Geordie Williamson was 13 when he solved one of his father's conundrums and realised he had a special knack for numbers.

His father, up on the roof of their Southern Highlands home, was trying to figure out how to mount some solar panels to maximise their exposure to the midday sun.

Professor Geordie Williamson, 36, has recently been elected the youngest Fellow of The Royal Society in London. Credit:James Alcock.

The boy, his head swirling with numbers, did some three-dimensional trigonometry and told his father how to cut the mountings.

"He said, 'You sure? I don't want to cut these things wrong,' so I went off and did the calculations again and it was incredibly satisfying to finally see [the panels] perfectly on the roof facing the sun," he said, reminiscing in his office at Sydney University.