I wholeheartedly agree with the above list. We had an Engineer at our company who regularly reduced testers to tears when they dared to “complain” about problems in the system. The man was brilliant, but no one wanted to interact with him and consequently no one wanted him on their team.
Sounds like a very second-rate maths guy who is compensating with arrogance, a frightfully dangerous combination.
I encountered, indirectly, someone who gave wrong information to a friend about a puzzle in geometry. As best as I could understand it, he was presented the puzzle and, not being clever enough to figure it out on the spot, went on about the theory of tesselations of the plane, blah blah, which dazzled the non-math friend, the latter duly repeating the entirely inapplicable packet in a chatroom. I argued that the maths guy should be ashamed for adopting the defensive and quite-wrong ruse, and instead should have said "I don't know", and then perhaps gone off and figured the thing out (this was the famous problem where triangles that are part of rectangles are assembled in two different ways, to seemingly produce two areas differing by one square unit).
And shame on the math guy here for not knowing a little Galois theory and the implications for general polynomials of degree higher than four. Even if that was not in his field of specialization, it's certainly something to which he'd been exposed and could easily come up in a PhD oral.
okay, so he is good, in fact better....okay I like to see him weld aluminum and solder a stainless steel drum.
we engineers are capable of that too just like that over, our top..
see how a mathematician do that....
To that list I would add:
3. He needs to be able to work effectively as a member of a team.
In a modern-day organization, rather than being the "go-to" guy, an employee like this would more likely be on the short list for termination.
A good analyst (engineer, mathmetician, or any other expert) consists of two things:
1. He know his subject matter.
2. He knows how to EFFECTIVELY communicate that knowledge to others. And part of being effective is having a genuine goal and desire to help others gain knowledge instead of being a "show-off."
Different people have different set of specialized skill set and there in nothing wrong in getting their help. To an organization it saves time and money. However, once in while, you may be little better of then go-to guy or an expert. It does not mean that they are no good at all. No one is omnicient. And even experts do make simple mistakes in hurry. But one should not take it so hard.
Another aspect is communication skills. Employing most suitable words and tone is very important. However, again some pople lack it. It this things happen many times, he may not be good in the subject. But with effort, we do get good go-to guy.
I had the good fortune to work with a good mathematician in very practical cascaded narrow band filter work.
The problem was that even though he explained it very well I was not good enough to understand it all, let alone retain it much after the project was done.
Like the engineer in the example above, I found a couple of good filter books to help me out when needed.