Timeline of Mathematics - 18th Century

18th Century

• 1706 – John Machin develops a quickly converging inverse-tangent series for π and computes π to 100 decimal places,
• 1712 – Brook Taylor develops Taylor series,
• 1722 – Abraham de Moivre states de Moivre's formula connecting trigonometric functions and complex numbers,
• 1724 – Abraham De Moivre studies mortality statistics and the foundation of the theory of annuities in Annuities on Lives,
• 1730 – James Stirling publishes The Differential Method,
• 1733 – Giovanni Gerolamo Saccheri studies what geometry would be like if Euclid's fifth postulate were false,
• 1733 – Abraham de Moivre introduces the normal distribution to approximate the binomial distribution in probability,
• 1734 – Leonhard Euler introduces the integrating factor technique for solving first-order ordinary differential equations,
• 1735 – Leonhard Euler solves the Basel problem, relating an infinite series to π,
• 1736 – Leonhard Euler solves the problem of the Seven bridges of Königsberg, in effect creating graph theory,
• 1739 – Leonhard Euler solves the general homogeneous linear ordinary differential equation with constant coefficients,
• 1742 – Christian Goldbach conjectures that every even number greater than two can be expressed as the sum of two primes, now known as Goldbach's conjecture,
• 1748 – Maria Gaetana Agnesi discusses analysis in Instituzioni Analitiche ad Uso della Gioventu Italiana,
• 1761 – Thomas Bayes proves Bayes' theorem,
• 1761 – Johann Heinrich Lambert proves that π is irrational,
• 1762 – Joseph Louis Lagrange discovers the divergence theorem,
• 1789 – Jurij Vega improves Machin's formula and computes π to 140 decimal places,
• 1794 – Jurij Vega publishes Thesaurus Logarithmorum Completus,
• 1796 – Carl Friedrich Gauss proves that the regular 17-gon can be constructed using only a compass and straightedge
• 1796 – Adrien-Marie Legendre conjectures the prime number theorem,
• 1797 – Caspar Wessel associates vectors with complex numbers and studies complex number operations in geometrical terms,
• 1799 – Carl Friedrich Gauss proves the fundamental theorem of algebra (every polynomial equation has a solution among the complex numbers),
• 1799 – Paolo Ruffini partially proves the Abel–Ruffini theorem that quintic or higher equations cannot be solved by a general formula,