What is the evidence that mathematicians are more likely to have autistic traits than the rest of the population?

Question

Baron-Cohen has conducted extensive studies [1,2] examining the prevalence of autism spectrum conditions (ASCs) and mathematical or scientific ability. Most of these studies, however, have focused mostly on (Cambridge) undergraduates or winners of the UK Mathematics Olympiad.

In one study, Baron-Cohen found in [2] that Olympiad winners scored the highest in the AQ test ($\mathrm{AQ}\colon 24.5,\mathrm{ SD}\colon 5.7$), with the second highest scoring group being the mathematics students ($\mathrm{AQ}\colon 21.5,\mathrm{ SD}\colon 6.4$).$^1$ This leads one to conjecture that autistic traits may be more prominent among individuals with higher mathematical ability.

Question: What is the population evidence$^2$ around autism/autistic traits in mathematics? If possible, at the postgraduate level in professional mathematicians?

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Disclaimer: There is a another question focused on the postgraduate maths skill set: Is there any evidence for the distinction between undergrad and postgrad mathematics?.

$^1$Note however that the sample is small: $n=16$ for UK Olympiad winners, $n=85$ for mathematics students.

$^2$As in measuring the average AQ of mathematicians against other groups, such as graduate students, undergraduates, and controls.

References

[1] Baron-Cohen, Simon, Sally Wheelwright, Amy Burtenshaw, and Esther Hobson. "Mathematical talent is linked to autism." Human nature 18, no. 2 (2007): 125-131.

[2] Baron-Cohen, Simon, Sally Wheelwright, Richard Skinner, Joanne Martin, and Emma Clubley. "The autism-spectrum quotient (AQ): Evidence from Asperger syndrome/high-functioning autism, males and females, scientists and mathematicians." Journal of autism and developmental disorders 31, no. 1 (2001): 5-17.

Answer 1

No. I can't seem to find a specific study into professional mathematicians or graduate students so far, the studies always seem to group the occupations together.

However, Baron-Cohen's team has done an impressive national survey (Ruzich et al., 2015) and recruited nearly half a million people through a UK TV show. They managed to get over 450,394 survey respondents which allowed them to analyse occupations. They found that people working in STEM scored higher in an autism screening questionnaire or AQ (Autism-Spectrum Quotient) test.

individuals working in a STEM career (m = 21.92, SD = 8.92) scored higher than individuals non-STEM careers (m = 18.92, SD = 8.48)

Unfortunately, there wasn't a specific category for mathematicians as probably it is too specific and too small a field to analyse. The three categories (figure 3) forming STEM was Comp & IT, Engineering and Sci & Tech. Mathematicians would fit into one of those occupational roles.

References

Ruzich, E., Allison, C., Chakrabarti, B., Smith, P., Musto, H., Ring, H., & Baron-Cohen, S. (2015). Sex and STEM Occupation Predict Autism-Spectrum Quotient (AQ) Scores in Half a Million People. PLOS ONE, 10(10), e0141229.