Mathematics is fundamental to many fields such as science, engineering, economics and medicine, and the understanding of basic numeracy and related skills is a crucial component of normal brain function. Despite widespread appreciation of the increasing importance of numeracy in modern society, research has revealed poor average performance in many countries, with extremely low enrolment in mathematical subjects after age 16 (Mazzocco & Myers 2003; Smith 2004). Defining disability in mathematics rests on establishing a cut-off, which can be performed in a variety of ways. One approach defines disability as obtaining arithmetic scores at least 2 years below expected grade level (American Psychiatric Association 1994). With this definition, mathematical disability has an estimated frequency of 6% in school children (Gross-Tsur *et al.* 1996), a prevalence similar to that of reading disability (Law *et al.* 1998). Understanding the etiology of mathematical ability and disability may prove an essential step in tackling mathematical underachievement, and could provide fresh insights into human brain function.

Quantitative genetic research indicates a genetic component to individual variation in mathematical ability, yielding heritability estimates of 0.2–0.9 (Alarcón *et al.* 2000; Husén 1959; Kovas *et al.* 2007a,b; Light *et al.* 1998; Loehlin & Nichols 1976; Oliver *et al.* 2004; Thompson *et al.* 1991; Wadsworth *et al.* 1995). In the absence of obvious neurological impediment mathematical disability is a complex disorder. As with variation in normal levels of mathematical ability, quantitative genetic studies have attributed a similar level of genetic influence to mathematical disability (Alarcón *et al.* 1997; Kovas *et al.* 2007a,b; Oliver *et al.* 2004). Importantly, quantitative genetic findings also suggest that rather than being a distinct clinical category, mathematical disability is the quantitative extreme of the normal distribution of ability—influenced by many of the same genetic factors affecting normal variation in ability (Alarcón *et al.*, 1997; Kovas *et al.* 2007a,b; Oliver *et al.* 2004). This supports a quantitative trait locus (QTL) approach to the molecular genetic study of mathematical ability and disability (Plomin *et al.*, 2009).

At present no molecular genetic research specifically investigating mathematical ability or disability has been reported. With linkage approaches lacking the power required to detect the small effects expected in complex traits (Plomin *et al.* 2008), and with no obvious candidate genes to explore, a scan of the entire genome for associations with mathematical ability is desirable. Highly multiplexed microarrays permit such genome-wide coverage. However, the cost involved in individually genotyping the large sample sizes required to detect small QTL effects is prohibitive to most researchers. DNA pooling methods offer a possible solution. The DNA of multiple individuals may be combined and assayed on SNP microarrays to accurately detect differences between groups across the entire genome (Butcher *et al.* 2004, 2005a, b; Docherty *et al.* 2007; Meaburn *et al.* 2005; Pearson *et al.* 2007; Steer *et al.* 2007). Although individual genotyping remains the ultimate test of association, such pooling stages can be used to nominate sites for further investigation.

Here, we use pooled DNA from 10-year-olds of high vs. low mathematical ability (*N* = 600 each) in a two-stage GWAS of mathematical ability and disability. The top-performing 46 SNPs nominated in these two scanning stages were individually genotyped in a sample of 2356 individuals spanning the entire distribution of ability, to test not only the association with low vs. high mathematical performance, but also the QTL hypothesis that most SNPs associated with mathematical ability at the extremes are also associated with the entire range of mathematical ability.