Blaise Pascal, according to contemporary observers, suffered migraines in his youth, deplorable health as an adult, and lived much of his brief life of 39 years in pain.

Nevertheless, he managed to make considerable contributions in his fields of interest, mathematics and physics, aided by keen curiosity and penetrating analytical ability.

Probability theory was Pascal's principal and perhaps most enduring contribution to mathematics, the foundations of probability theory established in a long exchange of letters between Pascal and fellow French mathematician Fermat.  While games of chance long preceded both of them, in the wake of probability theory the vagaries of such games could be viewed through the lens of a measurable percentage of certainty, which we have come to refer to as the "odds".

Pascal is pictured overlaid by a Pascal's triangle in which the numbers have been translated to relative color densities.

Pascal created his famous triangle as a ready reckoner for calculating the "odds" governing combinations.

Each number in a Pascal triangle is calculated by adding together the two adjacent numbers in the wider adjacent row.  The sum bf the numbers in any row gives the total arrangement of combinations possible within that group. The numbers at the end of each row give the the "odds" of the least likely combinations, with each succeeding pair of triangles giving the chances of combinations which are increasingly likely.

Though apparently simple and relatively simple to generate, Pascal's triangle holds within itself a complex depth of numerical patterns, applicable to the physical world and beyond, and the theory of probabilities has found increasingly wide application in modern mathematics and sciences, extending well beyond seemingly simple games of chance.

Pascal also did seminal work in the field of binomial coefficients which in some senses paved the way for Newton's discovery of the general binomial theorem for fractional and negative powers.

Pascal is also considered the father of the "digital" calculator. In 1642, at the age of 19, Pascal had invented the first digital calculator, the "Pascaline". 

Mechanical calculators based on a logarithmic principle had already been constructed years previously by the mathematician Shickard, who had built machines to calculate astronomical dates, Hebrew grammar, and to assist Kepler with astronomical calculations.

Pascal's device, capable of adding two decimal numbers, was based on a design described in Greek antiquity by Hero of Alexandria. It employed the principle of a one tooth gear engaging a ten-tooth gear once every time it revolved. Thus, it took ten revolutions of the first gear in order to make next gear rotate once. The train of gears produced mechanically an answer equivalent to that obtained using manual arithmetic.

Pascal's mechanical calculating device offered significant improvement over manual calculations,

Unfortunately, Pascal's invention served primarily as an early lesson in the vagaries of business, and the problems of new technology. Pascal himself was the only one who could repair the device, and the cost of the machine cost exceeded the cost of the people it replaced.  The people themselves objected to the very idea of the machine, fearing loss of their skilled jobs.

Pascal worked on the "Pascaline" digital calculator for three years -- from 1642 to 1645 -- and produced approximately 50 machines, before giving up.

The world would have to wait another 300 years for the electronic computer. The principle used in Pascal's calculator was eventually used in analog water meters and odometers.