Here is an article which quotes the scientific journal Cell:
Prof Lahn's team examined the DNA of 214 genes involved in brain development in humans, macaques, rats and mice.
By comparing mutations that had no effect on the function of the genes with those mutations that did, they came up with a measure of the pressure of natural selection on those genes.
The scientists found that the human brain's genes had gone through an intense amount of evolution in a short amount of time - a process that far outstripped the evolution of the genes of other animals.
"We've proven that there is a big distinction," Prof Lahn said. "Human evolution is, in fact, a privileged process because it involves a large number of mutations in a large number of genes.
"To accomplish so much in so little evolutionary time - a few tens of millions of years - requires a selective process that is perhaps categorically different from the typical processes of acquiring new biological traits."
As for how all of this happened, the professor 
suggests that the development of human society may be the reason.
https://www.google.com/amp/s/amp.theguardian.com/science/2004/dec/29/evolution.science
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The evolutionary explanation for the human brain relies heavily on speculation [similar speculations haunt evolution—-it’s one of the reasons I tend to be skeptical of it] but that’s not why I pasted the article.
It was to demonstrate that scientists agree with me—the human brain is unique, which makes us unique amongst the animals.