# Mathematician:Blaise Pascal

## Contents

## Mathematician

French mathematician and philosopher who explored probability theory and projective geometry.

Most famous for the construction now commonly known as Pascal's Triangle.

Also known for:

- Inventing the wrist watch
- Age 17 -- 19: Inventing the calculating machine
- Age 23: Progressing the concept of the mercury-tube barometer (extending and confirming Evangelista Torricelli's work). Used it to observe the difference in atmospheric pressure according to the weather, and also (by a famous experiment performed on Puy de Dôme), according to differences in altitude
- Inventing the syringe (as a byproduct of his work on the barometer)
- Organising the first public transportation system
- Solving De Méré's Paradox

Said to have mastered Euclid's *The Elements* at a young age, but some of the legends often quoted can be considered as no more than boasting engendered of sibling pride.

Son of Étienne Pascal.

A member of the informal Académie Parisienne.

## Nationality

French

## History

- Born: June 19, 1623, Clermont (now Clermont-Ferrand), Auvergne, France
- 1631: Moved to Paris
- 1646: Experienced his "first conversion", when he felt compelled to turn away from the world towards God, but this did not last
- 1654: Had a second religious vision, which again turned him away from mathematics and towards mysticism
- 1658: Briefly returned to mathematics as a way of taking his mind off a toothache
- Died: August 19, 1662, Paris, France of a brain tumour and stomach cancer.

## Theorems and Definitions

- Pascal's Wager (employing probability theory to answer deep philosophical questions)
- Pascal's Triangle
- Pascal's Law (a physical law lying at the basis of hydrostatics)
- Pascal's Rule
- Pascal's Theorem (concerning a hexagon inscribed in a conic section)
- Pascal's Mystic Hexagram

Results named for **Blaise Pascal** can be found here.

Definitions of concepts named for **Blaise Pascal** can be found here.

## Publications

- 1639:
*Essay pour les Coniques*(in which Pascal's Theorem appears) - 1647:
*Experiences nouvelles touchant le vide* - 1655:
*Traité du Triangle Arithmétique*(in which Pascal's Triangle is discussed) - 1656–7:
*Lettres provinciales*(under a fictitious name) - 1657 or 1658:
*De l'Esprit géométrique* - 1658:
*Traité des Sinus du Quart de Cercle*(Treatise on the Sines of a Quadrant of the Circle) - 1661:
*Écrit sur la signature du formulaire* - Also:
*Pensées*(incomplete at his death)

## Notable Quotes

- On the barometer:
*This knowledge can be very useful to farmers, travellers, etc., to learn the present state of the weather, and that which is to follow immediately, but not to know that which is to come in three weeks.*

*The heart has its reasons that the reason does not know.*

*Men never do evil so completely and cheerfully as when they do it from religious conviction.*

## Critical View

*If only the man could have been human enough to let himself go when his whole nature told him to do so, he might have lived out everything that was in him, instead of smothering the better half of it under a mass of meaningless mysticism and platitudinous observations on the misery and dignity of man.*- -- 1937: Eric Temple Bell:
*Men of Mathematics*: Chapter $\text{V}$

- -- 1937: Eric Temple Bell:

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{V}$: "Greatness and Misery of Man" - 1952: T. Ewan Faulkner:
*Projective Geometry*(2nd ed.) ... (previous) ... (next): $1.1$: Historical Note - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.16$: Pascal ($1623$ – $1662$) - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence