Breast feeding has little or no effect on intelligence in children. While breast feeding has many advantages for the child and mother, enhancement of the child's intelligence is unlikely to be among them.

Effect of breast feeding on intelligence in children: prospective study, sibling pairs analysis, and meta-analysis.

Results The mother's IQ was more highly predictive of breastfeeding status than were her race, education, age, poverty status, smoking, the home environment, or the child's birth weight or birth order. One standard deviation advantage in maternal IQ more than doubled the odds of breast feeding. Before adjustment, breast feeding was associated with an increase of around 4 points in mental ability. Adjustment for maternal intelligence accounted for most of this effect. When fully adjusted for a range of relevant confounders, the effect was small (0.52) and non-significant (95% confidence interval -0.19 to 1.23). The results of the sibling comparisons and meta-analysis corroborated these findings.
Via: British Medical Journal