If I were taking a test in graduate school and this email was a case given to me and I were asked what I thought was going on, the first thing I would think of is that this very accomplished person most likely has a learning disability — one that they have compensated for and got by not having it been detected. You describe symptoms of learning disabilities dyscalculia and dyslexia
Dyscalculia is the difficulty understanding numbers, using them, and learning facts with them. Calculations are difficult and facts can get jumbled. Dyslexia, another type of learning disability, often happens when there is a functional confusion between left and right. As this article explains difficulty executing left and right is often found in children, but my experience is that if it isn’t identified then the adult will have compensated for it and it shows up in the ways you are describing. You can learn more about this condition here. There is also a piece of interesting research here, and a forum for those struggling with it here.
While my thoughts are not a diagnosis, they lead me to encourage you to get a thorough battery of tests by a neuropsychologist, or clinical psychologist with significant experience in educational testing. This will help pinpoint what is going on. More importantly, it will lead to solutions for coping with and overcoming these symptoms.