Using data on academic citations, career and educational histories of mathematicians, and disaggregated distance data for the world's top 1000 math departments, we study how geography and ties affect knowledge flows among scholars. The ties we consider are co-authorship, past colocation, advisor-mediated relationships, and alma mater relationships (holding a Ph.D. from the institution where another scholar is affiliated). Logit regressions using fixed effects that control for subject similarity, article quality, and temporal lags, show linkages are strongly associated with citation. Controlling for ties generally halves the negative impact of geographic barriers on citations. Ties matter more for less prominent and more recent papers and show no decline in importance in recent years. The impact of distance--controlling for ties--has fallen and is statistically insignificant after 2004. [This paper was produced as part of the Centre for Economic Performance's Trade Programme.]