We don't need to be told that exercise is good for us. We know that it combats cholesterol, we know boosts our hearts and we know it stops the pounds from piling on. But, beyond the obvious physical benefits of a good cycle, run or swim, a growing body of evidence suggests that getting breathless can also build the brain.

Spark: The Revolutionary New Science of Exercise and the Brain, which is published later this year, shows how even regular brisk walks can boost memory, alleviate stress, enhance intelligence and allay aggression. John Ratey, an associate professor of psychiatry at Harvard Medical School in Boston and the book's author, says that exercise stimulates our grey matter to produce what he calls "Miracle-Gro" for the brain. "I can't understate how important regular exercise is in improving the function and performance of the brain," he says. "It's such a wonderful medicine."

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Happiness

If the mere thought of trudging round ice-bound playing fields at school was enough to bring you out in a cold sweat, the idea that exercise makes us happy might sound perverse. But, beyond the (potential) mood-lifting effects of fresh air and scenery, evidence suggests that pounding the pavement can also change the way our brains work to make us happier, or even stave off depression. "Exercise is as good as any anti-depressant I know," Ratey claims.

Last December, scientists from Yale University wrote in the journal Nature Medicine that regular exertion affects the hippocampus, the area of the brain responsible for mood. Tests on mice showed that exercise activated a gene there called VGF, which is linked to a "growth factor" chemical involved in the development of new nerve cells. Tests show that this brain activation lifts a person's mood. Participants in one recent German survey were asked to walk quickly on a treadmill for 30 minutes a day over a 10-day period. At the end of the experiment, researchers recorded a significant drop in depression scores. Scientists are now working on a drug that mimics the effects of the VGF gene to market it as an alternative to conventional antidepressants.

Stress

If, by around 4pm, it feels as if a stressful day at work has turned your brain to blancmange, it might not only be down to overwork or a shortage of double espressos. We respond to stress in the same way our ancestors did – by adopting a "fight or flight" response. Adrenalin and other hormones are released into our bloodstreams and our muscles are primed for response. The problem is that, these days, stress is more likely to be brought on by a tricky PowerPoint presentation or a job interview than an attack by marauding lions, so the toxins that build up for a physical response have no outlet. The results can be good; the cardiovascular system is accelerated and we can work harder (for a while, at least), but others are not so good; stress slows down the gastrointestinal system and reduces appetite, and can overexcite the brain, fuzzing our thought. By responding to or anticipating stress with fight (kickboxing or judo, say) or flight (30 minutes on the treadmill, say, or 50 lengths of the pool), blood flow to the brain is increased, allowing the body to purge the potentially toxic by-products of stress. According to Ratey, exercise also helps in the long term. "It builds up armies of antioxidants such as Vitamins E and C," he says. "These help brain cells protect us from future stress."

Intelligence

Observers of the game of football might refute the claim that exercise leads to greater intelligence – and they would be partly right, says Ratey. "Exercise doesn't make you smarter, but what it does do is optimise the brain for learning."

Physical activity boosts the flow of blood to the part of the brain that is responsible for memory and learning, promoting the production of new brain cells. Several schools in the US and the Netherlands have taken note. Pupils at Naperville Central High School near Chicago, for example, start the day with a fitness class they call "Zero Hour PE". Equipped with heart monitors, they run laps of the playground, and teachers say exam results have soared since the keep-fit initiative kicked off.

Meanwhile, in Amsterdam, a test involving 241 people, aged 15-71, compared physical activity with the results of cognitive tasks. The researchers documented improved results among people who were more active, especially those in younger age groups.

Yet more research suggests that exercise boosts intelligence in the very, very young. Experiments on rats at the Delbrück Centre for Molecular Medicine in Berlin showed that baby rats born to mothers who were more active during pregnancy had 40 per cent more cells in the hippocampus, the area of the brain responsible for intelligence. If the same is true in humans, we can expect Paula Radcliffe's baby, Isla, to be a genius; Radcliffe was training for the New York marathon until the day before she went in to hospital to be induced – and won the race just nine months after giving birth.

Aggression

A few rounds with a punch bag or a game of squash are great ways to release pent-up aggression, but exercise does more than "get it out your system", says John Ratey. "People assume exercise reduces aggression by burning energy. In fact, exercise changes your brain so you don't feel aggressive in the first place."

The frontal cortex is the part of the brain that decides whether you throw a punch or take something on the chin. Reduced activity in the region, a trauma or abnormal development can result in an inability to control violent urges. "This area makes us evaluate the consequences of our actions," Ratey says. "It's the part of the brain that puts the brakes on when the ref makes a terrible decision and you want to beat him up." Exercise increases activity in that area, boosting rational thought, which makesus less likely to lash out.

Memory

Most of the competitors at the annual World Memory Championships could hardly be described as the epitome of physical fitness but, according to Ratey and other scientists in the field, a good workout does much to boost recall, especially as we clock up the years.

"When we're exercising, we're using nerve cells in the brain which help build up what I call brain fertiliser," he says. Ratey is talking about new research that suggests exercise increases blood flow to the part of the brain responsible for memory, and improves its function. In MRI scans on mice, conducted last year by neurologists at Columbia University Medical Centre in New York, the animals were shown to grow new brain cells in the dentate gyrus, which is affected in age-related memory decline.

Research on humans is ongoing but Ratey is convinced that physical activity has a similar effect. He says: "Exercise does more than anything we know of to boost memory."

Addiction

Smokers keen to quit cigarettes probably won't celebrate the news that exercise could be the key to a fag-free life. But research by British scientists suggests that as little as five minutes of brisk walking can reduce the intensity of nicotine withdrawal symptoms. In the tests, researchers asked participants to rate their need for a cigarette after various types of physical exertion. Those who had exercised reported a reduced desire to smoke. "If we found the same effects in a drug, it would immediately be sold as an aid to help people quit smoking," Adrian Taylor, the study's lead author at the University of Exeter, said last year.

The principle is that exercise can stimulate production of the mood-enhancing hormone dopamine, which can, in turn, reduce smokers' dependence on nicotine. "Dopamine works by replacing or satisfying the need for nicotine," Ratey explains.

Whether the findings will lead office-based smokers to dash out for a jog remains to be seen. After all, you wouldn't want to get addicted to exercise.

How much do you need?

You don't have to become a marathon runner to benefit your brain. The mainstay of exercise is simple, brisk walking, Professor Ratey says.

You'll feel the benefit even from a 30-minute walk. "That's what people need to be doing as a minimum, ideally four or five times a week. If you want to do more, then great."

Professor Ratey also recommends interval training – really pushing yourself hard for between 20 and 30 seconds while running, cycling or swimming, so that you are momentarily exhausted.

Do, say, two minutes of walking, 30 seconds' sprinting, then two minutes of walking again. It doesn't have to be a lot for a long time, but you will really notice the difference. "The side effects on the body aren't bad either - I lost 10 pounds in no time," Professor Ratey says.