I worked for Ms. Whitman at eBay. She is exceptionally smart and very good at being a leader. I met her a few times, and after the first time, she remembered who I was and what I did at the company every time after, even though I was inconsequential to her.
This skill however was also her downfall. I was at eBay when it grew from 3,000 to 13,000 employees. As it got bigger, she could no longer know what was happening everywhere.
Her leadership success comes from knowing everything that is happening and being able to make sure the right people are doing the right things and talking to the right people. But it breaks down when she can no longer have total knowledge of all happenings.
I think she'll make a good leader at Uber, but given that they are already at 12K+ employees, I wonder if she's learned to delegate better since I last worked for her. I hope she has, because it was really her only weakness.