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18th-Century Mathematician Rankings

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A curated ranking of the 50 most influential mathematicians of the 18th century, chronicling the maturation of calculus, variational mechanics, and probability theory.

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Leonhard Euler (1707–1783) β€” Graph theory, infinitesimal analysis, and unifying modern mathematical notationβ€”
Joseph-Louis Lagrange (1736–1813) β€” Analytical mechanics, calculus of variations, and polynomial root theoryβ€”
Pierre-Simon Laplace (1749–1827) β€” Celestial mechanics, Bayesian probability, and the Laplace transformβ€”
Daniel Bernoulli (1700–1782) β€” Hydrodynamics, kinetic theory of gases, and expected utility theoryβ€”
Jean le Rond d'Alembert (1717–1783) β€” D'Alembert's principle, the wave equation, and fundamental theorem of algebra proofsβ€”
Adrien-Marie Legendre (1752–1833) β€” Legendre polynomials, quadratic reciprocity conjectures, and elliptic integralsβ€”
Gaspard Monge (1746–1818) β€” Descriptive geometry, differential geometry of surfaces, and Monge-AmpΓ¨re equationsβ€”
Johann Heinrich Lambert (1728–1777) β€” Proving pi is irrational, hyperbolic trigonometry, and map projectionsβ€”
Abraham de Moivre (1667–1754) β€” De Moivre's formula connecting trigonometry to complex analysis, and normal approximationβ€”
Thomas Bayes (c. 1701–1761) β€” Formulating Bayes' theorem establishing the foundations of statistical inferenceβ€”
Colin Maclaurin (1698–1746) β€” Maclaurin series expansion, Euler-Maclaurin formula, and defending Newtonian calculusβ€”
Brook Taylor (1685–1731) β€” Taylor's theorem, Taylor series expansions, and early finite difference calculusβ€”
Christian Goldbach (1690–1764) β€” Goldbach's conjecture on primes and foundational correspondence on analysisβ€”
Gabriel Cramer (1704–1752) β€” Cramer's rule for linear systems and algebraic curve singularity classificationβ€”
Alexis Clairaut (1713–1765) β€” Clairaut's theorem on geodesics, singular solutions of ODEs, and earth's geoid shapeβ€”
Γ‰milie du ChΓ’telet (1706–1749) β€” Translation, synthesis, and commentary on Newton's Principia establishing kinetic energy conservationβ€”
Maria Gaetana Agnesi (1718–1799) β€” First systematic calculus treatise integrating differential and integral calculusβ€”
Thomas Simpson (1710–1761) β€” Simpson's rule for numerical quadrature and treatises on fluxions and probabilityβ€”
Edward Waring (1736–1798) β€” Waring's problem in additive number theory and polynomial root boundsβ€”
Johann Bernoulli (1667–1748) β€” Solution to the brachistochrone problem and popularizing infinitesimal analysis across Europeβ€”
Nicolaus I Bernoulli (1687–1759) β€” Formulating the St. Petersburg paradox and early probability limit theoremsβ€”
Nicolaus II Bernoulli (1695–1726) β€” Curves, trajectory differential equations, and early fluid mechanicsβ€”
Johann II Bernoulli (1710–1790) β€” Research on heat propagation, mechanics, and physical mathematicsβ€”
Jacopo Riccati (1676–1754) β€” The Riccati differential equation and pioneering non-linear ODE techniquesβ€”
Vincenzo Riccati (1707–1775) β€” Introducing hyperbolic functions and investigating their differential equationsβ€”
Γ‰tienne BΓ©zout (1730–1783) β€” BΓ©zout's theorem on intersections of algebraic plane curves and resultant determinantsβ€”
Alexandre-ThΓ©ophile Vandermonde (1735–1796) β€” Systematic determinant theory and foundational ideas in topological knot theoryβ€”
Paolo Ruffini (1765–1822) β€” Ruffini's rule and the earliest incomplete proof of the unsolvability of the quinticβ€”
Lazare Carnot (1753–1823) β€” Projective geometry foundations, geometric cross-ratios, and mechanicsβ€”
Gian Francesco Malfatti (1731–1807) β€” Malfatti circles problem and resolving algebraic quintic equationsβ€”
Jean-Γ‰tienne Montucla (1725–1799) β€” Authoring the first definitive, comprehensive history of mathematical sciencesβ€”
Charles Bossut (1730–1814) β€” Influential encyclopedic textbooks in rational mechanics and hydrodynamicsβ€”
Sylvestre FranΓ§ois Lacroix (1765–1843) β€” Standardizing modern calculus curricula with comprehensive multi-volume textbooksβ€”
Roger Cotes (1682–1716) β€” Newton-Cotes quadrature formulas and early logarithmic relations to trigonometryβ€”
John Landen (1719–1790) β€” Landen's transformation in elliptic integrals and residual analysisβ€”
Jurij Vega (1754–1802) β€” High-precision logarithmic tables standardizing ballistics and engineering calculationsβ€”
Benjamin Banneker (1731–1806) β€” Self-taught astronomer calculating complex planetary ephemerides and eclipse cyclesβ€”
John Playfair (1748–1819) β€” Playfair's axiom reformulating Euclid's parallel postulate and geological physicsβ€”
Matthew Stewart (1717–1785) β€” Stewart's theorem regarding triangle cevian lengths and planetary distance geometriesβ€”
Charles Hutton (1737–1823) β€” Calculation of the Earth's mean density in the Schiehallion experiment and mathematical tractsβ€”
Franz Aepinus (1724–1802) β€” Mathematical formalization of the action-at-a-distance theory for electrostatics and magnetismβ€”
William Emerson (1701–1782) β€” Treatises systematizing fluxions, mechanics, and Newtonian navigation mathβ€”
Giovanni Salvemini / Castillon (1708–1791) β€” Castillon's problem in geometry and algebraic analysis of conic sectionsβ€”
Patrick d'Arcy (1725–1779) β€” Formulating variational principles in dynamics and early angular momentum conservationβ€”
Antoine Deparcieux (1703–1768) β€” Actuarial mathematics, life tables, and empirical mortality curvesβ€”
Charles-RenΓ© Reyneau (1656–1728) β€” Authoring Analyse DΓ©montrΓ©e to synthesize Cartesian algebra with differential calculusβ€”
Pierre Bouguer (1698–1758) β€” Heliometer invention, optical photometry attenuation law, and naval geometryβ€”
Abraham Gotthelf KΓ€stner (1719–1800) β€” Influential geometric textbooks and critical early inquiries into non-Euclidean parallel axiomsβ€”
Pierre Varignon (1654–1722) β€” Varignon's theorem on vector polygons and formalizing Newtonian force balance via calculusβ€”
Carl Friedrich Gauss (1777–1855) β€” Construction of the regular 17-gon (1796) and fundamental theorem of algebra proof (1799)β€”