Pick up a Gemara. Nothing in the world will build your brain muscle like a Gemara. And it's the toughest form of resistance training too - wait till you see the resistance that you get from the Yetzer Hara (evil inclination) the minute you decide to pick up a Gemara.
I invite you to visit an old age home in the ultra-Orthodox areas of Jerusalem and Bnei Brak. Don't be alarmed when you walk into the Bet Midrash (study hall, which every Charedi old age home has), and you'll find two spry nonagenarians animatedly waving their hands in the air, banging on the table and yelling at each other while arguing a point in Talmudic logic and debate. There's no one here with Alzheimer's - these old gents have been doing resistance training for their brains all their lives. Maybe many of their body functions are limited, but they suffer no atrophy of the mind. Their brains work hard.
The Koreans have always been pioneers in fitness. It's no surprise that the Talmud (Mishna and Gemara) has become a smash bestseller in Korea. The Koreans too want to strengthen their brains...
How is it that Alzheimer's is so rare in the Torah world? While 11% of the general population in the USA over age 65, and 32% of the population over the age of 85 suffers from Alzheimer's and other forms of dementia, the estimated numbers are less than a tenth of that among Torah scholars. Take for example Rabbi Leib Steinman shlit'a, one of this generation's greatest spiritual leaders - he's past 100 and his mind is still razor sharp. So were the minds of Rabbi Vosner and Rabbi Elyashiv, of sacred and blessed memories, who left us in recent years, both well over 100 years old.
What is it about the Gemara that strengthens the mind so much? First of all, it's Divine nutrition for the brain as opposed to the passive junk-food that most people feed their brains today. Second, understanding the Gemara requires conscious, sustained mental effort - it does for the brain what an HIIT (high intensity interval training) workout does for the body. Even when a person gets up from his Gemara session, his mind is still contempleting what he learned, just like the afterburn effect of a good workout. Third, learning with a chavruta (learning partner) forces the Gemara learner to be alert, attentive and mentally sharp. There's no boredom here. In fact, chavruta-style learning is fantastic for those who are kinesthetic or audial learners, because of the back-and-forth give-and-take style of learning where it's OK to fly out of your chair, learn standing up or any way else you like.
Bottom line - for a strong mind, nothing beats a Gemara.