Scientific Discoveries and When They Were Made

Rule that in a right triangle the square on the longest side equals the sum of the other two

Procedure to find the greatest common divisor of two numbers by repeated division and remainders

Irrational number approximately 1.618 appearing in geometry, art and nature through self-similar proportions

Euclid's fifth axiom stating that through a point not on a line exactly one parallel can be drawn

Numbers divisible only by one and themselves, the building blocks of every whole number

Ratio of a circle's circumference to its diameter, studied in many ancient cultures for practical measurements

Quantities less than zero, used for debts in China and India long before Europe would accept them

Expression for the area of a triangle using only the lengths of its three sides

Equations with more unknowns than equations, which admit whole families of integer solutions

Placeholder symbol and number representing absence of quantity, essential for positional numeral systems

Systematic method of solving linear and quadratic equations by balancing operations on both sides

Method for solving equations of the form ax squared plus bx plus c equals zero using radicals

In any triangle the ratio of sides equals the ratio of sines of opposite angles

Series where each number is the sum of the two preceding ones, starting from zero and one

Triangular array of the binomial coefficients, each number the sum of the two above it

Mathematical device that turns multiplication into addition by using exponents of a fixed base

Approach that represents curves and surfaces with algebraic equations on a coordinate plane

Claim that no three whole numbers satisfy a certain equation for any power above two

Numbers built on a square root of minus one, dismissed as impossible and now essential to physics

Framework for assigning numbers to uncertain events and calculating their combined chances

Method for handling rates of change and accumulated quantities, and the language most of physics is written in

Study of networks formed by points connected by lines and the properties of those connections

Integral tool that converts differential equations into algebraic ones for easier solving

Bell-shaped curve that describes how many natural measurements cluster around an average value

Technique for expressing any repeating wave as a sum of simple sine and cosine waves

Geometry built on axioms that replace Euclid's parallel postulate with a different rule

Study of sets closed under an operation that obeys associativity and inverses

Use of the methods of calculus to prove results about whole numbers and primes

Four-part numbers extending the complex numbers, still used to describe rotations in three dimensions

Foundation of mathematics that treats collections of objects as the basic building blocks

Mathematical description of how points evolve under repeated application of a rule

Study of properties that remain unchanged when shapes are stretched or bent without tearing

Rigorous way to assign sizes to sets that generalizes length area and volume

Special number associated with a matrix that shows how much a vector is scaled

Study of vector spaces of functions and the operators acting on them

Sequence of states where the next state depends only on the current one

Proof that any consistent formal system powerful enough for arithmetic contains true statements it cannot prove

Mathematical analysis of strategic decisions where each player's outcome depends on others

Abstract framework that studies mathematical structures through objects and arrows between them

Method for finding the best outcome under a set of linear constraints on the available resources

Measure of how much information a message carries, and of the limits on sending it reliably

Grid of cells that evolve by simple local rules producing complex global patterns

Field showing that tiny changes in starting conditions can produce wildly different outcomes

Geometry of shapes that repeat their own structure at every scale of magnification

Encryption system that lets strangers exchange secret messages without sharing a key beforehand

Waxy solid that glows in the dark after exposure to air and was first prepared by heating urine residues

Dense gray metal first brought from South America and long mistaken for a worthless form of silver

Gas given off by burning, fermenting and breathing, the first shown to be distinct from air itself

The lightest of all gases, which combines with oxygen to form water and was formerly known as inflammable air

Colorless gas forming nearly four fifths of the air, identified as the part that will not support a flame

Greenish gas with a sharp smell obtained by reacting acid with manganese dioxide and once called dephlogisticated muriatic acid

Element making up a fifth of the air, whose isolation ended the theory that burning released a substance called phlogiston

Law that matter is neither created nor destroyed in a reaction, only rearranged into other substances

Proposal that each element is made of identical atoms of a characteristic weight, which combine in whole-number ratios

Process of splitting compounds into elements by passing an electric current through a liquid solution

Soft metal whose compounds are used in fertilizers and whose name comes from potash

Soft reactive metal that gives yellow color to street lamps and is essential in table salt

Violet solid element used in disinfectants and in the production of photographic film

Colorless liquid hydrocarbon whose ring structure became the foundation for understanding aromatic compounds

Red-brown liquid element once used in sedatives and still used in flame retardants

Lightweight metal now used in aircraft, cans and foil, once rarer than gold

Laboratory production of an organic compound from inorganic ingredients, which broke the line drawn between living and dead matter

First synthetic dye, a purple compound that launched the modern chemical industry

Technique of identifying elements by the unique colors they emit when heated in a flame

Lightest noble gas, first identified by its bright yellow spectral line during a solar eclipse

Arrangement of the chemical elements by atomic structure, which groups together those that behave in chemically similar ways

Most abundant noble gas, used in light bulbs to prevent filament oxidation

Inert gas that produces the bright red light in many advertising signs

Highly radioactive metal once used in luminous paints and early cancer treatments

