Numbers & Symbols

This is the “#” band of the HBD2 Encyclopedia — every entry whose headword is a number or a symbol rather than a letter. It runs from 0 and the constants pi and the golden ratio up to the digits of the largest known prime and the speed of light, then on to the signs of mathematics (and their inventors), the planets and the zodiac, and the world’s currencies. Each entry is fact-checked.

Numbers and mathematical constants

Listed in value order, with the irrational constants φ, e, and π placed where they fall on the number line.

0
  • The only integer that is neither positive nor negative, and the additive identity in arithmetic.
  • The number of moons of Mercury and Venus, the only two planets with no moon.
  • 0 °C (32 °F), the freezing point of pure water at standard atmospheric pressure.
  • 0 kelvin, or absolute zero — the lowest temperature physically possible.
1
  • The first and smallest positive integer, and the multiplicative identity.
  • Earth’s number of natural satellites: the Moon.
  • The atomic number of hydrogen, the lightest element and the most abundant in the known universe.
  • The number of works Michelangelo signed — the Pietà in St. Peter’s Basilica.
1.618…

The golden ratio (φ): the proportion of a line divided so that the whole is to the larger part as the larger part is to the smaller.

2
  • The only even prime number.
  • The number of moons of Mars: Phobos and Deimos.
  • The base of the binary number system used by computers.
  • The number of gas giants in the solar system: Jupiter and Saturn.
  • The number of ice giants in the solar system: Uranus and Neptune.
  • According to the Bible, the number of people taken into heaven while still alive: Enoch and Elijah.
2.718…

e, Euler’s number — the base of the natural logarithm.

3
  • The first odd prime, and the first Mersenne prime (2² − 1).
  • The only prime that is also a triangular number.
  • The only prime that is one less than a perfect square.
  • The number of sides of a triangle, the simplest polygon.
  • The number of cone-cell types in the human eye, sensitive to short, medium, and long wavelengths of light.
  • The traditional primary colors of pigment: red, yellow, and blue.
  • The primary colors of light: red, green, and blue.
  • The three weapons of modern fencing: foil, épée, and saber.
  • The Fates of Greek mythology: Clotho, Lachesis, and Atropos.
  • In Hindu tradition, the gods of the Trimurti: Brahma, Vishnu, and Shiva.
  • In Buddhism, the Three Jewels: the Buddha, the Dharma, and the Sangha.
  • The Three Sacred Treasures of Japan (the Imperial Regalia): a sword, a mirror, and a jewel.
3.14159…

Pi (π): the ratio of a circle’s circumference to its diameter, an irrational number that never ends or repeats.

