A Kurdish man who came to Britain as a refugee after fleeing conflict two decades ago is one of four men who have been awarded the Fields medal, considered the equivalent of a Nobel prize for mathematics.

The winners of the prize, presented at the International Congress of the International Mathematical Union in Rio de Janeiro, have been announced as Prof Caucher Birkar, 40, from Cambridge University, Prof Akshay Venkatesh, 36, an Australian based at Princeton and Stanford in the US, Prof Alessio Figalli, 34, from ETH in Zurich and Prof Peter Scholze, 30, from Bonn University.

The Fields medal is perhaps the most famous mathematical award. It was first awarded in 1936 and since 1950 has been presented every four years to up to four mathematicians who are under 40. As well as the medal, each recipient receives prize money of 15,000 Canadian dollars (£8,750). With all the prizes this year going to men, the late Maryam Mirzakhani remains the only woman to have received the accolade.

Birkar was born in Marivan in Iran – a Kurdish city heavily affected by the Iran-Iraq war of the 1980s – and studied mathematics at the University of Tehran before coming to the UK in 2000. After a year, he was granted refugee status, became a British citizen and began a PhD.

“When I was in school it was a chaotic period, there was the war between Iran and Iraq and the economic situation was pretty bad,” said Birkar. “My parents are farmers, so I spent a huge amount of time actually doing farming. In many ways it was not the ideal place for a kid to get interested in something like mathematics.”

Birkar says it was his brother who at an early age introduced him to more advanced mathematical techniques.

Prof Ivan Fesenko of the University of Nottingham, one of Birkar’s PhD supervisors, told the Guardian how Birkar, who initially spoke very little English, came to study with him.

“The Home Office sent him to live in Nottingham while they were processing his application for asylum status,” said Fesenko. “He came to me because he was interested in research work related to my general areas.”

Birkar’s talent, says Fesenko, quickly became apparent as he began his PhD. “I thought I should give him some problem – if he solves it, then this will be his PhD. Typically a PhD lasts three or four years. I gave him a problem and he solved it in three months,” said Fesenko.

“He is very, very smart; you start to talk with him and you recognise that he can read your thoughts several steps ahead. But he never uses this to his advantage, he is very, very respectful and he gently helps people to develop further,” said Fesenko.

As with many of the winners of the Fields medal, Birkar’s research is in areas of mathematics that can seem incomprehensible to a lay audience. His citation for the award says he won the medal “for his proof of the boundedness of fano varieties and for contributions to the minimal model program.”

Prof Paolo Cascini of Imperial College London has worked with Birkar. He said that in simple terms Birkar’s work focused on classifying geometrical shapes and describing their building blocks.

Birkar said he hoped the news may “put a little smile on the lips” of the world’s 40 million Kurds.

The youngest for the four winners, Germany’s Peter Scholze, became a professor at the age of just 24, and has been described by previous award committees as “already one of the most influential mathematicians in the world.” Among his achievements, Scholze invented the theory of perfectoid spaces – which are noted in his citation for the Fields medal, and have been described as a class of fractal structures allowing problems to be moved from one number system to another, making them easier to solve.

“Geometry is the study of space and shape,” said Kevin Buzzard of Imperial College London. “One technique that geometers have introduced is the idea of studying a complicated space by mapping a simpler space onto it. For example, a line is a simpler object than a circle. But if you imagine wrapping a line up into a spring shape and compressing the spring, you have found a way of mapping a line into a circle. Geometers might use this technique to analyse questions about circles, by turning them into perhaps more complex questions about lines.”

Perfectoid spaces, he says, turns this logic on its head. “The counterintuitive idea introduced by Scholze is that to study a geometric object, you might instead want to find a mapping from a space which is so grotesque and twisted that in some sense it cannot be twisted up any more. The result is that instead of ending up having to solve complicated questions about simple objects, you have to solve simple questions about extremely complicated objects.”

The Italian winner, Figalli*, *works in the field of optimal transport, which has its roots in the research of 18th-century mathematician Gaspard Monge, who studied where to send material dug from the ground for use in construction so that the transport costs are as low as possible.

Venkatesh becomes only the second Australian to win the prestigious medal, after Terence Tao in 2006.Venkatesh was recognised for his use of dynamics theory, which studies the equations of moving objects to solve problems in number theory, which is the study of whole numbers, integers and prime numbers.

Venkatesh grew up in Perth and at age 13 became the youngest person to study at the University of Western Australia. He earned first class honours in pure mathematics aged 16 before studying at Princeton.

At UWA, he went straight into second-year maths courses after he proved he could write the exam papers for all the first year subjects he had never taken.

His work also uses representation theory, which represents abstract algebra in terms of more easily-understood linear algebra, and topology theory, which studies the properties of structures that are deformed through stretching or twisting, like a Mobius strip.

Receiving his award on Wednesday, he said: “A lot of the time when you do math, you’re stuck, but at the same time there are all these moments where you feel privileged that you get to work with it.

“You have this sensation of transcendence, you feel like you’ve been part of something really meaningful.”

One of his early mentors, Prof Cheryl Praeger, who has known Venkatesh since he was 12, and supervised his honours thesis when he was 15, said he was always “extraordinary”.

“At our first meeting, I was speaking with Akshay’s mother Svetha, while Akshay was sitting at a table in my office reading my blackboard which contained fragments from a supervision of one of my PhD students.

“At Akshay’s request I explained what the problem was. He coped with quite a lot of detail and I found that he could easily grasp the essence of the research.”