1642 – 1727
Architect of the Principia and the calculus of fluxions — who unified terrestrial and celestial mechanics and transformed mathematics, optics, and physics
During 18 months of plague isolation at Woolsthorpe, Newton developed:
• The calculus of fluxions
• The generalized binomial theorem
• The theory of colours (prism experiments)
• The inverse-square law of gravitation
Perhaps the most productive period in the history of science by a single individual.
At age 26, Newton succeeded Isaac Barrow as Lucasian Professor of Mathematics at Cambridge, a position he held for 33 years. He lectured on optics, algebra, and the Principia.
Published with financial support from Edmond Halley. Three books presenting the laws of motion, the law of universal gravitation, and their application to the solar system. Perhaps the most important scientific work ever written.
Published after Hooke's death (Newton feared his criticism). Established the corpuscular theory of light, the nature of colour, and diffraction phenomena.
Appointed Warden (then Master) of the Royal Mint, overseeing the Great Recoinage. Newton pursued counterfeiters with prosecutorial zeal. Became wealthy and socially prominent.
Newton conceived quantities as flowing (fluents) and their rates of change as fluxions. If x is a fluent, then ẋ is its fluxion (our dx/dt).
Newton extended the binomial theorem to non-integer exponents, obtaining infinite series:
(1+x)r = 1 + rx + r(r-1)x²/2! + r(r-1)(r-2)x³/3! + ...
Valid for |x| < 1 and any real r. This gave him a universal tool for computation.
The Philosophiae Naturalis Principia Mathematica (1687) established:
Remarkably, Newton wrote the Principia using geometric language, not the algebraic calculus he had invented. He proved results using limiting geometric arguments.
Scholars debate this. Newton may have wanted to reach a wider audience trained in Euclid, or he may have found geometric arguments more rigorous than his still-developing algebraic methods. The geometric proofs are often more elegant but harder to generalize.
Newton was the first to tackle the gravitational interaction of three bodies (Sun-Earth-Moon). He found it enormously difficult — reportedly saying it made his head ache. This problem remains unsolvable in closed form today.
Proved that white light is a mixture of colours, each with a different refrangibility. A second prism could not further decompose a single colour, proving colours are fundamental properties of light.
Invented the Newtonian reflector, using a concave mirror instead of a lens to avoid chromatic aberration. This design remains in use in modern astronomy.
Discovered the interference pattern created by a convex lens placed on a flat surface — ironically, these are a wave phenomenon, yet Newton maintained a corpuscular theory of light.
Newton argued light consists of particles, not waves (contra Huygens). This view dominated for a century until Young's double-slit experiment (1801). Modern quantum mechanics vindicates both views.
Start from physical or mathematical phenomena
Express as flowing quantities (fluents & fluxions)
Use infinite series to compute difficult quantities
Check against geometric proof or experiment
"I do not feign hypotheses." Newton insisted on deriving results from mathematical law and observation, not speculative mechanisms. When asked what causes gravity, he refused to guess — the inverse-square law was enough.
Newton hoarded results for decades, publishing only when forced by priority disputes. The calculus, developed in 1665–66, was not properly published until 1704–11. This trait led directly to the bitter priority war with Leibniz.
The most acrimonious dispute in the history of mathematics pitted Newton against Gottfried Wilhelm Leibniz.
"Taking mathematics from the beginning of the world to the time when Newton lived, what he had done was much the better half."
— Leibniz (despite the feud, acknowledging Newton's genius)British mathematics stagnated for over a century, clinging to Newton's cumbersome fluxional notation while Continental mathematicians using Leibniz's notation (dx, ∫) made revolutionary advances: the Bernoullis, Euler, Lagrange, Laplace.
Newton's work on power series, the binomial theorem, and the fundamental theorem of calculus are cornerstones of modern real analysis. Every student of mathematics learns Newtonian calculus.
Newton's method for root-finding remains one of the most important algorithms in computational mathematics, used in virtually every scientific computing application.
Newtonian mechanics remains the foundation for engineering, rocket science, and everyday physics. Only at relativistic speeds or quantum scales do we need Einstein or Schrödinger.
Newton's forward and backward difference formulas, and Newton-Cotes quadrature rules, remain fundamental in numerical methods and data science.
Every rocket trajectory is computed using Newton's laws of motion and gravitation. Apollo missions relied on Newtonian orbital mechanics.
Newton's second law (F=ma) and the calculus of continuous media underpin all structural analysis in civil and mechanical engineering.
Newton's method and its variants (quasi-Newton, BFGS) are core optimization algorithms used to train neural networks and fit statistical models.
The Navier-Stokes equations governing fluid flow are direct descendants of Newton's second law applied to continuous media.
GPS satellite orbits are predicted using Newtonian mechanics (with relativistic corrections), while signal timing uses calculus-based integration.
Newton's theory of colour and his reflecting telescope design remain foundational for optical engineering, spectroscopy, and astronomical instrumentation.
Richard Westfall (1980). The definitive biography — magisterial in scope, covering Newton's science, personality, and obsessions in extraordinary detail.
Isaac Newton, trans. I. Bernard Cohen & Anne Whitman (1999). The authoritative modern translation with extensive guide.
James Gleick (2003). An accessible and elegant popular biography capturing Newton's brilliance and strangeness.
D.T. Whiteside, ed. (1967–81). The complete mathematical manuscripts with detailed commentary. The scholarly standard.
Jed Buchwald & Mordechai Feingold (2013). Examines Newton's lesser-known chronological and historical researches.
Rob Iliffe (2017). Explores Newton's theological writings, which he considered as important as his scientific work.
"If I have seen further, it is by standing on the shoulders of giants."
— Isaac Newton, letter to Robert Hooke (1675)Isaac Newton · 1642–1727 · The Principia and the Calculus