Wallis, John (1616–1703) British Calculus Born on

November 23, 1616, in Kent, England, mathematician

John Wallis is remembered for his substantial contribu-

tions to the early development of

CALCULUS

, which laid

the groundwork for S

IR

I

SAAC

N

EWTON

(1642–1727)

to later fully develop the subject. His contributions to

mechanics also helped Newton formulate the laws of

motion. He was considered the leading English mathe-

matician of his time.

Wallis had little exposure to mathematics during

the early part of his life. He received a bachelor of arts

degree in 1637 and a master’s degree in 1640 in theol-

ogy and was ordained as a minister in 1640.

By happenstance, while working as chaplain during

the time of civil unrest in England, Wallis discovered

that he could easily decipher the coded messages parish-

ioners shared with him. This demonstrated a talent for

mathematical thinking, and Wallis was soon hired by

the Parliamentarians to decode Royalist messages.

During this time Wallis read the works of

J

OHANNES

K

EPLER

and B

ONAVENTURA

C

AVALIERI

and

others, and developed an interest to expand on the

ideas of infinitesimal calculus as developed by these

authors. In 1656 Wallis wrote his influential text Arith-

metica infinitorum (Infinite series), which contains,

among many things, his famous product formula for .

Wallis also studied and wrote on the topics of

CONIC

SECTIONS

and

ALGEBRA

. He was the first to explain

the meaning of zero, negative, and fractional powers

π

–

2

528

W

John Wallis, an eminent mathematician of the 17th century,

used infinitesimals to develop important techniques of compu-

tation. Sir Isaac Newton built much of his development of cal-

culus on Wallis’s ideas. (Photo courtesy of the Science

Museum, London/Topham-HIP/The Image Works)