Heavy noble gas used in high-intensity lamps and as an anesthetic in some surgeries

First fully synthetic plastic, made from phenol and formaldehyde under heat and pressure

Method of combining atmospheric nitrogen with hydrogen under pressure to make ammonia, and so fertilizer from air

Scale from zero to fourteen measuring how acidic or alkaline a solution is, each step tenfold

Method of working out where every atom sits in a solid by measuring how it scatters X-rays

Steel alloyed with chromium so that it forms an invisible oxide skin and does not rust

Essential nutrient whose structure was determined after it was isolated from paprika peppers

Most common plastic, used in bags, bottles and pipes because it is cheap and flexible

Strong synthetic polymer first sold as toothbrush bristles and then as women's stockings

Nonstick fluoropolymer discovered accidentally while trying to make a new refrigerant gas

Synthetic insecticide once widely used against malaria mosquitoes before environmental concerns arose

Synthetic radioactive metal made in reactors from uranium, and the material of most nuclear weapons

Carbon molecule shaped like a soccer ball, also called buckyball, with sixty atoms in a closed cage

Single layer of carbon atoms arranged in a hexagonal lattice, known for extreme strength and conductivity

Idea that all matter consists of tiny indivisible particles moving through empty space

System asserting that all bodies seek their natural place and that motion requires continuous force

Rule that a body in fluid is pushed up by a force equal to the weight of fluid it displaces

First accurate estimate of the distance around the planet made by measuring the angle of the Sun at two latitudes

Slow westward shift of the equinox points along the ecliptic caused by Earth's axial wobble

Solar calendar of 365 days with a leap day every fourth year, imposed across the Roman world

Ancient description of the cosmos with Earth fixed at the center and all other bodies circling it

Theory placing the Sun at the center of the known planets with Earth orbiting it once a year

New star that blazed out in 1572 brighter than Venus, proving the heavens were not changeless

Reform of the Julian calendar dropping three leap days every four centuries to stop Easter drifting

Four largest moons of Jupiter discovered by Galileo showing that not everything orbits the Earth

Three mathematical rules describing the motion of planets around the Sun in elliptical orbits with varying speeds

Rule that pressure of a gas is inversely proportional to its volume at constant temperature

First demonstration that light takes time to travel, measured from the timing of Jupiter's moons

Three fundamental rules governing how objects move when forces act upon them including inertia and action reaction

Law that every mass attracts every other in proportion to their masses and inversely to the distance squared

Idea that light travels as waves rather than particles explaining interference and diffraction phenomena

Newton's view that light consists of tiny particles traveling in straight lines at finite speed

Reappearance of a comet on the date Halley predicted from Newtonian gravity, confirming the laws beyond Saturn

Principle that the force between two electric charges is proportional to their product and inversely to distance squared

Dark absorption lines in the solar spectrum caused by elements in the Sun's cooler outer layers

Ideal thermodynamic cycle defining maximum efficiency of heat engines between two temperatures

Continuous random jiggling of tiny particles suspended in fluid due to molecular collisions

Relation that electric current through a conductor is proportional to applied voltage at constant temperature

Rule that a changing magnetic field induces an electric current in a nearby conductor

Tiny annual shift in star positions proving Earth's orbit around the Sun on a vast scale

Principle that heat produced in a resistor equals current squared times resistance times time

Change in observed frequency of waves when source and observer move relative to each other

Planet found by mathematical prediction from Uranus orbital irregularities rather than visual search

Four equations unifying electricity magnetism and light as aspects of a single electromagnetic field

Experiment that looked for the Earth's motion through the ether and found no trace of it

Emission of electrons from metal surfaces when struck by light above a threshold frequency

High energy electromagnetic radiation discovered when cathode rays struck glass producing penetrating shadows

Spontaneous emission of particles or energy from certain heavy elements without external cause

First subatomic particle identified as the carrier of negative electric charge in cathode rays

Theory stating that the speed of light is constant and time and space are relative to the observer

Discovery that an atom's mass and positive charge sit in a tiny dense nucleus, the rest empty

Complete disappearance of electrical resistance in some materials cooled close to absolute zero

High-energy particles arriving from outside the solar system and striking the atmosphere continuously

Theory treating gravity as the curving of space and time by mass rather than a force between bodies

Intrinsic angular momentum of the electron that explains fine structure in atomic spectra

Quantum rule that no two fermions can occupy the same quantum state simultaneously

Theory explaining the behavior of matter and energy at atomic and subatomic scales using discrete packets

Fundamental equation describing how the quantum state of a physical system changes over time

Quantum rule that position and momentum of a particle cannot both be known with arbitrary precision

Observation that galaxies are moving apart indicating space itself is stretching over time

Model describing the universe beginning from an extremely hot and dense state and expanding ever since

Material composed of antiparticles that annihilates with ordinary matter to release energy

Uncharged particle in the atomic nucleus, whose discovery made fission and the bomb conceivable

Invisible substance inferred from its gravitational effects on visible galaxies and galaxy clusters

