I have had the good fortune to have known some very, very smart people in my life, including my youngest brother who was literally a genius.
None of them ever said they were smart. For one thing, really smart people know what they do not know or understand better than the rest of us.
More importantly, and this is for Trump more than anyone, if you really are smart, you would think that you need not say it, that people would notice, if people noticing it were important to you. Truly smart people rarely require the attention or recognition by others of their intelligence that Trump seems to crave. Many are embarrassed when others comment on it.
As Malcolm Gladwell (Outliers) and Daniel Goleman (Emotional Intelligence) have explained, beyond a certain IQ (130s) the most important success skill is "emotional intelligence": roughly, the ability to notice, evaluate, label and use emotional and psychological constructs to guide behavior and performance. It includes cooperation, grace under pressure, insight into others' needs, seeing yourself as others see you... and, yes, humility.
In Built to Last (Porras and Collins), and Good to Great (Collins), the authors note that the the great leaders were not bombastic or charismatic, nor do they engage in what Veblen called "conspicuous consumption". They are clock-builders, not time-tellers.
I become instantly skeptical when someone tells me they are smart, or have great interpersonal skills, or anything that cannot be easily tested. (By contrast, if you say you are a very fast runner, we could time you; if you say you are a great pianist, we could listen to you play.) But, if you say you are well-liked, or smart, or a great dealmaker, or highly intuitive.... Well, I would just doubt it until shown otherwise.
Trump keeps telling us that he is smart, terrific, and a great dealmaker. Perhaps he is. But, he has not volunteered his college transcripts or his SAT scores. Perhaps he will cut much better deals, as he calls them, with China. Perhaps his deal to have his clothing line made in China is lightyears better than any other similar deal for offshore manufacturing instead of creating jobs in the United States. We do not know. We have not seen that deal.
All we know is that Trump is a great huckster.
He has not had to say that for us to know it.