Zeno of Elea was a philosopher, the pupil and friend of Parmenides. He gave
four paradoxes which had a profound influence on the
development of mathematics.

The flavour of the paradoxes is given by the proof that motion is
impossible. In order the traverse a line segment it is necessary to reach
its midpoint. To do this one must reach the 1/4 point, to do this one must
reach the 1/8 point and so on ad infinitum. Hence motion can
never begin.

The paradoxes were important in the development of the notion of
infinitesimals.