Some mammals have smooth brains (rat), while others have a lot of folds (dolphins). Higher folds lead to greater surface area and denser connections between neurons, which in turn help increase the brain’s computing speed and allow for specialisation of certain regions.
The obvious question then, and one that Robert Toro asks in a new paper is: Are these folds encoded in our genes or is it because larger brains have to fold up to be accommodated in a smaller space?
Toro finds that it has little to do with genes and mostly to do with brain size. This observation explains it succinctly: The back part of our brain which develops earlier has greater space to grow in and thus has fewer folds compared to the front of our brains (ie the neocortex).
The growth of the human brain is the most important thing that happened in our evolution. Understanding how it happened is just as important as having a large, wrinkly brain to wield.
Reference: Roberto Toro, Evol. Bio. 2013, 600. http://dx.doi.org/10.1007/s11692-012-9201-8
Further reading: Carl Zimmer on the Loom (http://phenomena.nationalgeographic.com/2013/02/22/on-the-possible-shapes-of-the-brain/)
Image credit: Roberto Toro
Akshat Rathi 
Just thinking out loud here…
I haven’t read the paper but I find it hard to believe that our brains’ wrinkly property is not to some extent related to genes. Because if the sole factor responsible for the wrinkles is the skull, it would mean that skull size and shape are actually prime factors in determining how our brain, and by extension how we, work. Such a view (that genes aren’t involved) would mean that if we are somehow able to “grow” a dolphin’s brain in a vessel that different from a dolphin’s skull, that brain may well be quite different. I wonder how this change will translate in terms of cognition and other processes.