These are some of the major contributions that Pascal made to the world of Mathematics and Science:

 
• Essay on Conics - When Pascal was 16, he published his Essay pour les coniques (roughly, Essay on conics), a one page essay proving several theorems, chief among them the theorem that now bears his name: "If a hexagon is inscribed in a circle[or other conic], the three points of intersection of pairs of opposite sides lie on a straight line[, the Pascal Line]." (Burton)
 
• The Pascaline - Before the age of nineteen, upon seeing Etienne exhausting himself over the endless calculations and recalculations of taxes owed and paid, Pascal invented and built a clockwork calculator, known as a Pascaline. Capable of addition and subtraction, this was of particular use to his father in his accounting work. Over the next decade, Pascal would produce about 20 or so machines.
 
• Treatise on the Arithmetical Triangle - Probably his most well-known contribution to mathematics comes from his Traite du triangle arithmetique (Treatise on the Aritmetical Triangle).
 
• Expected Value - Pascal also worked Pierre de Fermat on inventing the theory of probability. This work was prompted by a friend, Chevalier de Mere, and his interest in gambling problems. From this work came the concept and mathematical construct of Expected Value.
 
• Barometrics and Pressure Experiments - Pascal did many experiments dealing with atmospheric pressure and pressure of fliuds in a closed system. This led to the SI unit for pressure (N/m²) being named after him.
 
• History of the Cycloid - Only for a very brief period in 1658 did Pascal return to mathematics, and published History of the Cycloid, along with four Letters, under the pseudonym Amos Dettonville. He discovered that the area of a cycloid was 3 times that of the generating circle. This work was the "immediate inspiration for Liebniz in his invention of the differential and integral calculus." (Burton)