Sir Isaac Newton (1643–1727) is probably the most influential mathematician-scientist in history. He co-invented calculus, formulated the laws of motion and universal gravitation, and wrote the Philosophiæ Naturalis Principia Mathematica — the book that made modern physics possible.
Life
Newton was born in Woolsthorpe, Lincolnshire, prematurely and so small that his mother said he would have fit in a quart mug. His father died before he was born, and his mother remarried when Isaac was three, leaving him to be raised by his grandmother. He was a quiet, obsessive child.
He entered Trinity College, Cambridge in 1661. When the plague closed the university in 1665, he returned home and spent an annus mirabilis — the “year of wonders” — during which he made fundamental discoveries in optics, calculus, and gravitation. He was 23.
He returned to Cambridge, became Lucasian Professor of Mathematics in 1669, published the Principia in 1687, and later served as Warden and Master of the Royal Mint. He was knighted in 1705 and died in 1727 at age 84.
Contributions
Calculus
Newton developed what he called the method of fluxions around 1665–1666 — a systematic treatment of rates of change (derivatives, though he didn’t call them that) and accumulated quantities (integrals). He used it to compute tangent lines, areas under curves, centers of mass, and planetary orbits.
Newton didn’t publish his calculus promptly. Most of it appeared only in the 1693 De quadratura curvarum and in the Principia itself. Meanwhile, Gottfried Wilhelm Leibniz — working independently in Germany — developed an equivalent theory, with better notation, in the 1670s. The resulting priority dispute consumed both men’s later years.
History agrees they both discovered calculus independently. Modern notation is Leibniz’s (dy/dx, ∫); the underlying theorems are identical.
The Generalized Binomial Theorem
While still a student, Newton extended the binomial theorem — known for positive integer exponents — to arbitrary real exponents. For fractional and negative powers, the expansion becomes an infinite series, which Newton handled with confident formal manipulation. This was his first major published result.
The Principia
Published in 1687, Philosophiæ Naturalis Principia Mathematica is a three-volume treatise that:
- States the three laws of motion (inertia, , action-reaction)
- States the law of universal gravitation (every mass attracts every other mass with force )
- Derives Kepler’s laws of planetary motion as consequences
The Principia is the founding document of classical mechanics. For the first time, the motion of Earth-bound objects (falling apples) and celestial objects (the moon, the planets) was explained by a single mathematical framework. This unification — the demonstration that the heavens obey the same laws as the Earth — was one of the greatest intellectual events in human history.
Optics
Newton’s book Opticks (1704) established the corpuscular theory of light, demonstrated that white light is a mixture of colors, and laid out the experimental method of modern physics.
Legacy
Newton transformed mathematics and physics from a collection of clever results into a unified deductive science. His methods dominated both subjects until the 19th century (for mathematics) and until Einstein (for physics).
He was buried in Westminster Abbey with an inscription ending: Let Mortals rejoice That there has existed such and so great an ornament of the human race.
Known for
- Co-invention of calculus
- Laws of motion and universal gravitation
- The Generalized Binomial Theorem
- Philosophiæ Naturalis Principia Mathematica
Frequently asked
Did Newton invent calculus?
Yes, around 1665–1666. He developed what he called the method of fluxions. Gottfried Wilhelm Leibniz developed an equivalent theory independently about a decade later. A bitter priority dispute between their followers poisoned Anglo-Continental mathematics for over a century.
What is Newton's most lasting contribution?
The Principia, published in 1687. It showed that the motion of the planets and the falling of an apple obey the same mathematical laws, and it presented those laws in a form that shaped physics for 220 years — until Einstein.
Was Newton really an alchemist too?
Yes. He spent much of his career on alchemy and on interpreting biblical prophecy. Economist John Maynard Keynes, examining Newton's unpublished papers, called him 'not the first of the age of reason' but 'the last of the magicians.'