Kramer et al 2008 is an excellent study of this question because it utilizes intervention, thus lending strength to the claim of causation, concluding that IQ was "significantly higher in the experimental group for both reading and writing".
But is it the milk itself? Some argue that it's also the skin-to-skin contact, and the mother-child bonding. Academic success has been shown to be strongly correlated with emotional intelligence (e.g., Parker et al, 2004 found $r=.33$ between GPA and EI in a large sample of high school students) and some Attachment Theory proponents claim closer parental relationships lead to stronger emotional intelligence. However, some studies demonstrate that only adults happiness is positively effected by percieved parental attachment, not emotional intelligence (e.g., Sillick & Schutte, 2006) and that emotional intelligence is correlated with a dismissive attachment style (Kafetsios, 2004).
The Arch Gen Psych article comments on potential mechanisms:
Even though the treatment difference appears causal, it remains unclear whether the observed cognitive benefits of breastfeeding are due to some constituent of breast milk or are related to the physical and social interactions inherent in breastfeeding. Concentrations of essential long-chain polyunsaturated fatty acids are higher in human milk than in infant formula. Randomized trials of supplementation of infant formula with long-chain polyunsaturated fatty acids, however, have yielded inconsistent results in both term  and preterm  infants. Another potentially important component of breast milk that could be responsible for the observed cognitive differences is insulinlike growth factor I, which is contained in higher concentration in breast milk than in formula  and has been shown to be absorbed intact across the newborn infant's gastrointestinal tract.
On the other hand, studies showing long-term epigenetic behavioral
effects of licking and grooming by mother rats of their pups  suggest
that the physical and/or emotional act of breastfeeding might also
lead to permanent physiologic changes that accelerate neurocognitive
development. Finally, it is possible that the increased frequency and
duration of maternal-infant contact implicit in breastfeeding vs
bottle-feeding could increase verbal interaction between mother and
infant, which might also have a stimulatory effect on cognitive
 Simmer K. Longchain polyunsaturated fatty acid supplementation
in infants born at term [update of: Cochrane Database Syst Rev.
2000;(2):CD000376]. Cochrane Database Syst Rev 2001; (4) CD000376
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supplementation in preterm infants [update of: Cochrane Database Syst
Rev. 2000;(2):CD000375]. Cochrane Database Syst Rev 2004; (1)
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factor I in full- and preterm human milk in comparison to levels in
cow's milk and in milk formulas. Biol Neonate 1990;58 (6) 343- 346
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Koldovsky O. Fate of insulin-like growth factors I and II
administered orogastrically to suckling rats. Pediatr Res 1995;37 (5)
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- Kafetsios, K. (2004). Attachment and emotional intelligence abilities across the life course. Personality and Individual Differences, 37, 129-145.
- Kramer, M.S., Aboud, F., Mironova, E., Vanilovich, I., Platt, R.W., Matush, L., Igumnov, S., Fombonne, E., Bogdanovich, N., Ducruet, T. & others (2008). Breastfeeding and child cognitive development: new evidence from a large randomized trial. Archives of General Psychiatry, 65, 578.
- Parker, J.D.A., Creque, R.E., Barnhart, D.L., Harris, J.I., Majeski, S.A., Wood, L.M., Bond, B.J. & Hogan, M.J. (2004). Academic achievement in high school: does emotional intelligence matter?. Personality and Individual Differences, 37, 1321-1330. PDF
- Sillick, T.J. & Schutte, N.S. (2006). Emotional intelligence and self-esteem mediate between perceived early parental love and adult happiness. E-Journal of Applied Psychology, 2. PDF