J. D. van der Waals introduced him to the theoretical works of J. Willard Gibbs on the phase rule which so far had little experimental verification in chemistry, prompting him to start a lifelong research programme on phase equilibria.
Yale professor Josiah Gibbs, seeking anyone who spoke the Mende language to assist him by interpreting for the Amistad captives, went to New York Harbor and loudly counted to ten in Mende until someone who could understand him approached.
Willard Gibbs Van Name, a zoologist with the American Museum of Natural History in New York and nephew of the mathematician Josiah Willard Gibbs, was a key mentor who wrote Emergency Conservation Committee (ECC) pamphlets, which Edge signed and distributed nationwide.
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Around this time Josiah Willard Gibbs and Oliver Heaviside developed vector calculus, which included separate cross product and dot products that were derived from quaternion multiplication.
Oliver Heaviside in England and Josiah Willard Gibbs, a professor at Yale University in Connecticut, also felt that quaternion methods were too cumbersome, often requiring the scalar or vector part of a result to be extracted.