Yes, your brain is like a muscle: If you don’t strengthen and stretch its capacities, it will not deliver high performance.

Which is not to say that engaging in lifelong mental calisthenics will protect you from cognitive decline in the end: New research has found that it probably will not.

But while late-life slides in mental performance afflict both the intellectually fit and the disengaged, people who stayed cognitively active will probably start their age-related mental descent from a higher perch. The downward trajectory of these two groups may be no different, but they appear to bottom out in different places.

A study conducted by researchers in the United Kingdom, published in BMJ, tackles the “use it or lose it” conjecture — the widely held belief that a person can maintain or enhance his or her cognitive function, and offset age-related declines in mental performance, by engaging in intellectual “exercise.”

The authors’ conclusion: “Investment in problem-solving throughout life could enhance cognitive performance, providing an individual with a higher cognitive point from which to decline.”

When older loved ones open a holiday gift of brain teasers, a chessboard or Sudoku puzzles, you can cheerfully remind them that such lifelong mental exercise will probably arrest their eventual mental slide at a slightly higher point than might otherwise be the case.

“Surely, this is as good a gift as any!” the authors write cheerily.

The findings were based on an unusual long-running study of cognitive health: On a single June day in 1947, every 11-year-old child who went to school in Scotland was administered the same standardized intelligence test. When those schoolchildren turned 64 around the year 2000, researchers caught up with a group of close to 1,000 Scotsmen and women who were tested in Aberdeen and who could still be found in that city.

In the end, the study allowed the researchers to compare the cognitive trajectories of 98 subjects essentially from grade school to the age of 82. While the study’s recruits differed in their levels of ingoing intelligence, educational attainment and lifelong intellectual engagement, the researchers could measure and account for these factors to show how they influenced cognitive aging in recruits.

Not surprisingly perhaps, a child’s intelligence tended to drive educational attainment. And both of those factors in turn tended to drive lifelong intellectual engagement, the study found. But even after accounting for those factors, the researchers found that the greater the engagement in problem-solving over the life span, the higher a person’s late-life cognitive performance level tended to be. And then — yes — it was downhill from there.