This myth is so ridiculous that I hesitated to include it; but some people believe it. They tend to be people who first heard of computers when Gates was at the height of his prominence. They are probably not using the Web or reading this anyway but never mind, and we might as well start at the beginning. This particular myth is on a par with believing that Al Gore invented the internet or that Jeremy Clarkson invented cars.
Electronic digital computers were invented about 15 years before Gates was born, by a man who by age could have been his grandfather. Mechanical and analog computers were invented even earlier. The Colossus of 1943 was the first computer in the modern sense, designed by Tommy Flowers and built at Bletchley Park in the United Kingdom.
Gates' face is all too familiar; but few people have even heard of Flowers; partly because of the secrecy surrounding Bletchley Park until recently, and also because of the post-war destruction of its equipment, including Colossus, because Churchill did not want it thought that the war had been won by anything but good soldiery.
Hence there has been something of a vacuum in early computer history, leading people to fill that vacuum with later figures like Gates, over-estimating their contributions.