Zeno defended his instructor's belief in monism, the idea that only one single entity exists that makes up all of reality.

Though his original writings are lost, subsequent descriptions by Plato, Aristotle, Diogenes Laertius, and Simplicius of Cilicia have allowed study of his ideas.

[5] By the time that Parmenides takes place, Zeno is shown to have matured and to be more content to overlook challenges to his instructor's Eleatic philosophy.

[9] Simplicius of Cilicia, who lived in the 6th century AD, is another one of the main sources of present day knowledge about Zeno.

[10] This school of philosophy was a form of monism, following Parmenides' belief that all of reality is one single indivisible object.

Previous philosophers had explained their worldview, but Zeno was the first one to create explicit arguments that were meant to be used for debate.

[1] In one argument, Zeno proposed that multiple objects cannot exist, because this would require everything to be finite and infinite simultaneously.

[22] Zeno's arguments against motion contrast the actual phenomena of happenings and experience with the way that they are described and perceived.

[26] Zeno's greatest influence was within the thought of the Eleatic school, as his arguments built on the ideas of Parmenides,[22] though his paradoxes were also of interest to Ancient Greek mathematicians.

[31] Zeno was succeeded by the Greek Atomists, who argued against the infinite division of objects by proposing an eventual stopping point: the atom.

[29] The paradox of Achilles and the tortoise may have influenced Aristotle's belief that actual infinity cannot exist, as this non-existence presents a solution to Zeno's arguments.

[22] Zeno's paradoxes are still debated, and they remain one of the archetypal examples of arguments to challenge commonly held perceptions.

[3] Zeno's philosophy shows a contrast between what one knows logically and what one observes with the senses with the goal of proving that the world is an illusion; this practice was later adopted by the modern philosophic schools of thought, empiricism and post-structuralism.

Bertrand Russell praised Zeno's paradoxes, crediting them for allowing the work of mathematician Karl Weierstrass.

Ideas relating to Zeno's plurality arguments are similarly affected by set theory and transfinite numbers.

[14] Modern physics has yet to determine whether space and time can be represented on a mathematical continuum or if it is made up of discrete units.

[3] Zeno's argument of Achilles and the tortoise can be addressed mathematically, as the distance is defined by a specific number.

His argument of the flying arrow has been challenged by modern physics, which allows the smallest instants of time to still have a minuscule non-zero duration.

[28] Other mathematical ideas, such as internal set theory and nonstandard analysis, may also resolve Zeno's paradoxes.