log listing over 675 specific stars and devised an effec-
tive calendar system that included leap years.
As an extraordinarily well-rounded scholar,
Eratosthenes wrote literary works on the topics of
theater and ethics, and also wrote poetry. His famous
poem “Hermes” was inspired by his studies of
astronomy.
It is believed that Eratosthenes stayed in Alexan-
dria for the entire latter part of his life. The exact date
of his death is not known.
Erdös, Paul (1913–1996) Hungarian Discrete math-
ematics, Number theory Born on March 25, 1913, in
Budapest, Hungary, prolific mathematician Paul Erdös
(pronounced “air-dish”) is remembered as one of the
greatest problem-solvers and problem posers of all
time. With an uncanny ability to create problems that
led to productive new areas of mathematics research,
Erdös is credited as founder of the field of “discrete
mathematics,” the mathematics of computer science.
With no permanent home, Erdös traveled the globe
multiple times throughout his life, collaborating and
writing papers with scholars from all countries. His
colleagues invented the term Erdös number to describe
their close connections to him, assigning an Erdös
number of 1 to all those who had coauthored a paper
with Erdös, the number 2 to those who had worked
with someone who had worked with Erdös, and so on.
According to his obituary in the New York Times, 458
mathematicians can claim an Erdös number of 1, and
over 4,500 scholars an Erdös number of 2.
Erdös entered the University of Budapest in 1930
at the age of 17, and within just a few years, he began
making significant contributions to the field of
NUMBER
THEORY
. At age 20 he discovered a new and elementary
proof of conjecture of Joseph Bertrand (1822–1900),
stating that at least one
PRIME
lies between any number
nand its double 2n. (Russian mathematician P
AFNUTY
L
IVOVICH
C
HEBYSHEV
established the validity of this
claim, by complicated means, in 1850.) Later in life,
Erdös also found an elementary proof of the famous
PRIME NUMBER THEOREM
.
In 1934, at the young age of 21, Erdös was
awarded a Ph.D. in mathematics from the University of
Budapest. Because of his Jewish heritage, Erdös was
forced to leave Hungary, and he accepted the offer of a
postdoctoral fellowship in Manchester, England. As the
situation in Europe worsened, Erdös decided to move
to the United States in 1938.
Erdös never accepted a permanent academic posi-
tion. He preferred to devote his entire waking hours to
the pursuit of mathematics and traveled from one
mathematics conference or seminar to another, building
up a growing circle of collaborators. In the latter part
of his life, Erdös owned nothing more than a suitcase
of clothes and traveled from university to university,
and from the home of one mathematician to another.
He developed a reputation as a brilliant mathematician
and an appalling houseguest. Sleeping only 3 to 5
hours a day, Erdös would often wake his mathematical
hosts at all hours of the night, eager to get cracking on
more mathematical research. By the end of his life,
Erdös had worked on over 1,500 mathematical papers.
He died in Warsaw, Poland, on September 20, 1996.
Erdös won many prizes during his life, including
the 1951 Cole Prize from the American Mathematical
Society for his 1949 paper “On a New Method in Ele-
mentary Number Theory which Leads to an Elemen-
tary Proof of the Prime Number Theorem,” and the
1983 Wolf Prize of $50,000 from the Wolf Foundation.
He was also awarded a salary from the Hungarian
Academy of Sciences. With no need of money, Erdös
often gave it away, either to students in need, or as
prizes for solving problems he had posed, of which
there were many. Mathematicians today are still pub-
lishing papers inspired by those challenges.
error The difference between the approximate value
of a quantity and the true numerical value of that
quantity is called the error of the approximation. There
is some confusion in the literature, however, as to how
to interpret this definition. If xis an approximation of
the value X, then some texts work with the difference
X– xwhen speaking of the error, whereas other texts
use the difference x– X. (Thus, the error in using 3.6
as an approximation for 3.59, say, could be deemed as
either 0.01 or –0.01.) For this reason, many authors
prefer to work with the “absolute error,” |X– x|, and
avoid the issue of sign altogether.
The term error is also used for the uncertainty in a
measurement. For example, one can typically read tem-
perature only to the nearest degree Fahrenheit. Thus a
temperature recording of 75°F should be written, or at
least interpreted as, (75 ±0.5)°F to indicate that there
error 167