Stephen Hawking's achievements would have been exceptional by any standards - that he suffered for the majority of his life with motor neurone disease make them all the more remarkable.
Professor Sir Venki Ramakrishnan, president of the Royal Society, said the physicist's life was "a testament to the power of human creativity and imagination".
He added: "Stephen Hawking overcame unimaginable challenges to become one of the most influential and renowned scientists of our time.
"He was also exceptional in his ability to connect with and inspire the public the world over.
"That he achieved all of this despite a long battle with motor neurone disease will serve as an inspiration to all. He will be sorely missed."