John Wallis, a renowned English mathematician, made significant contributions to the field of mathematics, particularly in the origins of calculus. Born in 1616 in Ashford, Kent, England, Wallis became a highly influential figure in mathematics prior to Isaac Newton’s time. He immersed himself in the study of various subjects during his early school years, including Latin, Greek, Hebrew, logic, and arithmetic. Wallis obtained his B.A. and M.A. degrees from the University of Cambridge in 1637 and 1640, respectively.

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Wallis’ interest in mathematics took root when he encountered William Oughtred’s “Clavis Mathematicae” in 1647. His passion for the subject grew, leading to his appointment as the Savilian professor of geometry at the University of Oxford in 1649. Throughout his life, Wallis engaged in intense mathematical activity, publishing notable works such as “Arithmetic of Infinities,” “Mathesis Universalis,” “Mechanica, sive Tractatus de Motu,” “Tractatus de Sectionibus Conicis,” and “Treatise on Algebra.”

### Key Takeaways:

- John Wallis was an influential English mathematician who made significant contributions to the origins of calculus.
- He studied a wide range of subjects, including Latin, Greek, Hebrew, logic, and arithmetic during his early school years.
- Wallis obtained his B.A. and M.A. degrees from the University of Cambridge.
- His notable works include “Arithmetic of Infinities,” “Mathesis Universalis,” “Mechanica, sive Tractatus de Motu,” “Tractatus de Sectionibus Conicis,” and “Treatise on Algebra.”
- Wallis introduced the concept of negative and fractional exponents and extended Cavalieri’s law of quadrature, making significant contributions to the calculus.

## Early Life and Education of John Wallis

John Wallis, a renowned mathematician, was born in Ashford, Kent, England, in 1616. His father, a respected minister, and his family raised him alongside his four siblings. Wallis began his education in Ashford but later moved to James Movat’s grammar school in Tenterden, Kent, due to a plague outbreak in the area. It was during his time at Movat’s school that Wallis’s intellect and affinity for mathematics began to shine.

In 1631, Wallis continued his education at Felsted School in Essex, where he delved into subjects such as Latin, Greek, and Hebrew. While mathematics was not a primary focus in traditional education at the time, Wallis’s older brother, a skilled mathematician, introduced him to arithmetic during the Christmas holidays in 1631. This introduction to mathematics sparked Wallis’s interest and set him on a path of further exploration.

Following his time at Felsted School, Wallis enrolled at Emmanuel College, Cambridge, in 1632. Throughout his studies, he expanded his knowledge in various fields, including ethics, metaphysics, astronomy, and medicine. In 1637, Wallis earned his Bachelor of Arts degree, and three years later, in 1640, he obtained his Master’s Degree. It was during his years at Cambridge that Wallis nurtured his mathematical interests and began developing his own theories in the field.

“I found solace and fascination in the world of numbers, leading me to explore the intricate beauty of mathematics.” – John Wallis

## Contributions and Achievements of John Wallis

John Wallis was a mathematician who left an indelible mark on the field of mathematics through his groundbreaking contributions. His work in calculus revolutionized the understanding of mathematical concepts and paved the way for future advancements.

In his influential book “Arithmetica Infinitorum,” published in 1656, Wallis expanded on the analysis methods of Descartes and Cavalieri. He introduced the concept of negative and fractional exponents, providing a more comprehensive understanding of mathematical principles. Wallis also introduced the symbol ∞ to represent infinity, a symbol widely used in mathematics today. Additionally, he utilized 1/∞ to represent infinitesimals, opening doors to new possibilities in mathematical calculations.

One of Wallis’ notable achievements was his work on continued fractions. His research in this area significantly advanced the field of calculus and mathematics as a whole. His innovative use of symbolism and rigorous mathematical reasoning greatly influenced future mathematicians, including the renowned Isaac Newton.

Throughout his career, Wallis published extensively across a range of topics, demonstrating his dedication to the pursuit of knowledge. His contributions to theology, logic, English grammar, and philosophy showcased his breadth of expertise and intellectual curiosity. As one of the greatest mathematicians of the early Renaissance period, John Wallis played a vital role in shaping the field of mathematics and continues to inspire generations of mathematicians today.

## FAQ

### What were John Wallis’ major contributions to mathematics?

John Wallis made significant contributions to the origins of calculus and mathematics. He introduced the concept of negative and fractional exponents, extended Cavalieri’s law of quadrature, and developed the concept of using symbols for infinity (∞) and infinitesimals (1/∞). His work on continued fractions also advanced the field of calculus.

### Where was John Wallis born and what was his educational background?

John Wallis was born in Ashford, Kent, England, in 1616. He received his Bachelor of Arts degree in 1637 and his Master’s Degree in 1640 from the University of Cambridge. He studied Latin, Greek, Hebrew, logic, and arithmetic during his early school years.

### What was John Wallis’ career and academic position?

John Wallis was appointed as the Savilian professor of geometry at the University of Oxford in 1649. He held this position until his death in 1703. He engaged in intense mathematical activity during his time at Oxford and published numerous works on various topics, including theology, logic, English grammar, and philosophy.

### How did John Wallis influence the development of mathematics?

John Wallis’ contributions to mathematics, such as his exploration of calculus, innovative use of symbolism, and development of continued fractions, greatly influenced the field. His work laid the foundation for future mathematicians like Isaac Newton and advanced the understanding and application of mathematical concepts.

### What were some of John Wallis’ notable works in mathematics?

Some of John Wallis’ notable works include “Arithmetic of Infinities,” “Mathesis Universalis,” “Mechanica, sive Tractatus de Motu,” “Tractatus de Sectionibus Conicis,” and “Treatise on Algebra.” These works showcase his contributions to the calculus, symbolic representation in mathematics, and the development of mathematical theories.