"Word of caution, I would not do your Stephen Hawking impression in front of him."
Over the years, Sheldon has looked down on both Howard and Penny, for having insufficient education. Howard has always felt like he was getting disrespected, and that his master's degree in engineering was not as worthless as Sheldon had treated it to be. In this episode, Howard proved his point.
While at work, Howard made the announcement that he was going to be hired by Stephen Hawking, to do some engineering work on his wheelchair. It also turned out that Sheldon was a huge fan of Hawking, and wanted Howard to pass his research paper to Hawking.
Now in a position of power, Howard took this as an opportunity to turn Sheldon into his own personal slave, making him do things like shining his belt buckle collection....
...wearing a french maid outfit that was originally bought for Bernadette at his work...
...and doing his laundry.
While folding Howard's clothes, Penny challenged Sheldon on his ego, and how he needs to correct people and to put them down to feel better about himself. Of course, it went nowhere, as Sheldon felt like he had to explain to Penny the definition of condescending.
When Bernadette found out what Howard had been putting Sheldon through, she expressed her objection. But in order for Bernadette to get out of going dress shopping with Howard's mom...
...Bernadette took advantage of the situation and sent Sheldon to do the job. While in the change room, Howard's mom got Sheldon to go inside, to "grab a hand-full, and start stuffing." Then it got worse. Offscreen, thankfully. Lamenting having put on weight, she expressed her regret at eating too much, and made Sheldon hold on to her.
The big day finally came, wherein Sheldon finally got to meet Stephen Hawking, and to discuss the research paper. Sadly, Sheldon made a simple arithmetic error on the second page. When he went to check on it, the shock sent him into fainting.
So after all of Sheldon's hard work, he proved to be his own worst enemy. His sense of his own superiority had led to him being careless in his calculations, and ruined his meeting with Stephen Hawking.