4
  • The first composite number.
  • The number of cardinal directions: north, south, east, and west.
  • The number of seasons.
  • The number of terrestrial planets: Mercury, Venus, Earth, and Mars.
  • The number of giant planets: Jupiter, Saturn, Uranus, and Neptune.
  • The number of Galilean moons of Jupiter: Io, Europa, Ganymede, and Callisto.
  • The number of DNA bases: adenine, guanine, cytosine, and thymine (RNA replaces thymine with uracil).
  • The number of blood groups in the ABO system: A, B, AB, and O.
  • The number of chambers in a mammalian heart.
  • The number of strings on a violin, viola, cello, and double bass.
  • The nations of the United Kingdom: England, Scotland, Wales, and Northern Ireland.
  • The number of suits in a deck of playing cards: hearts, diamonds, clubs, and spades.
  • In Hindu tradition, the four Vedas: the Rig, Yajur, Sama, and Atharva Veda.
  • In Hindu tradition, the four yugas, or world ages: Satya, Treta, Dvapara, and Kali.
  • In the Gospels, the four evangelists: Matthew, Mark, Luke, and John.
  • In Revelation, the Four Horsemen of the Apocalypse, often identified as Conquest, War, Famine, and Death.
  • In Buddhism, the Four Noble Truths: that suffering exists, that it arises from craving, that it can cease, and that the Noble Eightfold Path leads to that end.
5
  • The number of oceans on Earth: the Pacific, Atlantic, Indian, Southern, and Arctic.
  • The number of interlocking rings of the Olympic symbol, which the IOC says represent the five inhabited continents.
  • The number of regular (Platonic) solids: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
  • The number of traditional human senses: sight, hearing, smell, taste, and touch.
  • The number of known moons of Pluto: Charon, Styx, Nix, Kerberos, and Hydra.
  • In Islam, the Five Pillars: the declaration of faith (Shahada), prayer (Salat), almsgiving (Zakat), fasting in Ramadan (Sawm), and pilgrimage to Mecca (Hajj).
  • In Islam, the five daily prayers: Fajr, Dhuhr, Asr, Maghrib, and Isha.
  • In Sikhism, the Five Ks: Kesh, Kara, Kangha, Kachera, and Kirpan.
  • In Hindu philosophy, the five great elements (Pancha Bhuta): earth, water, fire, air, and ether.
6
  • The first perfect number: it equals the sum of its proper divisors (1 + 2 + 3).
  • The number of strings on a standard guitar.
  • The number of faces on a cube.
  • The number of points on the Star of David.
  • The number of legs on an insect.
  • The number of days of creation in the Book of Genesis.
  • The number of branches on a snowflake, a consequence of the hexagonal structure of ice crystals.
7
  • The number of days in a week.
  • The number of continents on Earth: Africa, Antarctica, Asia, Europe, North America, South America, and Australia (Oceania).
  • The number of colors traditionally named in a rainbow: red, orange, yellow, green, blue, indigo, and violet.
  • The number of hills of Rome.
  • The only prime that is one less than a perfect cube (2³).
  • The number of notes in the Western diatonic scale.
  • The number of branches on a menorah.
  • The pH of a neutral solution at 25 °C (77 °F).
  • The Seven Wonders of the Ancient World: the Great Pyramid of Giza, the Hanging Gardens of Babylon, the Statue of Zeus at Olympia, the Temple of Artemis, the Mausoleum at Halicarnassus, the Colossus of Rhodes, and the Lighthouse of Alexandria.
  • In Christian tradition, the seven deadly sins: pride, greed, wrath, envy, lust, gluttony, and sloth.
  • In Christian tradition, the seven heavenly virtues: chastity, temperance, charity, diligence, patience, kindness, and humility.
  • In Shakespeare’s As You Like It, the “seven ages” of a man’s life.
  • In Islam, the seven circuits pilgrims walk around the Kaaba during the Hajj and Umrah.
8
  • The number of planets in the solar system: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.
  • The number of bits in a byte.
  • The number of arms on an octopus.
  • The number of legs on a spider.
  • The number of sides of an octagon.
  • In Buddhism, the eight spokes of the Dharmachakra, one for each step of the Noble Eightfold Path: right view, intention, speech, action, livelihood, effort, mindfulness, and concentration.
  • In Hindu tradition, the eight forms of the goddess Lakshmi (Ashta Lakshmi).
9
  • The number of Muses in Greek mythology.
  • The number of justices on the United States Supreme Court.
  • The number of innings in a regulation Major League Baseball game.
  • The approximate number of months a human pregnancy lasts.
  • The number of points on the star that is the symbol of the Bahá’í Faith.
10
  • The base of the decimal system, the most widely used number system.
  • In the Bible, the Ten Commandments revealed to Moses at Mount Sinai.
  • The number the Pythagoreans held to be perfect, represented by the triangular tetractys.
  • In the Ramayana, the ten heads of the demon king Ravana.
11
  • The number of players on each side in soccer, cricket, and field hockey.
  • The approximate length, in years, of the Sun’s magnetic activity cycle.
12
  • The number of inches in a foot (30.48 cm).
  • The number of items in a dozen.
  • The number of months in a calendar year.
  • The number of signs of the zodiac.
  • The number of people who have walked on the Moon.
  • The number of stars on the flag of the European Union — a fixed symbol of unity, not a count of members.
  • The number of labors of Heracles (Hercules) in Greek mythology.
  • In the Bible, the twelve tribes of Israel.
  • In the Gospels, the twelve apostles of Jesus.
  • Time zones spanned by France, counting its overseas territories — more than any other country.
13
  • The original number of British colonies that declared independence in 1776 to form the United States.
  • The number of cards in each suit of a standard 52-card deck.
  • The number of loaves in a baker’s dozen.
  • In the Gospels, the number at the table of the Last Supper: Jesus and the twelve apostles.
14
  • The number of lines in a sonnet.
  • The number of days in a fortnight.
15

The number of players on each side in rugby union.

