is it true that classical music can make your baby smarter?

Music actually stimulates the brain. There's been research showing the brain engagement while doing different activities and the brain is at its full capacity when you play some instrument. In a layman's (like me) understanding, listening to music intently and playing an instrument also makes one do mental calculations like how many keys you need to move on a keyboard, what's the tempo of a song etc. This does boost mathematical thinking as well if channeled properly.