Here's a short summary from a January 2014 metaanalysis on what we currently know about sex differences regarding cognitive tasks. It's rather nuanced. I have to insert the disclaimer that I know nothing about any agenda on the authors' parts.

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What cognitive tasks show sex differences?

Some spatial tasks such as mentally rotating 3D objects show the largest sex differences, favoring men by ∼0.5–1 standard deviations [26]. Much research has understandably focused on spatial tasks that show large sex differences, but this focus does not address how typical male advantages would be on a fuller range of spatial tasks. For instance, despite their presumed demands on spatial processing, geometry problems on mathematics tests typically show small-to-nonexistent sex differences 13 and 77.

Task characteristics influence spatial sex differences. For instance, male advantages in mental rotation are larger when the task involves 3D objects versus 2D objects [26] and has strict time limits versus no time limits [25]. However, other task differences are less well understood, such as why mentally rotating objects shows sex differences but mentally folding paper does not reliably (see Figure 1 in main text) 26 and 112. For instance, Harris and colleagues recently reviewed comparisons between mental rotation and mental folding, finding evidence for many similarities in the underlying cognitive processes [112]. That review paper speculated that the differences in male advantages may reflect task differences in requiring rigid versus non-rigid transformations of objects, but noted that current evidence is limited.

At least one spatial task (remembering object locations) moderately favors women [22]. This finding aligns with small to moderate female advantages on some memory tasks such as remembering object identities, faces, and lists of words and numbers 11, 18 and 22. Some other memory tasks show more mixed findings 17, 19, 20 and 21. For instance, when described as a test of geometry ability, a task involving recalling an abstract spatial diagram showed differences favoring boys (d = 0.51) [20]. However, when described as a test of drawing ability, the task showed differences favoring girls (d = 0.50). This study (n = 199) [20] replicated two earlier studies [19].

Sex differences in average mathematics test performance tend to be small to nonexistent 13, 16 and 77, although boys outnumber girls among high performers (e.g., top 1% or higher) in most but not all nations 9, 10, 16 and 78. These differences often do not reliably differ by task characteristics (e.g., geometry versus non-geometry problems), although girls sometimes slightly outperform boys on problems requiring algebraic solutions or short-answer responses 13 and 77. These small female advantages for algebra and short-answer problems align with findings regarding verbal tasks. For instance, girls outperform boys in reading across the globe (∼0.2–0.6 standard deviations) 11, 16 and 79. These female advantages are larger among lower-performing students 16 and 79 and are even larger for writing tasks [11].

Research conducted in the 1970s to 1980s suggested an alarming finding that boys outnumber girls 13 to 1 among American students with exceptional mathematics talent [9]. However, this tail ratio has dropped to about 2–4 to 1 in recent years, according to both self-selected [9] and nationally representative samples [10]. Sex differences in average mathematics test performance also decreased during the 1970s to 1980s 11 and 12 and have since remained small to negligible 10 and 13.These changes over time have led some scholars to conclude that cognitive sex differences are disappearing. However, the data indicate nuanced trends. For instance, the overrepresentation of males among high mathematics performers decreased during the 1980s, but has not been decreasing since the 1990s 9 and 10. Since at least 1990, girls have earned higher mathematics grades by approximately 0.1–0.2 Grade Point Average (GPA) points [14]. Other data also indicate complex findings. Earlier meta-analytic evidence suggested few sex differences in verbal abilities [15], but recent analyses of large-scale international assessments call for reexamination of this claim. In an analysis of 1.5 million children's reading achievements, girls outperformed boys in all 75 nations in all testing administrations (in total, 213 independent samples) [16]. These sex differences were moderately large in 55% of cases (0.36 ≤ d < 0.65) and may be increasing over time. Small-to-moderate female advantages are also consistently found for some but not all memory tasks ( Box 2) 11, 17, 18, 19, 20, 21 and 22. Male advantages are found on some but not all spatial tasks ( Figure 1) 22, 23, 24, 25 and 26; cross-temporal trends on spatial tasks are mixed

Other studies have shown that spatial ability, in particular, is quite "trainable." Hence, GoldieBlox.

Personally, I'm not tempted to conclude anything particularly sweeping from all of these findings. Some differences appear to exist at this time in some situations. It varies by country. It has changed drastically over time. Even within a skill ("spatial tasks") we have some areas where the stereotypical pattern is not found. And we have the interesting finding that girls who identify less with a "feminine" identity are better at these skills. (Who knows why? This could be biological, or it could be environment/personality, or a combo.)