Research suggests that the answer to this question is multifaceted, depending on what aspect of "mental strength" you're considering. There isn't one single age at which the mind is universally strongest.
Peak Processing Power and Memory
Studies indicate that around age 18, the brain reaches its peak processing power and memory capacity. Source. This is when the brain's ability to process information and retain memories is at its optimal level. This doesn't necessarily mean overall mental strength, but rather a specific measure of cognitive function.
Mental Abilities Peak Later in Life
However, other aspects of mental ability may peak later. Researchers have found that many mental abilities don't reach their highest point until around age 40 or later. Source This includes things like judgment, problem-solving skills, and accumulated knowledge and experience.
Maintaining Mental Strength Throughout Life
It's also important to note that maintaining mental strength is an ongoing process. Engaging in mentally stimulating activities, like learning new skills or challenging yourself intellectually, can help keep your mind sharp throughout your life. Source. One individual even reported feeling mentally stronger later in their career than ever before. Source
Conclusion
The age at which your mind is "strongest" is not a single number but depends on which cognitive functions are considered. While peak processing power and memory occur around 18, other mental abilities continue to develop and may peak much later in life. Maintaining a mentally active lifestyle is key to preserving cognitive health regardless of age.