3.6 Additional Mathematical Methods | 121Blaise Pascal
One of the great historical figures in the world of computing was the French mathematician
and religious philosopher Blaise Pascal (1623–1662), the inventor of one of the earliest known
mechanical calculators.
Pascal’s father, Etienne, was a noble in the French court, a tax collector, and a
mathematician. His mother died when Pascal was three years old. Five years later, the family
moved to Paris, where Etienne took over the education of the children. Pascal quickly showed a
talent for mathematics. When he was only 17, he published a mathematical essay that earned
the jealous envy of René Descartes, one of the founders of modern geometry. (Pascal’s work ac-
tually had been completed before he was 16.) It was based on a theorem, which he called the
hexagrammum mysticum(mystic hexagram) that described the inscription of hexagons in conic
sections (parabolas, hyperbolas, and ellipses). In addition to the theorem (now called Pascal’s
theorem), his essay included more than 400 corollaries.
When Pascal was about 20, he constructed a mechanical calculator that performed addition
and subtraction of eight-digit numbers. That calculator required the user to dial in the numbers
to be added or subtracted; the sum or difference then appeared in a set of windows. His
motivation for building this machine may have been to aid his father in collecting taxes. The
earliest version of the machine does, indeed, split the numbers into six decimal digits and two
fractional digits, as would be used for calculating sums of money. It was hailed by his contem-
poraries as a great advance in mathematics, and Pascal built several more forms of his calcula-
tor. It achieved such popularity that many fake, nonfunctional copies were built by others and
displayed as novelties. Several of Pascal’s calculators still exist in various museums.
Pascal’s box, as it is called, was long believed to be the first mechanical calculator. However,
in 1950, a letter from Wilhelm Shickard to Johannes Kepler written in 1624 was discovered. This
letter described an even more sophisticated calculator built by Shickard 20 years prior to
Pascal’s box. Unfortunately, the machine was destroyed in a fire and never rebuilt.
During his twenties, Pascal solved several difficult problems related to the cycloid curve, in-
directly contributing to the development of differential calculus. Working with Pierre de
Fermat, he laid the foundation of the calculus of probabilities and combinatorial analysis. One
result of this work came to be known as Pascal’s triangle, which simplifies the calculation of
the coefficients of the expansion of (X+ Y)N, where Nis a positive integer.
Pascal also published a treatise on air pressure and conducted experiments showing that
barometric pressure decreases with altitude, helping to confirm theories that had been
proposed by Galileo and Torricelli. His work on fluid dynamics forms a significant part of the
foundation of that field. Among the most famous of his contributions is Pascal’s law, which
states that pressure applied to a fluid in a closed vessel is transmitted uniformly throughout
the fluid.
When Pascal was 23, his father became ill, and the family was visited by two disciples of
Jansenism, a reform movement in the Catholic Church that had begun six years earlier. The
family converted, and five years later one of his sisters entered a convent. Initially, Pascal was
not so taken with the new movement, but by the time he was 31, his sister had persuaded him
to abandon the world and devote himself to religion. His religious works are considered no less
brilliant than his mathematical and scientific writings. Some consider Provincial Letters, his se-
ries of 18 essays on various aspects of religion, to be the beginning of modern French prose.
Pascal returned briefly to mathematics when he was 35, but a year later his health, which
had always been poor, took a turn for the worse. Unable to perform his usual work, he devoted
himself to helping the less fortunate. Three years later, he died while staying with his sister,
having given his own house to a poor family.