While the jury is out as to whether listening to music will really make your baby smarter, there have been quite a few studies on older children that might indicate that there is some connection. For instance, it’s been shown that children who study music do better at maths, and children who take piano lessons at age three or four have a better spatial reasoning ability.
While there’s no concrete proof that listening to music will make your baby cleverer, and while babies don’t really grasp the words of the music (they do enjoy melodies though) there are plenty of positive effects that music does have.
Since it’s a mood enhancer, and since every parent wants a happier baby, there’s no harm in playing music to your baby! Plus, just because it hasn’t been proven that music makes babies cleverer, that doesn’t mean that’s not the case!