Lucretius has been enduringly relevant to mathematics, because of his presence in the intellectual background of scientists during the development of classical physics and because of the similarities between Lucretius’ atomic motion and a stochastic dynamical system. Newton and Leibniz, physicists and mathematicians who simultaneously developed calculus, both engaged with Lucretius in their writing. Newton wanted to use certain passages of Lucretius’ De Rerum Natura to prove that the ancients understood the concept of inertia. At the end of Opticks in a summary of his metaphysical beliefs, Newton drew from Lucretius to argue for the indivisibility of atoms and made other references to Epicureanism and specifically to De Rerum Natura. Leibniz did not reference Lucretius in a work about physics, but he drew from Lucretius in his essay “On the Ultimate Origin of Things”, in which Leibniz used mathematical language to discuss metaphysics. Furthermore, Leibniz seriously considered Lucretius as a philosopher, because he saw Epicureanism as a threat to Christian thinking. Because Newton and Leibniz both treated Lucretius as a serious thinker and were influenced by him in their writing, it is possible that they could have seen mathematical ideas in Lucretius’ writing. Furthermore, because of similarities between Lucretius’ swerve and some concepts in calculus, it is even possible that Lucretius could have influenced the development of calculus. Lucretius still remains relevant to modern developments in mathematics because his description of the atoms’ swerve in Book II and the order and regularity that results in the universe in Book V resembles equilibrium in a stochastic dynamical system or random walk. In mathematics, a dynamical system is an equation or system of equations that can model the change of something over time, such as two competing populations of animals. A stochastic dynamical system can model the change in probabilities over time, such as the probability of rain. A specific type of stochastic dynamical system is called a random walk, which can be used to model things such as particles of food dye diffusing in a liquid. Dynamical systems can approach an equilibrium value, meaning that as time goes on, the thing modeled does not change. For example, an animal population has reached equilibrium if it stays at a certain number of animals. Lucretius’ description of atomic motion resembles a random walk because the atoms swerve randomly, as he describes in Book II. The atoms’ motion results in the regularity of the seasons, described in Book V, which resembles equilibrium in a random walk. Repetition of similar phrases in the passage from Book II and the passage from Book V suggest that the two passages should be considered together. Though a random walk is not exactly the same as the atomic motion described in De Rerum Natura, Lucretius displays an intuition about the mathematical concept of equilibrium arising from randomness. This suggests that other mathematical ideas could be older than originally thought and could originate from surprising sources, such as poetry or philosophy.
The Next Generation: Papers by Undergraduate Classics Students