I thought I'd register to add a few interesting points to this thread.
'Classical' GWAS are a top-down approach, where we try to find strong associations betweens a genetic locus and a trait (in this case intelligence), and they rely on very stringent p-value corrections due to the number of tests performed. This is why although height is >0.6 heritable (meaning genetics explain more than 60% of the trait variance in a given population), only 20% of the variance can be attributed to GWAS finds [1], such as the 52 genes in this article. Bear in mind that the height results were obtained with the largest GWAS ever with more than 250,000 samples and 300 institutes [2].
So where is the missing heritability? This is the starting point of a bottom-up approach, where we try to predict a trait from the genotype. With some clever but simple calculation, we know that most heritability can be found in the data (even if it does not pass the stringent significant thresholds). This is what is called 'chip heritability', the heritability explained by all the common genetic variants present on commercial chips taken together. With height, the chip heritability reaches 62.5% [1]. The bottom-up approach is especially looked at for psychiatric disorders, and already delivered some interesting results such as 0.8 genetic correlation between schizophrenia and bipolar disorder [3]. But useful clinical diagnostics based on genetic data are still a long way off.
This should please the HN crowd to know that we still have one tough prediction problem to crack. Current results can be improved either with more sophisticated machine learning methods or by integrating various biological annotations to try to unearth the missing heritability that GWAS can't seem to find with the current sample sizes.
Here are a few more links for those interested [4] [5].
[1] https://www.ncbi.nlm.nih.gov/pubmed/25282103?dopt=Citation
[2] https://www.broadinstitute.org/news/giant-study-reveals-gian...
[3] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4797329/
[4] http://onlinelibrary.wiley.com/doi/10.1002/gepi.21966/full
[5] https://academic.oup.com/bioinformatics/article/29/2/206/202...