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 Ptolemaic system and proposed a heliocentric system in which the planets "including" orbited the sun ("Helios"). This more mathematically satisfying way of arranging the solar system did not attract many supporters at first, since the available data did not yet support a wholesale abandonment of Ptolemy's system. By the end of the 16th century, however, astronomers like Johannes kepler (1571-1630) had begun to embrace Copernicus's theory.