16
  • The number of pieces each player starts with in chess.
  • The number of ounces in a pound, avoirdupois (453.6 g).
  • The number of personality types defined by the Myers–Briggs Type Indicator.
  • The number of known moons of Neptune (as of 2026).
17
  • The number of named fundamental particles in the Standard Model of physics (twelve fermions and five bosons).
  • The only prime that is the sum of four consecutive primes (2 + 3 + 5 + 7).
  • The minimum number of starting clues a Sudoku puzzle needs to have a single solution, proved in 2012.
  • The number of syllables in a haiku (five, seven, then five).
18
  • The number of holes in a standard round of golf.
  • In Hindu tradition, the number of books (parvas) of the epic Mahabharata.
19
  • In the Bahá’í calendar, the number of months in a year.
  • In the Bahá’í calendar, the number of days in a month.
  • In the Quran, the number of angels said to guard Hell (74:30).
20
  • The number of standard amino acids encoded by the genetic code.
  • The base of the Maya number system (vigesimal).
  • The number of things in a score.
  • The most moves ever needed to solve a Rubik’s Cube from any position — “God’s number,” proved in 2010 (half-turn metric).
  • The maximum number of horses allowed to run in the Kentucky Derby.
  • The number of scoring sectors on a dartboard.
21
  • The total number of pips on a standard six-sided die (1 + 2 + 3 + 4 + 5 + 6).
  • The number of gun rounds in a 21-gun salute, the highest honor rendered by firing.
  • The number of letters in the Italian alphabet.
22
  • The length of a cricket pitch, in yards (20.12 m).
  • The length of a surveyor’s chain, in yards (20.12 m).
  • The number of bones in the adult human skull (eight cranial, fourteen facial).
  • The number of letters in the Hebrew alphabet.
  • The number of letters in the Phoenician alphabet, the parent of the Hebrew and Greek scripts.
  • The number of cards in the Major Arcana of a tarot deck.
  • The number of cars on the 2026 Formula 1 grid, after Cadillac joined as the eleventh team.
23

The number of pairs of chromosomes in a human body cell (46 in total); a sex cell carries a single set of 23.

24
  • The number of hours in a day.
  • The number of standard time zones around the world.
  • The karat figure for pure (100%) gold.
  • The number of spokes on the Ashoka Chakra at the center of India’s flag.
  • The number of letters in the Greek alphabet.
  • In Jainism, the number of Tirthankaras.
25
  • The number of years marking a silver jubilee.
  • The minimum age to be elected to the United States House of Representatives.
26
  • The number of letters in the English, French, German, and modern Latin alphabets.
  • The number of bones in the human foot.
  • The number of cantons of Switzerland.
  • The number of counties in the Republic of Ireland.
27
  • The number of member states in the European Union.
  • The number of ratified amendments to the United States Constitution.
  • The number of books in the New Testament.
  • The number of bones in the human hand.
  • The number of letters in the Spanish alphabet.
  • Historically, the ampersand (&) was recited as a 27th character after Z; “and per se and” gave us the word ampersand.
27.3

The number of days the Moon takes to orbit Earth once against the stars (a sidereal month).

28
  • The number of days in February in a common year.
  • The rough length, in days, of a menstrual cycle.
  • The number of tiles in a standard double-six set of dominoes.
  • The number of letters in the Arabic and Esperanto alphabets.
29
  • The number of days in February in a leap year.
  • The number of letters in the Danish and Swedish alphabets.
29.5

The number of days in a full cycle of lunar phases, from one new Moon to the next (a synodic month).

30
  • The smallest sphenic number — a product of three distinct primes (2 × 3 × 5).
  • The number of days in April, June, September, and November.
  • The minimum age to be a United States senator.
  • The number of letters in the Bulgarian and Serbian (Cyrillic) alphabets.
  • In the Gospels, the thirty pieces of silver Judas received to betray Jesus.
31
  • The number of days in January, March, May, July, August, October, and December.
  • The number of flavors Baskin-Robbins launched with — one for each day of the month.
  • The number of letters in the Macedonian alphabet.
32
  • The number of teeth in a full adult set.
  • The total number of pieces on a chessboard at the start of a game.
  • The number of numbered piano sonatas composed by Ludwig van Beethoven.
  • The freezing point of water in degrees Fahrenheit (0 °C).
33
  • The number of vertebrae a human spine has at birth, several of which later fuse.
  • The number of letters in the modern Russian alphabet.
  • The longest winning streak in NBA history: 33 straight by the 1971–72 Los Angeles Lakers.
  • In Hindu tradition, the thirty-three principal deities of the Vedas.
34
  • The magic constant of the 4×4 magic square: every row, column, and diagonal sums to 34.
  • The total of every line of the magic square in Albrecht Dürer’s engraving Melencolia I, whose bottom row spells out the work’s date, 1514.
35

The minimum age to serve as president or vice president of the United States.

