We believe too many myths about performance and ability. That’s why this quote is very applicable:
“Everybody is a genius. But if you judge a fish by its ability to climb a tree, it will live its whole life believing that it is stupid.” ― Albert Einstein
I’ve seen this in a few places recently, including from Garr Reynolds. What made this stick was I heard an example at an HR briefing recently where because someone was good at his field, the HR person referred to him as really smart. This is a mistake we often make about certain fields. We think that because they appeal to the intellect, that therefore someone who is in successful in that field must be smart. This is true of chess, of stock trading, of engineering, and of many other pursuits. But when folks in the field are tested, it’s not surprising to find successful people who are of average intelligence or less. Likewise it’s also not unusual to find folks who are not successful who are of greater than average intelligence.
The key to remember is that if we’ve put a lot of time and effort in a particular domain working on our weaknesses and intentionally seeking improvement, we should make progress in that field. We may become rather good in that domain. For instance, if I put in multiple hours each week working on tactical positions and chess and studying the different parts of the game, especially as my own play reveals weaknesses that I seek to improve, I will get better at chess. However, my ability to remember positions in chess, to remember multiple move orders in different openings translates only to chess. Scientific research shows that these gains are domain specific. They do not carry over.
Therefore, if someone isn’t particularly good at one area, we cannot conclude that they aren’t smart, or aren’t capable, or anything else, except not good in that domain at the present time. If that person is you, don’t allow the lack of ability in one area cause you to think less of yourself. What scientific studies have shown is that our abilities in just about any field, unless related to physical attributes, are actually dependent more on our work in that domain, especially the proper type of work towards improvement. So don’t be like the fish who believes he is stupid because he can’t climb a tree. Instead, remember that you have areas of strength, too. And if there is an area that is a weakness that you want to work on, it is possible to improve.
Moreover, remember that you are more than the sum of what your strengths are. We often refer to ourselves by what we do or what we are known for. But we are more than that as individuals. Steve Jones (blog | twitter) has written on this multiple times in his blogging and as editor of SQLServerCentral.com, the largest community site in the world for Microsoft SQL Server professionals like me. Steve is and has been considered one of the top guys in our industry for a long time. But if you only see Steve as a SQL Server person, you miss out on a lot. That’s true of all of us. Don’t fall into the trap of defining yourself by your strengths and successes or your weaknesses and failures, or even a combination of the two sets. You are more than that. Also don’t fall into the trap of judging people solely on theirs.

“However, my ability to remember positions in chess, to remember multiple move orders in different openings translates only to chess. Scientific research shows that these gains are domain specific. They do not carry over.”
I would turn this a little – I appreciate your message regarding strengths and weaknesses, but I would use this to point out the flaw in progression into management that we see so often in specialized fields like IT (but it also applies in medicine, etc.):
Just because someone is a good XXX does not mean they will be a good manager of XXX.
How many times have you seen a technology superstar crash and burn once they become the manager of their group because the skills required to be a good DBA do not directly apply to being a good manager?
While some people do make that transition well – at a previous job I worked for someone who was previously a Jr. DBA, then the Lead, and then the DBA Manager, and she was great at all three jobs – but it was because she had both management skills and DBA skills.