Peter Scholze is regarded as one of the finest mathematical talents of his generation. (YouTube: IHÉS)
Mathematics is popularly considered to be a solitary activity practised out of the public spotlight, but every four years that perception briefly changes.
- Fields Medals were first awarded in 1936 and are today regarded as equivalents of the Nobel Prize
- Only 56 mathematicians have received one, including Terry Tao — the sole Australian
- German mathematician Peter Scholze is among this year’s favourites to secure one
On Wednesday night Australian time, the discipline’s brightest minds gathered in Rio de Janeiro, Brazil, where an Australian, Akshay Venkatesh, received mathematics’ most coveted prize — the Fields Medal.
As highlighted in the movie Good Will Hunting, the Fields is the closest thing maths has to a Nobel Prize, and it has been growing in profile in recent decades.
“It’s an award for career achievement, not one-off discovery, for mathematicians 40 or under,” said broadcaster, author and self-professed maths nerd Adam Spencer.
“It’s the highest individual prize in mathematics and so every four years when the International Mathematical Union gets together to give away two, three or four Fields Medals, there is a frisson of excitement.”
Maryam Mirzakhani was the first female and the first Iranian to win a Fields Medal. (Supplied: Stanford University)
In 2014, the Iranian mathematician Maryam Mirzakhani became the first female to receive a Fields Medal for her outstanding work in geometry.
The professor, who died in 2017, spent much of her time thinking about the complex maths involved in the ways billiard balls interact around differently shaped tables.
But the Fields Medal has not been without controversy, and a closer look at its history reveals a collection of characters who defy the stereotype of mathematicians as individuals out of touch with the ‘real’ world.
Why should we care about the Fields Medal?
Great scientific breakthroughs often have unexpected consequences.
For example, cryptography that secures data transmissions relies on facts about prime numbers that were discovered without any thought that they would turn out to be ‘useful’.
“It’s research for the sake of research that then eventually becomes of great benefit to us all,” Spencer said.
“Some people make breakthroughs in pure mathematics that might sit around for decades or even centuries before we suddenly find an amazing relevant practical application for that mathematics.”
Maths is so prevalent throughout the modern world that it is easy to overlook the tremendous role it plays, influencing everything from traffic light sequences to stock market trades.
“The most brilliant mathematical minds end up shaping our world directly and our lives indirectly in ways that we probably never even realise our happening.”
Has anyone ever refused a medal?
In 2006, the reclusive Russian genius Grigori Perelman — who proved an outstanding problem in a branch of maths known as topology, which deals with shapes and surfaces — is the only winner to have declined the medal.
He is understood to have been dissatisfied with the mathematical community following an academic dispute over credit for his work.
Fields medallist Cedric Villani was elected to the French Parliament. (Reuters: Charles Platiau)
Political activists have also been honoured, including Stephen Smale — who was outspoken against the Vietnam War — and Alexander Grothendieck, who is widely considered to be one of the greatest mathematicians of the 20th century.
In 1966, Grothendieck refused to travel to Moscow to collect his Fields Medal in protest against the Soviet Union’s imprisonment of two writers.
In 2017, another Fields Medal winner Cedric Villani took a political turn and was elected to the French Parliament, representing Emmanuel Macron’s party En Marche.
So, again, why should we care?
Earlier this month, the Federal Government announced every high school across the country would have to employ science and maths teachers who have studied those subjects at university level.
The move is aimed at boosting the number of high school graduates who go onto study STEM subjects at university.
“There’s a realisation in government and the general community that we certainly need our share of talented, brilliant nerds in this country to carry us through the next few decades,” Spencer said.
“This century will be built by mathematicians, whether it’s computer coding, algorithms, machine learning, artificial intelligence, app design and the like.
“We as a country, can either choose to be on that bus or spend the rest of this century begging the intellectual property that they’ve developed.”
That is one of the strongest practical reasons why we should all take an interest when the Fields Medals are handed down, Spencer believes.
“If we’re going to give away Olympic gold medals,” he said, “for being really good at running fast … and if we’re going to let people win world cups of football and have billions of people watch the grand finals … then we should also acknowledge the magnificence of the mathematical mind.”