36

The number of inches in a yard (91.44 cm).

37
  • The traditional average human body temperature, 37 °C (98.6 °F).
  • The traditional count of Shakespeare’s plays, though estimates range from 37 to 39.
39
  • The number of books in the Old Testament of the Protestant Bible.
  • The number of letters in the modern Armenian alphabet, counting the ligature «և» (38 without it).
40

The number of years marking a ruby jubilee.

42

In The Hitchhiker’s Guide to the Galaxy, the answer to the ultimate question of life, the universe and everything.

46
  • The number of chromosomes in a human body cell.
  • The number of books in the Old Testament of the Catholic Bible.
50
  • The number of states in the United States.
  • The number of years marking a golden jubilee.
52

The number of cards in a standard deck, excluding jokers.

54
  • The number of cards in a standard deck when the two jokers are included.
  • The number of colored squares on a Rubik’s Cube: nine on each of its six faces.
56

The number of signers of the United States Declaration of Independence.

60
  • The number of seconds in a minute.
  • The number of minutes in an hour.
  • The number of years marking a diamond jubilee.
64

The number of squares on a chessboard.

65

The number of years marking a sapphire jubilee.

66

The number of books in the Protestant Bible (39 in the Old Testament, 27 in the New).

70

The number of years marking a platinum jubilee.

74

The number of letters in the Khmer alphabet, the longest alphabet in the world.

78

The number of cards in a tarot deck: 22 Major Arcana and 56 Minor Arcana.

88
  • The number of constellations recognized by the International Astronomical Union.
  • The number of keys on a standard piano.
90

The number of degrees in a right angle.

95

The number of theses Martin Luther posted in 1517, which helped to spark the Reformation.

99

In Islamic tradition, the ninety-nine names of God (al-Asma al-Husna).

100
  • The boiling point of water at standard pressure, 100 °C (212 °F).
  • The number of zeros in a googol (10100).
  • The number of tiles in an English-language Scrabble set.
108
  • The number of stitches (double-stitched) on a Major League baseball.
  • A sacred number in Hindu and Buddhist tradition.
  • The usual number of beads on a mala, a loop of prayer beads.
112

The European Union’s common emergency telephone number, which GSM mobile phones worldwide also route to the local emergency service.

114

The number of surahs (chapters) in the Quran.

117

The Population Reference Bureau’s estimate, in billions, of all the people ever born on Earth.

118

The highest atomic number on the official IUPAC periodic table: oganesson.

144

The number of items in a gross (a dozen dozen).

150

Dunbar’s number — the rough upper limit on the stable social relationships a person can maintain.

153
  • In the Gospel of John, the number of fish in the miraculous catch.
  • A number equal to the sum of the cubes of its own digits: 1³ + 5³ + 3³.
168

The number of hours in a week (24 × 7).

172

Aaron Finch’s score for Australia against Zimbabwe in 2018, the highest individual innings in a men’s Twenty20 International.

180

The maximum score from three darts on a standard board (three treble-20s).

204

The total number of squares of every size on a chessboard (1² + 2² + … + 8²).

206

The number of bones in the adult human body.

212

The boiling point of water at standard pressure in degrees Fahrenheit (100 °C).

264

Rohit Sharma’s score for India against Sri Lanka in 2014, the highest individual innings in a men’s One Day International.

300

A perfect game in ten-pin bowling, scored by rolling twelve consecutive strikes.

360

The number of degrees in a full circle.

365
  • The number of days in a common year of the Gregorian calendar.
  • In Genesis, Enoch’s age when God took him.
400

Brian Lara’s unbeaten score for the West Indies against England in 2004, the highest individual innings in Test cricket.

