‘You can't teach an old dog new tricks,' so the saying goes, and lots of us believe it. We tend to think that there comes a certain time in middle life when taking on new challenges or breaking old habits, changing the way we look, the way we act, the way we think or feel, what we do or say, is well, frankly, beyond us. The ship's sailed and we're simply stuck with the people we are today, forever. The father of modern psychology, William James, pulled no punches on the subject. He argued that by the age of thirty, "the character has set like plaster, never to soften again".

But William James was wrong. His statement came in an essay from the 1890s – no beach read, by the way – in which he gave an early and often overlooked account of brain plasticity as the neurological engine room of how we change as individuals.

The point about the plaster was a rallying call to get your personality and habits shipshape before it was too late. As brain science then developed through the 20th century, this idea stuck fast. Neuroplasticity (the carving out of new pathways and connections in our brains) continued to be considered more or less a function of youth. But numerous recent studies have turned that assumption on its head, showing that both neuroplasticity and neurogenesis (the production of new brain cells) continue even into old age. Indeed, give the ageing brain a combination of mental variety and physical activity and it can remain nimble and flexible as a ballroom dancer.

My own research has focused on how and why we change at different stages in our lives, both the gradual, natural changes that take us from decade to decade and those moments when we seize the reins and send our lives off in surprising new directions.

I've spent two years talking to men and women of all ages who've experienced or pursued great transformations in their lives. And if I've learned one thing, it's that change is not only a constant, but a dynamic, democratic force that's within everyone's grasp, if they're open to it, want it enough and are prepared to work hard at it.

Which is why understanding that we're physiologically built to change, that it sits within the fabric and structure of our brains, is so key. Psychologists have shown that a belief in your ability to change turns out to be a key indicator of whether you actually can. One study in particular, from the Stanford Center on Longevity, suggests that the unique vantage point of riper years can, for many, bring about positive changes in outlook and motivation. Call it happiness, but what's so interesting is that this isn't simply to do with having been round the block a few times. No, the clincher, according to the study, is that realising that you don't necessarily have all the time in the world can trigger a little cascade of change in many people. They realign their priorities. They sweat the small stuff a bit less, savour the things that matter a bit more. They don't decline - they grow, they adapt and in the process, find themselves happier day-to-day than ever before. Change is not just for the under-fifties. It's a life-long reality and a long-life skill.

So yes, it may well be later than you think, but the message is that it’s also never too late to change.

Polly's new book Metamorphosis: How and Why We Change is published by Profile Books and is available from Amazon.