54 Brouncker, Lord William

Briggs graduated from St. John’s College of Cam-

bridge University in 1581 with a master’s degree and

was appointed a lectureship at the same institution 11

years later in 1592 to practice both medicine and math-

ematics. Four years later Briggs became the first profes-

sor of geometry at Gresham College, London, when he

also developed an avid interest in astronomy.

Around this time Napier had just developed his

theory of logarithms as a mathematical device specifi-

cally aimed at assisting astronomers with difficult arith-

metical computations. Briggs read Napier’s text on the

subject in 1614 and, with keen excitement, arranged to

visit the Scottish scholar in the summer of 1615. The

two men agreed that the theory of logarithms would

indeed be greatly simplified under a base-10 system,

and two years later Briggs published his first tables of

logarithmic values in Logarithmorum chilias prima

(Logarithms of numbers 1 to 1,000). Later, in his

famous 1624 piece, Briggs published logarithmic values

for the numbers 1 through 20,000 and from 90,000 to

100,000. (The gap of 70,000 numbers was filled three

years later by the two Dutch scholars, Adriaan Vlacq

and Ezechiel de Decker.)

Briggs was appointed chair of geometry at Oxford

University in 1619. He remained at Oxford pursuing

interests in astronomy and classical geometry until his

death on January 26, 1630. In his inaugural lecture at

Gresham College, I

SAAC

B

ARROW

(1630–77) expressed

gratitude on behalf of all mathematicians for the out-

standing work Briggs had accomplished through the

study of logarithms.

Brouncker, Lord William (ca. 1620–1684) British

Calculus William Brouncker is best remembered for

his work in the early development of

CALCULUS

and

also as one of the first mathematicians in Britain to use

CONTINUED FRACTION

s.

Very little is known of Brouncker’s early life,

including the exact year of his birth, for example, and

his nationality. Records do show, however, that he

entered Oxford University at the age of 16 to study

mathematics, languages, and medicine. He received a

doctorate of medicine in 1647, pursuing mathematics

and its applications to music, mechanics, and experi-

mental physics as an outside interest throughout his life.

Brouncker held Royalist views and took an active

part in the political turmoil of the time in England.

With the restoration of the monarchy in 1660 and the

election of King Charles II to the throne, Brouncker was

appointed chancellor to Queen Anne and keeper of the

Great Seal. Brouncker was also appointed president of

the newly created R

OYAL

S

OCIETY

of London in 1662.

In mathematics, Brouncker studied infinite

SERIES

and made a number of remarkable discoveries. He

devised a series method for computing

LOGARITHM

s

and a surprising continued-fraction expression for π:

Brouncker used this formula to correctly calculate the

value of πto the 10th decimal place. The great English

mathematician J

OHN

W

ALLIS

later published these

results on Brouncker’s behalf.

Brouncker also studied

DIOPHANTINE EQUATION

s

and found a general method for solving equations of

the form nx2+ 1 = y2. L

EONHARD

E

ULER

later called

this equation “Pell’s equation,” after English mathe-

matician John Pell (1611–84), not realizing that it was

Brouncker, not Pell, who had studied it so intensively.

Pell’s name, unfortunately, remains attached to this

equation to this day.

Brouncker died on April 5, 1684, in London, Eng-

land. He never received fame as a great mathematician

for he tended to focus on solving problems posed by

others rather than forging original pathways in mathe-

matics research.

brute force The method of establishing the validity

of a claim by individually checking each and every

instance of the claim is called brute force. Mathemati-

cians much prefer devising general arguments and prin-

ciples to demonstrate the validity of a claim, rather

than resort to this method. Some claims, however, seem

amenable only to the technique of brute force. For

instance, the following number-naming puzzle can be

solved only via brute force:

Think of a number between one and 100.

Count the number of letters in its name to

obtain a second number. Count the number of

letters in the name of the second number to