451

In Ray Bradbury’s Fahrenheit 451, the temperature at which book paper is said to catch fire and burn.

500

The lifespan, in years, that some classical accounts give the phoenix before it is reborn from its ashes.

555

The telephone exchange reserved for use in North American film and television (numbers such as 555-0100 to 555-0199), so no real line is dialed.

640

The number of acres in a square mile (2.59 km²).

666
  • In the Book of Revelation, the “number of the beast.”
  • The sum of every number on a roulette wheel (0 through 36).
777
  • A classic jackpot combination on slot machines.
  • In Genesis, the age at which Lamech, father of Noah, died.
786

In Islamic tradition, an auspicious number — the abjad numerical value of the phrase “Bismillah al-Rahman al-Rahim.”

911

The emergency telephone number across most of North America; the first 911 call was placed in Haleyville, Alabama, in 1968.

969

In Genesis, the age at which Methuselah died — the longest life span recorded in the Bible.

999

The emergency telephone number of the United Kingdom — the world’s first, introduced in London in 1937.

1,001

The number of nights over which Scheherazade tells her tales in the One Thousand and One Nights.

1,679

The number of binary digits in the Arecibo message, beamed into space in 1974 in the search for extraterrestrial intelligence.

1,729

The Hardy–Ramanujan, or “taxicab,” number — the smallest expressible as a sum of two cubes in two ways (1³ + 12³ = 9³ + 10³).

2,520

The smallest positive integer divisible by every whole number from 1 to 10.

5,280

The number of feet in a mile (1.61 km).

6,174

Kaprekar’s constant: repeatedly subtracting the ascending from the descending arrangement of a four-digit number’s digits leads here.

10,000

A myriad — the classical word for ten thousand.

20,000

In Jules Verne’s Twenty Thousand Leagues Under the Sea, the distance the submarine Nautilus travels — the length of the voyage, not its depth.

24,601

Jean Valjean’s prisoner number in Victor Hugo’s Les Misérables.

86,400

The number of seconds in a day (24 × 60 × 60).

41,024,320

The number of digits in the largest known prime number, 2136,279,841 − 1 — a Mersenne prime found by the GIMPS project in October 2024.

299,792,458

The speed of light in a vacuum, in meters per second — an exact value, because the meter itself has been defined from it since 1983.

Mathematical symbols

The working signs of arithmetic, algebra, geometry, analysis, and logic — from the everyday to the specialist’s shorthand, each credited to its inventor where history records a first use.

+︎
  • The plus sign, a shorthand for the Latin et (“and”).
  • Together with the minus sign, it first appeared in print in Johannes Widmann’s 1489 arithmetic book.
−︎

The minus sign. In Widmann’s 1489 book the pair first marked surplus and deficit in trade, and only later settled into addition and subtraction.

±︎

Plus-or-minus: a tolerance, or both square roots at once. William Oughtred used it in his Clavis Mathematicae (1631).

×︎

The multiplication sign, introduced by William Oughtred in 1631.

⋅︎

The raised multiplication dot. Leibniz pushed for it from 1698, objecting that Oughtred’s cross was too easily confused with the letter x — both signs survive today.

÷︎

The obelus. Originally an ancient editor’s mark for doubtful passages, it was first used for division by Johann Rahn in 1659.

⁄︎

The fraction slash, or solidus, for setting fractions on a single line of type — a printer’s economy that mathematics adopted in the nineteenth century.

=︎
  • The equals sign, invented by the Welsh mathematician Robert Recorde in The Whetstone of Witte (1557).
  • He chose a pair of parallel lines because, he wrote, no two things can be more equal.
≠︎

Not equal: an equals sign canceled by a stroke.

≈︎

Approximately equal — the double tilde.

≡︎

The triple bar: identically equal. In number theory it is Gauss’s sign for congruence, from the Disquisitiones Arithmeticae (1801).

≅︎

Congruent — a similarity tilde stacked on an equals sign; the combination goes back to Leibniz.

∝︎

Proportional to; in use since the eighteenth century.

<︎

Less than. With its mirror image, it was introduced by Thomas Harriot and published posthumously in 1631.

>︎

Greater than — Harriot’s companion sign. The open side always faces the larger quantity.

≤ ≥︎

Less-than-or-equal and greater-than-or-equal, added by the French scientist Pierre Bouguer in 1734.

