Willard Gibbs was one of the most important scientists of all time. His ideas revolutionized not one, but three different fields of science and mathematics, and are critical to our modern understanding of physics, chemistry, and mathematics.

## Who Was Willard Gibbs?

In 1863, Willard Gibbs received a Ph. D from Yale University – the first person in the history of the United States to receive a doctorate in engineering. Although his thesis focused on the relatively mundane topic of gear design, he would go on to become one of the world’s most prolific scientists, mathematicians, and engineers.

He revolutionized mathematics by developing a new way to work with vectors, did groundbreaking work in statistical mechanics, and created the entire field of chemical thermodynamics.

However, despite his many accomplishments, he remains relatively unknown outside of the scientific community. Who exactly was this remarkable man who did so much to create our modern world?

## Early Life and Education

Willard Gibbs was born in 1839 in New Haven, Connecticut. His father was a literature and linguistics professor at the nearby Yale University. In fact, Gibbs came from a long line of academics, stretching back at least seven generations. As a child, he attended a local grammar school, where he excelled academically, and in 1854, he enrolled as a student at Yale at the age of 15.

At Yale, Gibbs initially studied Latin and mathematics before turning his attention to engineering. After his Ph.D., he continued to work there for the next three years, first as a Latin teacher and then as a Physics teacher.

## Research in Europe

While Gibbs was still a student at Yale, his parents both died. For a while, he continued to live in the family home in New Haven with his sisters, and then in 1866, they decided to spend some time in Europe.

For the next three years, Gibbs studied with some of the most important scientists working at the time, spending a year at the Sorbonne in Paris, followed by two years in Germany at the Universities of Heidelberg and Berlin.

Although this trip to Europe would be one of the only times in his life that he ever left New Haven, it would have a profound impact. His future work was more aligned with that of contemporary European scientists and was ignored by most Americans until much later.

## Work in Thermodynamics

In 1871, he was appointed as the first professor of mathematical physics at Yale, a position he held for the rest of his life. Initially, this position was unpaid, but that was fine with Gibbs. As an unmarried man who spent most of his time at home or work, he had inherited plenty of money from his parents for his modest needs.

Over the next few decades, Gibbs would make several major breakthroughs in science and mathematics, but he initially turned his attention to the science that studies heat and energy, **thermodynamics**.

He wanted to find a way to represent what happened in a chemical reaction mathematically. He therefore developed a new equation that took into account all the variables (temperature, pressure, energy, and volume) that could affect a chemical reaction. This equation, which is still widely used by chemists today, is known as the **Phase rule**.

He also came up with the idea of free energy, which measures the tendency of a system to give off energy and become more disordered. Today, this is known as **Gibbs free energy** in his honor.

In 1878, less than ten years after he returned to Yale, he published a revolutionary paper that laid out the basis of a new science, which we now call chemical thermodynamics. Chemical thermodynamics is used to determine which reactions are possible and forms the basis for modern physical chemistry!

## Invention of Vector Analysis

Around the same time that Gibbs was revolutionizing the study of thermodynamics, another scientist named James Clerk Maxwell was working on developing a new theory of light. Gibbs wanted to teach his students about Maxwell’s new electromagnetic theory, but he found the mathematics used by Maxwell to be difficult to understand and overly complicated.

So what did he do? He invented a new form of mathematics called **vector analysis** that standardized a lot of vocabulary and notation. Today, vector analysis is used extensively in mathematics, physics, and many other fields. We still primarily use the notation first introduced by Gibbs in the 1880s.

## Statistical Mechanics

Not content to invent entirely new fields in mathematics and chemistry, Gibbs now turned his attention to physics. In 1902, he published his last major scientific work, *The Elementary Principles of Statistical Mechanics*.

In it, he proposed a new mathematical framework called **statistical mechanics** that he used to understand the behavior of matter at a macroscopic level, averaging the behavior of very large numbers of atoms and molecules. His ideas would soon be used to connect classical mechanics with the new field of quantum mechanics, making them incredibly important in modern physics.

After spending almost all his life in the same house in New Haven, Connecticut, Willard Gibbs, one of the greatest scientists of all time, died in 1903 at the age of 64.

## Lesson Summary

**Willard Gibbs** (1839 – 1903) was a quiet and reserved American scientist and mathematician. After receiving his doctorate in engineering, he spent three years studying in Europe before dedicating his entire career to Yale University. Willard Gibbs:

- made huge strides in our understanding of
**thermodynamics**(the study of heat and energy) - assisted in developing mathematical equations to describe chemical reactions.
- proposed the idea of
**Gibbs free energy**, which is used to quantify the tendency of systems to give of energy and increase disorder. - invented a new branch of mathematics known as
**vector analysis**, a standard notation that is still used in many fields today. - invented the field of
**statistical mechanics**, which connects the microscopic and macroscopic behavior of matter and was critical in the development of quantum mechanics just a few years after his death.