Testy relations between Donald Trump and his secretary of state, Rex Tillerson, have reached a new low. So bad has the braggadocio become that it seems the two silverbacks may be about to go out and settle things the old-fashioned way – with a pencil and a series of rotated geometric shapes.

Tillerson’s reported allegation that Trump was “a moron” resulted in Trump declaring to Forbes magazine that “I guess we’ll have to compare IQ tests. And I can tell you who is going to win.”

High-IQ readers will have inferred that Trump meant he would win (and Mensa, the society for such endowed people, has offered to administer the face-off). This, however, isn’t the opinion of psychologists polled on the issue, who have pointed to the 45th president’s seemingly limited vocabulary as a strong predictor of poor intelligence. At least Joel Schneider, a professor at Temple University, did suggest that he has strong working memory – one of the five basic components of IQ. “His mind wanders as he talks a lot, but what’s striking to me is that he usually finishes his sentences, no matter how long they are,” Schneider says. “He doesn’t lose track.”

Regardless of Trump’s bragging, IQ may be the best thing we have got to measure intelligence, but it’s by no means a perfect system.

Early contributions to the topic were made by English polymath Francis Galton, but most credit French psychologist Alfred Binet with the first universal test in 1908. By 1916, it had been revised into the Stanford-Binet Test, popularised the following year when it was used in grading troops sent off to fight in the first world war.

The scale wraps itself around the bell curve. An IQ of 100 isn’t an absolute quantity of intelligence, it simply means that 50% of people scored better and 50% worse on the test. In fact, IQ tests are re-calibrated every decade, to take account of the fact that humans are getting smarter, the so-called Flynn effect, equivalent to about two or three points a decade. The sharpest IQ rises have been in developing nations, where better nutrition and iodine supplementation have spiked the graphs.

Being above the first standard deviation – an IQ of 115 – means you’re “smarter” than 84% of the population. Go another standard deviation up, to the final 2.2% of the population, and you’ve achieved an IQ of 130-plus. The graph drops off rapidly from there; only 0.1% of the population achieve more than 145. The highest score ever recorded is Marilyn vos Savant’s 228, although the Guinness Book of Records retired the category Most Intelligent Human in which she held the record between 1986 and 1989 when it was realised that IQ tests were too unreliable at the extremes of the scale.

They might not be perfect: within the different tests available, an individual’s score can vary more than 10 points. But, other things being equal, IQ remains a very strong predictor of career success. In fact, it trumps almost any other factor. However, it is still no predictor of wealth. Especially if that wealth came from a rich property-developer daddy. So before he sits down to mentally rotate a dodecahedron, Trump may also wish to acquaint himself with the cognitive illusions of the Dunning-Kruger effect.