His earliest mathematical work was on projective geometry; he wrote a significant treatise on the subject of conic sections at the age of 16.

He later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science.

He made important contributions to the study of fluids, and clarified the concepts of pressure and vacuum by generalising the work of Evangelista Torricelli.

Following Torricelli and Galileo Galilei, in 1647 he rebutted the likes of Aristotle and Descartes who insisted that nature abhors a vacuum.

When assured by Mersenne that it was, indeed, the product of the son and not the father, Descartes dismissed it with a sniff: "I do not find it strange that he has offered demonstrations about conics more appropriate than those of the ancients," adding, "but other matters related to this subject can be proposed that would scarcely occur to a 16-year-old child.

[citation needed] Like so many others, Étienne was eventually forced to flee Paris because of his opposition to the fiscal policies of Richelieu, leaving his three children in the care of his neighbour Madame Sainctot, a great beauty with an infamous past who kept one of the most glittering and intellectual salons in all France.

Of the eight Pascalines known to have survived, four are held by the Musée des Arts et Métiers in Paris and one more by the Zwinger museum in Dresden, Germany, exhibit two of his original mechanical calculators.

Partly because it was still quite cumbersome to use in practice, but probably primarily because it was extraordinarily expensive, the Pascaline became little more than a toy, and a status symbol, for the very rich both in France and elsewhere in Europe.

John Ross writes, "Probability theory and the discoveries following it changed the way we regard uncertainty, risk, decision-making, and an individual's and society's ability to influence the course of future events.

The account, written by Périer, reads: The weather was chancy last Saturday...[but] around five o'clock that morning...the Puy-de-Dôme was visible...so I decided to give it a try.

Several important people of the city of Clermont had asked me to let them know when I would make the ascent...I was delighted to have them with me in this great work... ...at eight o'clock we met in the gardens of the Minim Fathers, which has the lowest elevation in town....First I poured 16 pounds of quicksilver...into a vessel...then took several glass tubes...each four feet long and hermetically sealed at one end and opened at the other...then placed them in the vessel [of quicksilver]...I found the quick silver stood at 26" and 3+1⁄2 lines above the quicksilver in the vessel...I repeated the experiment two more times while standing in the same spot...[they] produced the same result each time...

"[36] Blaise Pascal Chairs are given to outstanding international scientists to conduct their research in the Ile de France region.

The elder Pascal "would not let anyone other than these men attend him...It was a good choice, for the old man survived and was able to walk again..."[38] However treatment and rehabilitation took three months, during which time La Bouteillerie and Deslandes had become regular visitors.

Pascal fell away from this initial religious engagement and experienced a few years of what some biographers have called his "worldly period" (1648–54).

[44] His belief and religious commitment revitalized, Pascal visited the older of two convents at Port-Royal for a two-week retreat in January 1655.

Beginning in 1656–57, Pascal published his memorable attack on casuistry, a popular ethical method used by Catholic thinkers in the early modern period (especially the Jesuits, and in particular Antonio Escobar).

Pascal denounced casuistry as the mere use of complex reasoning to justify moral laxity and all sorts of sins.

Pascal's use of humor, mockery, and vicious satire in his arguments made the letters ripe for public consumption, and influenced the prose of later French writers like Voltaire and Jean-Jacques Rousseau.

Charles Perrault wrote of the Letters: "Everything is there—purity of language, nobility of thought, solidity in reasoning, finesse in raillery, and throughout an agrément not to be found anywhere else.

[47] He opposed the rationalism of people like Descartes as applied to the existence of a God, preferring faith as "reason can decide nothing here".

Pascal claimed that only definitions of the first type were important to science and mathematics, arguing that those fields should adopt the philosophy of formalism as formulated by Descartes.

Man is only a reed, the weakest in nature, but he is a thinking reed.Pascal's most influential theological work, referred to posthumously as the Pensées ("Thoughts") is widely considered to be a masterpiece, and a landmark in French prose.

One of the Apologie's main strategies was to use the contradictory philosophies of Pyrrhonism and Stoicism, personalized by Montaigne on one hand, and Epictetus on the other, in order to bring the unbeliever to such despair and confusion that he would embrace God.

In 1659, Pascal fell seriously ill. During his last years, he frequently tried to reject the ministrations of his doctors, saying, "Don't pity me, sickness is the natural state of Christians, because in it we are, as we should always be, in the suffering of evils, in the deprivation of all the goods and pleasures of the senses, free from all the passions that work throughout the course of life, without ambition, without avarice, in the continual expectation of death.

In response, Pascal wrote one of his final works, Écrit sur la signature du formulaire ("Writ on the Signing of the Form"), exhorting the Jansenists not to give in.

Pascal's last major achievement, returning to his mechanical genius, was inaugurating one of the first land-based public transport services, the carrosses à cinq sols, a network of horse-drawn multi-seat carriages that carried passengers on five fixed routes.

Aware that his health was fading quickly, he sought a move to the hospital for incurable diseases, but his doctors declared that he was too unstable to be carried.

[53] An autopsy performed after his death revealed grave problems with his stomach and other organs of his abdomen, along with damage to his brain.

Despite the autopsy, the cause of his poor health was never precisely determined, though speculation focuses on tuberculosis, stomach cancer, or a combination of the two.

[64]In 2023, Pope Francis released an apostolic letter, Sublimitas et miseria hominis, dedicated to Blaise Pascal, in commemoration of the fourth centenary of his birth.