Quick – what’s the No. 1 thing you can do for your brain’s health? Differential calculus, you say? Chess? Chaos theory? No, the best brain sharpener may be... running shoes? Yup. Once they’re on your feet, you can pump up your heart rate.

"The best advice I can give to keep your brain healthy and young is to do aerobic exercise," says Dr Donald Stuss, a neuropsychologist and director of the Rotman Research Institute in Toronto, Canada.

Dr Mark McDaniel, professor of psychology at Washington University in St Louis, agrees, but adds, "I would suggest a combined programme of aerobics and weight training. Studies show the best outcomes for those engaged in both types of exercise."

As we age, our brain cells, called neurons, lose the tree-branch-like connections between them. These connections, or synapses, are essential to thought.

Quite literally, over time, our brains lose their heft. Perhaps the most striking brain research today is the strong evidence we now have that "exercise may forestall some kinds of mental decline", notes McDaniel. It may even restore our memory. Studies on animals have shown that, among other brain benefits, aerobic exercise increases capillary development in the brain, meaning more blood supply, more nutrients and – a big requirement for brain health – more oxygen.

The pre-eminent exercise and brain-health researcher in humans is Arthur Kramer at the University of Illinois at Urbana-Champaign. In a dozen studies over the past few years, with titles such as Aerobic Fitness Reduces Brain Tissue Loss in Ageing Humans, Kramer and his colleagues have proved two critical findings: fit people have sharper brains, and people who are out of shape, but then get into shape, sharpen up their brains.

This second finding is vital. There’s no question that working out makes you smarter, and it does so, Kramer notes, at all stages of life. Also, exercise staves off heart disease, obesity, diabetes and other maladies that increase the risk of brain problems as we age.