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John WallisEnglish mathematician
Date of Birth: 03.12.1616
Country:  Great Britain |
Content:
- Early Life and Education
- University and Religious Career
- Mathematical Research and Oxford Professorship
- John Wallis: A Mathematical Giant
- Royal Patronage and Royal Society
- Contributions to Mathematical Analysis
- Cavalieri's Method of Indivisibles
- Practical Mathematics
- Influence on Newton
- Other Contributions
Early Life and Education
John Wallis, an English mathematician and one of the forebears of mathematical analysis, was born in Ashford, Kent, as the son of a clergyman. Exhibiting exceptional mathematical abilities from a young age, he astounded onlookers by extracting the square root of a 53-digit number mentally. Despite his mathematical prowess, Wallis received no formal mathematical education, pursuing it independently.
University and Religious Career
In 1632, Wallis matriculated at Emmanuel College, Cambridge, where he excelled in mathematics and received his master's degree. Upon his ordination as an Anglican clergyman, he faced the university's requirement of celibacy. Following his marriage in 1645, he left Cambridge.
Mathematical Research and Oxford Professorship
Notwithstanding his departure from the university, Wallis continued his mathematical endeavors. He mastered Latin, Greek, and Hebrew, enabling him to study the works of Descartes and Oughtred. In 1647-1648, he embarked on original mathematical investigations. During the English Revolution, he gained fame for deciphering intercepted letters from royalists. However, Wallis opposed the execution of King Charles I.
John Wallis: A Mathematical Giant
In 1649, Wallis' mathematical reputation earned him an invitation to fill the vacant geometry professorship at Oxford, which he held until his death in 1703. He also served as the esteemed Keeper of the University Archives.
Royal Patronage and Royal Society
With the Restoration of the monarchy in 1660, Wallis garnered the favor of King Charles II and became his royal chaplain. He played a pivotal role in the establishment of the Royal Society of London in 1660, becoming one of its founding members. Wallis passed away in Oxford and was laid to rest at St. Mary's Church.
Contributions to Mathematical Analysis
The Arithmetic of InfinitesIn 1655, Wallis published his seminal work, "Arithmetica Infinitorum." In it, he introduced the symbol for infinity and provided a rigorous definition of the limit of a variable. Wallis extended Descartes' ideas, introduced negative abscissas, and calculated sums of infinite series, effectively using integral sums despite the concept of an integral being尚未提出。
Cavalieri's Method of Indivisibles
In his "Treatise on Conic Sections," an appendix to "Arithmetica Infinitorum," Wallis adapted Cavalieri's "Method of Indivisibles" to an algebraic approach using the concept of infinitesimals. He also calculated definite integrals for power functions and related functions. Wallis initiated the study of conic sections as plane curves, employing not only Cartesian but also oblique coordinates.
Practical Mathematics
Throughout his mathematical career, Wallis emphasized practical and computational aspects, often neglecting rigorous proofs. He published his university lectures on algebra as "Mathesis Universalis" in 1657, creatively synthesizing algebraic advancements from Vieta to Descartes. His "Treatise on Algebra" (1685) expanded upon these concepts, introducing a comprehensive theory of logarithms, binomial expansions, and approximation methods. Wallis gave the first modern definition of logarithms as the inverse operation of exponentiation.
Influence on Newton
Wallis's work had a profound impact on Isaac Newton. It was in letters to Wallis that Newton first openly formulated the principles of his differential calculus in 1692. Wallis published these letters in a reprint of his "Treatise on Algebra" (1693).
Other Contributions
Beyond his mathematical achievements, Wallis made significant contributions in diverse fields, including logic, English grammar, deaf education, theology, and philosophy.
