Ugh. It doesn't matter how good your math is if your model is wrong.
Here's an outline of what I believe to be a useful model, and some useful questions to ask, and experiments to run in real life to change things.
+-------------------+
| |
+ |
+---->X1+---+ |
| | |
| +-->Q |
M+------+ | + |
| | | v
| | +--------+W
| | ^
+---->X2+---+ |
+ |
| |
+-------------------+
M = male / female
X1 = math ability
X2, X3 ... Xn = other factors (analytical ability, ability to work in teams, ability to understand real problems, etc, also bias of interviewers against women)
Q = performance on interview questions
W = performance in real life work
The slides, and most peoples argument is based on the model where there is only one factor math ability, which is why people go 'oh but that doesn't account for it / the disparity is so small'.
The important question is how do all the factors ADD UP?
Now,
If Q does not correlate with W, fix your interview questions first.
Then, if you want more women to do well in the interview, well, ...
-- the wrong approach is to compromise the integrity of the interview, which compromises the company's business, and which is demeaning to women, although you could use this as a proxy to make the interview more comprehensive
-- the correct approach is to investigate X1, Xn factors and train to remove these discrepancies earlier on way before the interview itself, if we decide that we want to. biases in the interview processes are only biases when removing them improves the correlation between Q and W
Another thing to do is to change the nature of the work itself. In which case the factors and interview questions will change accordingly. Play to peoples' strengths!
The nature of the work must include the performance of the team including the individuals as there may be a benefit to representation when it comes to solving problems of a crowd with varied people.
Interestingly, the Google article covers a lot of this, and even suggests some changes that can be made.
A large number of factors can quickly add up even if the individual factors as small.
I welcome comments from the more knowledgable, but I feel that a lot of knee jerk reactions here are just taking individual statements from the argument and loudly saying NO, or saying well there's no difference here.