three spatial dimensions plus time), conformal geometry helps scientists understand which features of spacetime are fundamental and which depend merely on scale.

Conformal geometry equations can become extremely complicated and tractor calculus provides a way of simplifying and organising those calculations.

Gover thanks family and friends, early teachers and mentors including Michael Eastwood and Robin Graham, collaborators including Andreas Cap, Andrew Waldron and the late Tom Branson, referees, the Marsden Fund, the Australian Research Council and other funders for support over many years.

Tractor? The name combines the first part of the name of Tracy Thomas, a foundational mathematician in Gover’s area of research, and the last part of the term "twistor" from physics.