66 Cauchy, Augustin-Louis

Augustin-Louis Cauchy, an eminent mathematician of the 19th

century, was the first to use the notion of a “limit,” as it is now

known, to develop a sound model of continuity and convergence

in the theory of calculus. (Photo courtesy of the Science

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

B

ERNOULLI FAMILY

was the first to write down the for-

mula for the catenary. Up to constants, it is given by:

This is the hyperbolic cosine function from the set of

HYPERBOLIC FUNCTION

s. Engineers, in designing sus-

pension bridges such as the Golden Gate Bridge in San

Francisco, make extensive use of this function in their

work. The name catenary comes from the Latin word

catena for “chain.”

Cauchy, Augustin-Louis (1789–1857) French Anal-

ysis, Calculus, Number theory Born on August 21,

1789, French scholar Augustin-Louis Cauchy is remem-

bered as one of the most important mathematicians of

his time. With 789 mathematical papers and seven

influential textbooks to his credit, Cauchy made signifi-

cant contributions to the study of

NUMBER THEORY

,

ANALYSIS

,

GROUP THEORY

,

DIFFERENTIAL EQUATION

s,

and

PROBABILITY

. In his famous 1821 text Cours d’ana-

lyse (A course of analysis), Cauchy was the first to pro-

vide an exact, rigorous meaning of the terms derivative

and integral as used in

CALCULUS

through the develop-

ment of the notion of a

LIMIT

. Cauchy also properly

defined the terms continuity and convergence. His insis-

tence on the absolute need for rigor and clarity in all of

mathematics had a lasting effect and set the standards

of rigor required today of all mathematical research.

After graduating from the L’École Polytechnique

in 1807 with a degree in mathematics, Cauchy pur-

sued a career in engineering. Noted as a promising

practitioner in the field, Cauchy was assigned to the

Ourcq Canal project and by age 21 managed to

receive a high-ranking commission in Cherbourg as a

military engineer.

Despite his busy work life, Cauchy continued to

pursue interests in mathematics. In 1811 he proved a

result on the geometry of polyhedra, which he submit-

ted for publication. He received considerable praise for

this accomplishment and decided to change careers and

pursue research in mathematics full time. A year later

he returned to Paris and began looking for a faculty

position at an academic institution. Cauchy was finally

awarded an assistant professorship at the L’École Poly-

technique in 1815.

All the while, Cauchy continued to produce and pub-

lish mathematical results. The same year as his appoint-

ment, Cauchy won the Grand Prize of the L’Académie

Royale des Sciences for his outstanding mathematical dis-

coveries on the theory of waves. This recognition gar-

nered him some notice in the scientific community, but

real fame came to Cauchy when, another year later, he

solved an outstanding problem posed by P

IERRE DE

F

ER

-

MAT

(1601–1665) on the properties of

FIGURATE NUM

-

BERS

. Cauchy had now proved himself an expert in a

surprisingly large number of disparate fields.

Cauchy published an incredible number of papers

during this early period of his life, at a rate of as many

as two a week. He was so prolific that the editors of

the French journal Comptes Rendu imposed a quota on

him. In response, Cauchy persuaded a family member,

who worked in the publishing field, to create a new

journal that contained nothing but papers by him!