Zhang Yitang is proof that for mathematicians, life begins at 40

No mathematician should ever allow himself to forget that mathematics, more than any art or science, is a young man's game," the British mathematician G.H. Hardy wrote in . But the older guys are now catching up.

Since Hardy wrote those lines in 1940, it has been conventional wisdom that mathematical breakthroughs are most often made in a moment of brilliance by a born genius at a young age, rather than an experienced practitioner after decades of work.

Last month, however, Zhang Yitang, a 50-year-old lecturer in mathematics at the University of New Hampshire, defied Hardy's glib assertion. Zhang, who had not published any original work since 2001, submitted a paper to the peer-reviewed in which he solved one of the most longstanding and difficult problems in pure maths. His proof - that there are an infinite number of consecutive pairs of prime numbers (those that are divisible only by 1 and themselves such as 3, 5, 7, 11) separated by less than 70 million - may be meaningless to the layperson, but to number theorists it is earth-shaking.

The fact that Zhang is well into middle age gives hope to legions of mid-career mathematicians oppressed by Hardy's dictum that groundbreaking work in their field should be left to the young.

Of course Hardy could point to many examples in the history of mathematics to support his assertion. The French mathematician Evariste Galois laid the foundations for modern algebra in the 1800s while he was still a teenager and died at the age of 21. During the same era, the Norwegian Niels Abel, aged 19, independently came up with group theory, which is invaluable in many areas of mathematics and physics. Srinivasa Ramanujan, the Indian maths prodigy mentored by Hardy at Cambridge University, compiled 3,900 results in identity and equations before he died at age 32 in 1920.

In more recent times, there's Terence Tao, whose parents emigrated to Australia from Hong Kong. Tao is a polymath who does brilliant work across many mathematical disciplines such as number theory, harmonic analysis and combinatorics. He received his PhD in mathematics from Princeton University at 20 years old, was at 24 appointed the youngest ever full professor at the University of California at Los Angeles, and at 30, in 2006, received the Fields Medal, the highest honour in mathematics.

The media reinforces the stereotype of youthful mathematical creativity. In the movie John Nash, who as a graduate student in his early twenties did pioneering work in game theory, is depicted hanging out at a bar in Princeton when a sudden insight leads him to the concept that became known as the Nash equilibrium, which is today widely applied in economics and conflict analysis.