Life Stories | John Wallis (1616-1703)

John Wallis, by Sir Godfrey Kneller, Bt (died 1723).

After Godfrey Kneller, Public domain, via Wikimedia Commons

Imagine a 15-year-old boy, home on holiday, who finds a mysterious arithmetic book in his brother’s hands. Intrigued by its symbols, he borrows it—and within two weeks, has mastered its secrets. This was John Wallis, born in 1616 in Ashford, England. Though originally steered toward a career in medicine, his passion for numbers couldn’t be tamed. He went on to Emmanuel College, Cambridge, and even defended the then-radical idea of blood circulation during academic disputation—a glimpse of the bold intellect he would become.

Despite entering the clergy and aiding the Puritan party as a codebreaker during England’s civil unrest, Wallis’s heart belonged to mathematics. In 1649, against the odds and political friction, he was appointed Savilian Professor of Geometry at Oxford, where he remained until his death in 1703.

Wallis’s mathematical influence was profound. His groundbreaking book Arithmetica Infinitorum (1656) revolutionized how mathematicians approached curves, series, and areas. He introduced infinite series as a practical tool, systematized the work of Descartes and Cavalieri, and laid the groundwork for what would later become integral calculus. Though he lacked the binomial theorem, he ingeniously used interpolation—a method of estimating unknown values—to approximate solutions and even developed an early version of what we now recognize as Wallis’s formula for π.

In his 1655 work De Sectionibus Conicis, Wallis used this symbol to represent the concept of infinity, a notation that has since become standard in mathematics.

He didn’t stop at pure math. Wallis was among the first to explore dynamics, momentum, and collisions in physics. Alongside contemporaries like Wren and Huygens, he theorized about motion and force, including bodies that weren’t perfectly elastic—a step toward the law of conservation of momentum.

He also championed education for the deaf, devised teaching systems for them, and published one of the first systematic works on algebra, introducing notation that modern scientists would recognize instantly—like the formula s = vt.

Yet, Wallis had quirks. He found the concept of negative numbers absurd, believing they were “greater than infinity.” Still, he advanced mathematical notation far beyond his time and nurtured talents like William Neil, who would help solve problems like curve rectification once thought impossible.

John Wallis wasn’t just a mathematician—he was a visionary who dared to write the rules of modern science long before the Enlightenment made it fashionable.

References:

  • MacTutor History of Mathematics. “John Wallis - Biography.” University of St Andrews. 

  • Wikipedia contributors. “John Wallis.” Wikipedia, The Free Encyclopedia.

  • Oxford Mathematical Institute. “John Wallis (1616–1703), Oxford’s Savilian Professor.”

For a visual exploration of Wallis’s contributions, you might find the following video  informative.

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