It's sometimes said that the number and complexity of gyri is an indication of intelligence. I suspect this belief was put forward by someone who noticed that humans tend to have more gyri than other species, and read it as confirmation of his preconceived notions about the relative intelligence scale, smugly concluding he was on the top of it.
Intelligence is a hard thing even to define, let alone test.
That humans are not necessarily smarter than other animals is shown by a cursory examination of any large city daily newspaper. And anyone who thinks people are smarter than dogs should try teaching a dog to bungee jump. People are willing do this, but dogs know better than to try.