Electromagnetic radiation emitted when a charged particle travels faster than light in a medium

Splitting of a heavy atomic nucleus into lighter ones, releasing energy and further neutrons that can split more nuclei

Nearly massless particle that interacts only weakly and passes through ordinary matter undetected

Extremely luminous active galactic nucleus powered by a supermassive black hole at its center

Fundamental particle that combines to form protons and neutrons inside atomic nuclei

Uniform radiation filling the universe left over from the Big Bang and discovered by accident

Region of spacetime where gravity is so strong that nothing can escape once it passes the event horizon

Rapidly rotating neutron star emitting regular beams of radio waves like a cosmic lighthouse

Framework attempting to unify quantum mechanics and gravity by modeling particles as vibrating strings

Planet orbiting a star other than the Sun, found by the wobble or the dimming it causes

Hypothetical energy causing the accelerated expansion of the universe discovered in the late 1990s

Particle that gives other particles mass through interaction with the Higgs field in the Standard Model

Ripples in spacetime caused by accelerating massive objects and predicted by general relativity

Discovery that blood is pumped round a closed loop and returns, rather than being consumed and made afresh

Basic structural unit of plants seen as small empty chambers in cork under magnification

Tiny living creatures visible only through lenses that were found in water and on teeth

Grouping of plants into families according to the number and arrangement of their stamens

System of naming species with two Latin words indicating genus and specific descriptor

Recognition that whole species have died out, which had been thought impossible in a created world

Large biomolecule made of amino acids that performs most cellular functions and structures

Idea that all living organisms are composed of one or more cells which arise from preexisting cells

Process by which plants use light to build sugars from carbon dioxide and water, releasing oxygen as waste

Mechanism by which heritable traits that aid survival become steadily more common in a population over many generations

Concept that many diseases are caused by microorganisms too small to be seen without a microscope

Study of interactions among organisms and their physical environment in natural systems

Rules showing that traits pass to offspring as discrete units in predictable ratios rather than blending together

Protein that acts as a biological catalyst to speed up chemical reactions inside living cells

Thread-like structures inside the nucleus that carry genes in a linear sequence of DNA

Protein the immune system makes to lock onto one specific foreign molecule and mark it for destruction

Finding that the nervous system is built from separate cells rather than one continuous connected web

Organelles inside cells that produce most of the chemical energy needed to power reactions

Infectious agent that can only replicate inside the living cells of another organism

Discovery that human blood comes in incompatible types, which is why some transfusions had worked and others killed

Chemical messenger produced by glands that travels through the blood to affect distant organs

Unit of heredity that is transferred from parent to offspring and determines a trait

Process by which living systems maintain stable internal conditions despite external changes

Series of chemical reactions that generate energy through the oxidation of acetyl-CoA

Substance produced by one microorganism that kills or inhibits the growth of others

Molecule that carries genetic instructions for the development and functioning of all known living organisms

Set of rules by which information encoded in DNA is translated into proteins

Molecule that carries instructions from DNA to the protein-making machinery of the cell

Cluster of genes controlled together by a single regulatory switch in bacteria

Undifferentiated cell that can divide indefinitely and turn into many specialized cell types

Theory that mitochondria and chloroplasts began as free-living bacteria swallowed by a larger cell

Technique that amplifies tiny amounts of DNA into millions of copies for analysis

Process of creating an identical genetic copy of an organism from a single cell

International effort to read the complete sequence of human DNA, finished ahead of schedule

Gene editing tool that uses bacterial immune system components to cut DNA at precise locations

Idea that the Earth is shaped like a sphere rather than flat or disk-like

Invisible shield generated by the planet's molten core that protects against solar wind

Weight of the whole column of air pressing down on every surface at the Earth's surface

Explanation that the tides are raised by the pull of the Moon's and the Sun's gravity

Discovery that lightning is an electrical discharge, the same thing as the spark from a charged jar

Movement of carbon between the atmosphere, the oceans, the rocks and every living thing

Periods when large parts of the Earth were covered by thick ice sheets

Vibrations that travel through and around the planet after rock suddenly gives way

Process by which certain gases trap heat in the atmosphere warming the planet's surface

Innermost region of the planet, a solid iron ball inside a molten iron and nickel shell

Hypothesis that continents slowly move across the Earth's surface over geological time

Region of the stratosphere containing high concentrations of ozone that blocks ultraviolet radiation

Supercontinent that held nearly all the world's land in one mass before it broke apart

Underwater mountain range running the length of the Atlantic where new seafloor is made

Slow circulation of hot rock inside the Earth that drives plate movement

Method of dating once-living material by measuring how much of its radioactive carbon has decayed away

Scientific estimate that the planet formed about four and a half billion years ago

Process where new oceanic crust forms at mid-ocean ridges and moves outward

Theory that the Earth's outer shell is broken into rigid plates that slowly drift, collide and pull apart

Discovery that an asteroid strike ended the age of dinosaurs, found first as a worldwide iridium layer