Preserving the brains of geniuses was not a new phenomenon—another brain to be preserved and discussed in a similar manner was that of the German mathematician Carl Friedrich Gauss almost a hundred years earlier. His brain was studied by Rudolf Wagner who found its weight to be 1,492 grams and the cerebral area equal to 219,588 square millimeters.[27] Also found were highly developed convolutions, which was suggested as the explanation of his genius.[28] Other brains that were removed and studied include those of Vladimir Lenin,[29] the mathematician Sofia Kovalevskaya,[30] and the Native American Ishi. The brain of Edward H. Rulloff, a noted philologist and criminal, was removed after his death in 1871; in 1972, it was still the second largest brain on record.[31]Source

If you read the last words there, "it was still the second largest in the world". These are real proves that geniuses have larger brains.

And to your other question, primates have fewer offspring when compared to other lesser organisms. And humans have even fewer offspring. All these are proves that the bigger brains that humans have in general is the reason for our fewer offsprings. And geniuses, who are higher humans show mental disorders for the bigger brains they have in comparison to an average or smaller human brain.

Thanks for coming around!!