Most of you have probably heard of Gibbs free energy, as it is one of the essential concepts in math and science. But how many of you know about the math wizard behind the well-known Gibbs free energy? 

Who is Josiah Willard Gibbs?

Josiah Willard Gibbs is an American mathematical engineer, physicist, and chemist renowned for his contributions to statistical mechanics and physical chemistry. It is widely believed that he was one of the most outstanding scientists of his time.1,2

Gibbs grew up in New Haven and was friendly as a child, but also reserved. He received his education at the nearby Hopkins Grammar School before enrolling at Yale College in 1854. Gibbs received numerous awards in both Latin and math before graduating from Yale College in 1858. He continued to study engineering there in the new graduate program, and earned one of the first Ph.D. degrees granted in the United States at the age of 24.1,2

He was hired as a tutor at Yale College in the same year and worked there for three years, instructing elementary Latin and natural philosophy students. During this period, he continued to deepen and broaden his understanding of engineering and the physical sciences and submitted a patent for an improved train brake. In 1866, Gibbs left New Haven to pursue higher studies in Europe. He traveled for nearly three years, attending lectures by European mathematicians and physicists and absorbing their intellectual flair. The foundation for his future career path was laid by his European studies rather than his earlier education.1,2

Gibbs’ Greatest Works and Scientific Contributions

Before he published his first scientific work, Gibbs received an appointment as Yale College’s professor of mathematical physics. He composed the memoirs on thermodynamics, which are considered his most significant contribution to science at the time. “Graphical Methods in the Thermodynamics of Fluids,” his first significant publication, was published in 1873, followed by “A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces.” His most well-known study, “On the Equilibrium of Heterogeneous Substances,” was published in 1876.1,2,3

Previously, Gibbs had demonstrated intellectual prowess by improving James Watt’s steam-engine governor. By analyzing its equilibrium, he developed a method for calculating chemical equilibrium. Gibbs’ exceptional geometrical abilities were also evident in his doctoral thesis, “On the Form of the Teeth of Wheels in Spur Gearing.”1,2,3

He wrote articles that significantly transformed how we understand thermodynamics. He began by pointing out that the Gibbs Equation of State, which is now considered to be a fundamental equation of thermodynamics, can be created by combining the first two laws of thermodynamics. He presented two seminal papers using 3D graphs to demonstrate completely new interpretations of matter’s behavior. These graphs had x, y, and z axes.4,5

The Scottish physicist Maxwell became aware of these articles’ importance, and in a subsequent revision of his work on heat, he included and improved upon Gibbs’ presentation. Maxwell was motivated to create a plaster model that incorporated Gibbs’ graphical formulas as they related to water and delivered the finished work to Gibbs.1,5

Contrary to others who simply viewed chemical equilibrium equations as empirical facts, Gibbs distinguished himself by deriving chemical equilibrium equations from mathematical premises. He is widely recognized as the creator of the Gibbs free energy idea, which is crucial to understanding chemical equilibria. In math, Gibbs developed the widely used application of vector analysis in R3, building on the work of Grassmann.1,3,4,5 

His last publication, “Elementary Principles in Statistical Mechanics,” is a beautiful account that solidifies the theoretical underpinnings of statistical mechanics. Given that Gibbs’ fatal illness struck within a year of the book’s release, he was unable to witness the real successes of statistical mechanics. 6

If you enjoyed reading this article and found it insightful and motivating, check out BYJU’S FutureSchool Blog for more intriguing posts on math and coding.


  1. J. Willard Gibbs | American scientist | Britannica. (n.d.). Retrieved January 4, 2023, from 
  2. J Willard Gibbs (1839 – 1903) – Biography – MacTutor History of Mathematics. (n.d.). Retrieved January 4, 2023, from 
  3. Josiah Willard Gibbs – New World Encyclopedia. (n.d.). Retrieved January 4, 2023, from 
  4. Josiah Willard Gibbs Issues The Principia of Thermodynamics : History of Information. (n.d.). Retrieved January 4, 2023, from 
  5. J. Willard Gibbs – Biography, Facts and Pictures. (n.d.). Retrieved January 4, 2023, from 
  6. Josiah Willard Gibbs | (n.d.). Retrieved January 4, 2023, from 

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