Gerolamo Cardano

September 24, 1501 — September 21, 1576

was an Italian Renaissance mathematician, physician, astrologer and gambler

Cardano was notoriously short of money and kept himself solvent by being an accomplished gambler and chess player. His book about games of chance,

Liber de ludo aleae, written in the 1560s, but not published until 1663, contains the first systematic

treatment of probability, as well as a section on effective cheating methods.

Through his correspondence with Blaise Pascal

in 1654, Fermat and Pascal helped lay the fundamental

groundwork for the theory of probability. From this brief but

productive collaboration on the problem of points, they are

now regarded as joint founders of probability theory. Pierre de Fermat

17 August 1601 – 12 January 1665

France

Blaise Pasca June 19, 1623 – August 19, 1662

Jacob Bernoulli

27 December 1654 – 16 August 1705

Jacob is best known for the work

Ars Conjectandi (The Art of Conjecture),

published eight years after his death in 1713

In this work, he described the known results in

probability theory and in enumeration, often

providing alternative proofs of known results.

This work also includes the application of

probability theory to games of chance and his

introduction of the theorem known as the law of large numbers.

Basel, Switzerland

Nicolaus Bernoulli (1623-1708)

Jakob Bernoulli (1654–1705) Nicolaus Bernoulli (1662–1716)

Johann Bernoulli (1667–1748)

Nicolaus I Bernoulli (1687-1759)

Nicolaus II Bernoulli (1695–1726)

Daniel Bernoulli (1700–1782)

Johann II Bernoulli (1710–1790)

Johann III Bernoulli (1744–1807)

Daniel II Bernoulli (1751–1834)

Jakob II Bernoulli (1759–1789)

Abraham de Moivre

France

26 May 1667 – 27 November 1754

De Moivre wrote a book on probability theory,

entitled The Doctrine of Chances. It was said

that his book was highly prized by gamblers. It

is reported in all seriousness that de Moivre

correctly predicted the day of his own death.

Noting that he was sleeping 15 minutes longer

each day, De Moivre surmised that he would die

on the day he would sleep for 24 hours. A simple

mathematical calculation quickly yielded the

date, 27 November 1754. He did indeed pass away on that day.

Pierre-Simon Laplace

23 March 1749 - 5 March 1827

French

In 1812, Laplace issued his

Théorie analytique des probabilités

in which he laid down many fundamental results in statistics.

Johann Carl Friedrich Gauss

30 April 1777 – 23 February 1855

Germany

The normal distribution, also called the Gaussian distribution,

The normal distribution was first introduced by Abraham de Moivre

in an article in 1733, which was reprinted in the second edition of his

The Doctrine of Chances, 1738 in the context of approximating certain

binomial distributions for large n. His result was extended by Laplace

in his book Analytical Theory of Probabilities (1812), and is now called the

theorem of de Moivre-Laplace.

Laplace used the normal distribution in the analysis of errors of experiments.

Its usefulness, however, became truly apparent only in 1809, when the famous

German mathematician K.F. Gauss used it as an integral part of his

approach to prediction the location of astronomical entities. As a result,

it became common after this time to call it the Gaussian distribution.

During the mid to late nineteenth century, however, most statisticians started to

believe that the majority of data sets would have histograms conforming to the

Gaussian bell-shaped form. Indeed, it came to be accepted that it was “normal”

for any well-behaved data set to follow this curve. As a result, following

the lead of the British statistician Karl Pearson, people began referring to

the Gaussian curve to calling it simply the normal curve.

The name "bell curve" goes back to Esprit Jouffret who first used

the term "bell surface" in 1872 for a bivariate normal with independent

components. The name "normal distribution" was coined independently

by Charles S. Peirce, Francis Galton and Wilhelm Lexis around 1875.

Andrey Nikolaevich Kolmogorov

25 April 1903 -- 20 Oct 1987

Moscow, Russia

His monograph on probability theory

Grundbegriffe der Wahrscheinlichkeitsrechnung

published in 1933 built up probability theory in a rigorous way

from fundamental axioms in a way

comparable with Euclid's treatment of geometry.

Buffon's Needle Problem

the French naturalist Buffon in 1733

Buffon's needle problem asks to find the probability that a needle of length

will land on a line, given a floor with equally spaced parallel lines a distance

apart. The problem was first posed by the French naturalist Buffon in 1733

(Buffon 1733, pp. 43-45), and reproduced with solution by Buffon in 1777

Several attempts have been made to experimentally determine

by needle-tossing.

π

Thomas Bayes

1702 - 1761

London, England

Bayes' theorem gives the rule for updating belief in a

Hypothesis H (i.e. the probability of H)

given additional evidence E, and background information (context) I

p(H|E,I) = p(H|I)*p(E|H,I)/p(E|I) [Bayes Rule]

p(H|E,I), is called the posterior probability,

The p(H|I) is just the prior probability of H given I alone

Bayes' theorem is particularly useful for inferring causes from their effects

since it is often fairly easy to discern the probability of an effect given the

presence or absence of a putative cause.

For instance, physicians often screen for diseases of known prevalence

using diagnostic tests of recognized sensitivity and specificity.

The sensitivity of a test, its "true positive" rate, is the fraction of times

that patients with the disease test positive for it.

The test's specificity, its "true negative" rate, is the proportion of healthy

patients who test negative.

one can use to determine the probability of disease given a positive test.

The essence of the Bayesian approach is to provide a mathematical rule

explaining how you should change your existing beliefs in the light of new

evidence. In other words, it allows scientists to combine new data with

their existing knowledge or expertise. The canonical example is to imagine that

a precocious newborn observes his first sunset, and wonders whether the sun will

rise again or not.