increasingly complex mathematical systems were necessary to reconcile these new observations with Ptolemy's system of interlocking orbits. Nicholas Copernicus, a Polish astronomer, openly questioned the Ptolematic system and proposed a heliocentric system in which This more mathematically satisfying way of arranging the solar system did not yet support a wholesale abandonment of Ptolemy's system. By the end of the 16th century, however, astronomers like Johannes Kepler (157-1630) had also began to embrace Copernicus's theory