#### 1761

#### 1763

- Monge begins the study of descriptive geometry.

#### 1764

- Bayes publishes
*An Essay Towards Solving a Problem in the Doctrine of Chances* which gives Bayes theory of probability. The work contains the important "Bayes' theorem".

#### 1765

- Euler publishes
*Theory of the Motions of Rigid Bodies* which lays the foundation of analytical mechanics.

#### 1766

#### 1767

- D'Alembert calls the problems to elementary geometry caused by failure to prove the parallel postulate "the scandal of elementary geometry".

#### 1768

#### 1769

- Euler publishes the first volume of his three volume work
*Dioptics*.
- Euler makes Euler's Conjecture, namely that it is impossible to exhibit three fourth powers whose sum is a fourth power, four fifth powers whose sum is a fifth power, and similarly for higher powers.

#### 1770

- Lagrange proves that any integer can be written as the sum of four squares.
- Lagrange publishes
*Réflexions sur la résolution algébrique des équations* which makes a fundamental investigation of why equations of degrees up to four can be solved by radicals. The paper is the first to consider the roots of a equation as abstract quantities rather than numbers. He studies permutations of the roots and this work leads to group theory.
- Euler publishes his textbook
*Algebra*.

#### 1771

- Lagrange proves Wilson's theorem (first stated without proof by Waring) that $n$ is prime if and only if $(n - 1)! + 1$ is divisible by $n$.

#### 1774

- Buffon uses a mathematical and scientific approach to calculate that the age of the Earth is about 75000 years.

#### 1777

- Euler introduces the symbol $i$ to represent the square root of -1 in a manuscript which will not appear in print until 1794.
- Buffon carries out his probability experiment calculating π by throwing sticks over his shoulder onto a tiled floor and counting the number of times the sticks fell across the lines between the tiles.

#### 1779

- Bézout publishes
*Théorie générale des équation algébraiques* on the theory of equations. The work includes a result now known as a result known as "Bézout's theorem".