The Friendship Theorem If every pair of people in a group have exactly one friend in common, then there’s always one person who is a friend to everyone. This rather heartwarming fact was proven by Paul Erdös, Alfréd Rényi, and Vera T. Sós in 1966. It’s sometimes more cynically known as the paradox of the politician. The Erdös proof uses combinatorics and linear algebra, but in 1972 Judith Longyear published a proof using elementary graph theory.
Nicolaus Bernoulli born on 21 October 1687 in Basel was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. In his early years he worked on probability theory in law. Then he focused on differential equations and geometry. His most important contributions is St. Petersburg Paradox ( a paradox related to probability and decision theory in economics). He also communicated with Gottfried Wilhelm Leibniz and Leonhard Euler.
Bertrand’s box paradox is a classic paradox of elementary probability theory, first posed by Joseph Bertrand in his Calcul des probabilités (1889).There are three boxes: a box containing two gold coins, a box containing two silver coins, and a box containing one gold coin and one silver coin. After choosing a box at random and withdrawing one coin at random, if that happens to be a gold coin, what is the probability that the remaining coin in the box is gold as well?