Small differences in talent are associated with sizeable differences in long-term achievements

From Invisible geniuses: The advancement of the knowledge frontier by Ruchir Agarwal and Patrick Gaulé. From the Absract:

Exceptional mathematics talents generate breakthroughs that move the entire field forward. This column explores how the talent of exceptional mathematics students from several countries affects their outcomes and contributions to the field. Small differences in talent during adolescence are associated with sizeable differences in long-term achievements, from getting a PhD to receiving a Fields medal. The research highlights the social losses associated with the lack of opportunities available to students in low-income countries.

They elaborate. Emphasis added.

In a new paper, we study knowledge production in mathematics and use a unique institutional feature of this discipline – the International Mathematics Olympiads (IMO), a prominent worldwide competition for high-school students (Agarwal and Gaule 2018). This setting allows us to measure talent in teenage years in a comparable way across multiple countries. We follow these participants over their lifetime and evaluate their lifetime knowledge production.

We find that even in this group of teenagers in the extreme right tail of the talent distribution, small differences in talent are associated with sizeable differences in long-term achievements, including getting a PhD, number of mathematics publications and cites, and being awarded a Fields medal. For instance, each additional point scored on the IMO by a participant in their teenage year (out of a total possible score of 42) is associated with a 2.6% increase in mathematics publications and a 4.5% increase in mathematics citations over their lifetime. The chance that an IMO gold medallist will become a Fields medallist is fifty times larger than the corresponding probability for a PhD graduate from a top 10 mathematics programme. We find that this is both because strong IMO performers are more likely to become professional mathematicians; and conditional on becoming professional mathematicians, they are more productive than lesser IMO performers, and are significantly more likely to produce frontier research in mathematics. We also show that this relationship reflects the underlying talent distribution and is not due to an effect of initial success of receiving a medal. For instance, we find no difference in lifetime performance of participants who ‘just’ made it to receiving a medal compared to those who nearly missed them.

Fascinating. We know IQ is measured with positive life outcomes, especially when conditional on other psychological traits such as purposefulness, self-control, persistence, etc.

And we know that in all sorts of areas, small initial differences lead to large long-term differences, i.e. the compounding effect.

But this is an elegant confirmation of that already existing knowledge. Which is useful because there are large segments of the Mandarin Class who insist that differences in capability are not causal to differences in outcomes.