Posted by: Alexandre Borovik | November 12, 2022

I do not know for which my sins Quora bombards me with questions about giftedness, IQ, etc. For several years I tried to ignore them, but finally I realised that I have to formulate my position.

Yes, professional mathematicians possess some mental traits and skills which majority of population do not have. But these traits are not what is called “gift”, “talent”, “ability” in the mass culture; they remained unnoticed, unregistered in the public discourse about mathematics and mathematics education. However, my mathematician friends, when we discuss this topic, know what I am talking about.

IQ is mostly irrelevant to discussion of mathematical “ability”; specific traits of mathematical thinking belong to a much higher cognitive level than skills tested in IQ tests.

A simple example: I had seen once how an eight years old boy was solving some standard puzzle (not of IQ type), with some pattern of hexagons which had to be filled with integers from 0 to 9 so that certain sums were equal — you perhaps had seen this boring stuff . At some point he paused and commented: “Hmm, I have to somehow move information from this corner to that corner”. Moreover, after some thought he had successfully moved the information. This was meta-thinking, ability to reflect on one’s thinking, ability to look at the problem from above. This boy now is quite a successful student in one of the best university mathematics departments in the world, in a pipeline to becoming a professional research mathematician.

Perhaps you have heard this definition:

“Mathematics is the science of patterns”.

IQ tests pay much attention to the speed of pattern recognition. It is a useful skill, but it is not a sign of mathematical abilities. In my life, I had a chance to see a lot of children and teenagers who had an instinct (or maybe it was a trait absorbed in the family?), to look deeper and try to detect the structure behind the pattern — and the boy mentioned above was one of them. Indeed, the simplest description of mathematics is

“Mathematics is the science of structures behind patterns”.

Perhaps my personal experience is outdatet, but I was privileged to go through a viciously academically selective system of mathematics education — see my paper “Free Maths Schools”: some international parallels. Aged 14, at a Summer School which was the final step of selection to the specialist boarding school described in the paper, I and my friends were subjected to a battery of IQ tests — which, however, had no relation to admission to the school.

We were tested by professional experimental psychologists who were commissioned by the Soviet Army to study and assess reliability of the IQ tests used by the US Army for assignment of conscripts to particular duties (you see how long ago it was). The psychologists translated real American IQ tests into Russian and tried them on various groups of population. They were excited to discover that our performance refuted a claim that apparently was universally accepted at that time: that practicing IT tests could not improve results.

Indeed our results were quickly improving beyond applicability of tables for conversion of counts of correct answers into IQ scores. Why? Because we did not practice IQ tests — we had access only to tests which we have already taken — but, after every test, we spent hours classifying test questions, analysing them, inventing our own questions and challenging each other to solve them, and we did that in a collective discussion, in brain storming sessions, attacking problems like a pack of enthusiastic young wolves. Perhaps we had already had some specific habits of mathematicians; but there was nothing special about that, even some 8 year old kids might have them, as I have already said.

As I explain in my paper that I mentioned above, in the selection process for my mathematics boarding school, and in the school itself, the use of words gifted, talented, able was explicitly forbidden — they were seen as misleading and divisive.

I am a staunch believer that majority (maybe even all) kids have strong potential for understanding and mastering mathematics. Unfortunately, their mathematical traits are systematically suppressed in the mainstream school mathematics education — mostly because many teacher have no idea what it is about.

You may wish to take a look at my papers, they say more:

A. V. Borovik, Mathematics for makers and mathematics for users, in Humanizing Mathematics and its Philosophy: Essays Celebrating the 90th Birthday of Reuben Hersh (B. Sriraman ed.), Birkhauser, 2017, pp. 309–327. bit.ly/2qYHtst

A. V . Borovik and A. D. Gardiner, Mathematical abilities and mathematical skills, The De Morgan Journal 2 no. 2 (2012) 75-86. bit.ly/2jTYy4r

## Responses

1. “I am a staunch believer that majority (maybe even all) kids have strong potential for understanding and mastering mathematics.”
Are you a father? Have you childs?

• Both my kids are grown-up professionals now and work in mathematically intensive industries.

2. Hilariously misinformed. Read a book or two on how real IQ tests are made/normed and what “trainability” means.