Huygens and Leibniz begin corresponding, exchanging ideas and discussing mathematical and scientific problems. Huygens becomes a mentor to Leibniz, guiding his early work in mathematics.

Leibniz visits Huygens in Paris, spending time with him and learning from his expertise in mathematics and physics. This direct interaction strengthens their intellectual bond.

Leibniz independently develops his version of calculus, which he shares with Huygens. While Huygens does not fully embrace Leibniz's notation, he recognizes the importance of Leibniz's work and encourages him to continue his research.

Huygens and Leibniz continue to correspond throughout their lives, discussing a wide range of scientific and philosophical topics. Their exchange of ideas contributes to the advancement of both mathematics and physics during the late 17th century.