- Ancient and Classical Periods: 6000 BCE-500 CE[rtoc]
- Numeral take their places: Positional numbers
- The square as the highest power: Quadratic equations
- The accurate reckoning for inquiring into all things: The Rhind papyrus
- The sum is the same in every direction: Magic squares
- Number is the cause of gods and daemons: Pythagoras
- A real number that is not rational: Irrational numbers
- The quickest runner can never overtake the slowest: Zeno’s paradoxes of motion
- Their combinations give rise to endless complexities: The Platonic solids
- Demonstrative knowledge must rest on necessary basic truths: Syllogistic logic
- The whole is greater than the part: Euclid’s Elements
- Counting without numbers: The abacus
- Exploring pi is like exploring the Universe: Calculating pi
- We separate the numbers as if by some sieve: Eratosthenes’ sieve
- A geometrical tour de force: Conic sections
- The art of measuring triangles: Trigonometry
- Numbers can be less than nothing: Negative numbers
- The very flower of arithmetic: Diophantine equations
- An incomparable star in the firmament of wisdom: Hypatia
- The closest approximation of pi for a millennium: Zu Chongzhi[/rtoc]
- The Middle Ages, 500-1500[rtoc]
- A fortune subtracted from zero is a debt: Zero
- Algebra is a scientific art: Algebra
- Freeing algebra from the constraints of geometry: The binomial theorem
- Fourteen forms with all their branches and cases: Cubic equations
- The ubiquitous music of the spheres: The Fibonnaci sequence
- The power of doubling: Wheat on a cheeseboard[/rtoc]
- The Renaissance, 1500-1680[rtoc]
- The geometry of art and life: The golden ratio
- Like a large diamond: Mersenne primes
- Sailing on a thumb: Rhumb lines
- A pair of equal-length lines: The equals sign and other symbology
- Plus of minus times plus of minus makes minus: Imaginary and complex numbers
- The art of tenths: Decimals
- Transforming multiplication into addition: Logarithms
- Nature uses as little as possible of anything: The problem of maxima
- The fly on the ceiling: Coordinates
- A device of marvellous invention: The area under a cycloid
- Three dimensions made by two: Projective geometry
- Symmetry is what we see at a glance: Pascal’s triangle
- Chance is bridled and governed by law: Probability
- The sum of the distance equals the altitude: Viviani’s triangle theorem
- The swing of a pendulum: Huygens’s tautochrone curve
- With calculus I can predict the future: Calculus
- The perfection of the science of numbers: Binary numbers[/rtoc]
- The Enlightenment: 1680-1800[rtoc]
- To every action there is an equal and opposite reaction: Newton’s laws of motion
- Empirical and expected results are the same: The law of large numbers
- One of those strange numbers that are creatures of their own: Euler’s number
- Random variation makes a pattern: Normal distribution
- The seven bridges of Königsberg: Graph theory
- Every even integer is the sum of two primes: The Goldbach conjecture
- The most beautiful equation: Euler’s identity
- No theory is perfect: Bayes’ theorem
- Simply a question of algebra: The algebraic resolution of equations
- Let us gather facts: Buffon’s needle experiment
- Algebra often gives more than is asked of her: The fundamental theorem of algebra[/rtoc]
- The 19th Century, 1800-1900[rtoc]
- Complex numbers are coordinates on a plane: The complex plane
- Nature is the most fertile source of mathematics discoveries: Fourier analysis
- The imp that knows the positions of every particle in the Universe: Laplace’s demon
- What are the chances? The Poisson distribution
- An indispensable tool in applied mathematics: Bessel functions
- It will guide the future course of science: The mechanical computer
- A new kind of function: Elliptic functions
- I have created another world out of nothing: Non-Euclidean geometries
- Algebraic structures have symmetries: Group theory
- Just like a pocket map: Quaternions
- Powers of natural numbers are almost never consecutive: Catalan’s conjecture
- The matrix is everywhere: Matrices
- An investigation into the laws of thought: Boolean algebra
- A shape with just one side: The Möbius strip
- The music of the primes: The Riemann hypothesis
- Some infinities are bigger than others: Transfinite numbers
- A diagrammatic representation of reasonings: Venn diagrams
- The tower will fall and the world will not end: The Tower of Hanoi
- Size and shape no not matter, only connections: Topology
- Lost in that silent, measured space: The prime number theorem[/rtoc]
- Modern Mathematics, 1900-present[rtoc]
- The veil behind which the future lies hidden: 23 problems for the 20th century
- Statistics is the grammar of science: The birth of modern statistics
- A freer logic emancipates us: The logic of mathematics
- The Universe is four-dimensional: Minkowski space
- Rather a dull number: Taxicab numbers
- A million monkeys banging on a million typewriters: The infinite monkey theorem
- She changed the face of algebra: Emmy Noether and abstract algebra
- Structures are the weapons of the mathematician: The Bourbaki group
- A single machine to compute any computable sequence: The Turing machine
- Small things are more numerous than large things: Benford’s law
- A blueprint for the digital age: Information theory
- We are all just six steps away from each other: Six degrees of separation
- A small positive vibration can change the entire cosmos: The butterfly effect
- Logically things can only partly be true: Fuzzy logic
- A grand unifying theory of mathematics: The Langlands Program
- Another roof, another proof: Social mathematics
- Pentagons are just nice to look at: The Penrose tile
- Endless variety and unlimited complication: Fractals
- Four colours but no more: The four-colour theorem
- Securing data with a one-way calculation: Cryptography
- Jewels strung on an as-yet invisible thread: Finite simple groups
- A truly marvellous proof: Proving Fermat’s last theorem
- No other recognition is needed: Proving the Poincaré conjecture[/rtoc]
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