≪ ≫︎

Much less than, and much greater than. In analytic number theory the pair is called Vinogradov’s notation, after Ivan Vinogradov.

%︎
  • The percent sign: parts per hundred.
  • No one invented it — it evolved over centuries of Italian commercial shorthand for per cento.
‰︎

The per-mille sign: parts per thousand, the percent sign’s finer sibling — and, like it, an evolution of commercial shorthand rather than any one person’s invention.

√︎

The radical sign for roots, introduced by Christoph Rudolff in 1525 — possibly a stylized letter r.

∞︎

The infinity symbol, or lemniscate, introduced by John Wallis in 1655.

π︎
  • The circle constant; its value, 3.14159…, has its own entry in the number list above.
  • The Welsh mathematician William Jones first used the letter for it in 1706, likely from the Greek for “periphery”; Leonhard Euler’s adoption made it universal.
e
  • Euler’s number, 2.718… (listed above), the base of the natural logarithm.
  • The letter is Leonhard Euler’s own choice, in his papers from 1727 and in print by 1736.
i

The imaginary unit — the square root of −1. Euler introduced the symbol in 1777.

φ︎

The golden ratio, 1.618… (listed above). The letter is credited to Mark Barr, honoring the sculptor Phidias, whose work was said to embody the proportion.

∠︎

The angle sign, coined by Pierre Hérigone in his Cursus mathematicus (1634) — a book that introduced dozens of symbols at a stroke.

⊥︎

Perpendicular — another of Hérigone’s 1634 coinages. In logic it doubles as “bottom,” the always-false proposition.

∥︎

Parallel — among the oldest signs still in service, with roots in Greek mathematics.

′ ″︎

The prime and double prime: Lagrange’s notation for first and second derivatives, and the everyday signs for feet and inches, or arc minutes and seconds.

ẋ︎

Newton’s dot — the fluxion, his sign for a rate of change in time. Mechanics still writes velocities this way.

dx

Leibniz’s differential: an infinitesimally small change in x, from the same 1675 manuscripts as the integral sign.

∂︎

The partial-derivative sign, a curled d — used by Adrien-Marie Legendre in 1786, and made standard by Carl Jacobi’s advocacy half a century later.

Δ︎

The capital delta: a finite change or difference in a quantity; in analysis, the Laplacian.

δ︎

The small delta: Lagrange’s sign for a variation (1755), and the arbitrarily small quantity paired with epsilon in the definition of a limit.

ε︎

Epsilon: an arbitrarily small positive quantity — a convention fixed by Augustin-Louis Cauchy’s analysis lectures of the 1820s.

lim︎

The limit. Simon l’Huilier abbreviated it to lim. in 1786; the arrow form, x → a, spread from G. H. Hardy’s usage in 1908.

Σ︎

The summation sign — Greek capital sigma, for “sum” — introduced by Euler in 1755.

∏︎

The product sign, sigma’s multiplicative sibling — Greek capital pi. Carl Friedrich Gauss used it in 1812.

∫︎

The integral sign — an elongated S, for the Latin summa — devised by Gottfried Wilhelm Leibniz in 1675.

∮︎

The contour integral, for integrating around a closed loop; credited to the physicist Arnold Sommerfeld.

∇︎

Nabla, or del — the gradient operator, introduced by William Rowan Hamilton. The name, after an ancient harp of similar shape, was suggested to the physicist P. G. Tait by the scholar William Robertson Smith.

| |︎

Absolute-value bars — distance from zero — introduced by Karl Weierstrass in 1841.

⌊⌋ ⌈⌉︎

Floor and ceiling — round down, round up — coined by Kenneth Iverson in 1962, in the same book that gave the programming language APL its name.

∘︎

Function composition, read “after”: (f ∘ g)(x) means f(g(x)).

℘︎

Weierstrass’s ℘, the letter he drew for his elliptic function — notation so personal that Unicode names the character after him.

∴︎

The “therefore” sign: three dots in a triangle. Johann Rahn used it in the same 1659 book that debuted the division sign.

∵︎

Because — the upside-down companion of the “therefore” sign.

∧ ∨︎

Logical and, and logical or. The vee, from the Latin vel, entered logic with Russell and Whitehead’s Principia Mathematica (1910); the matching wedge followed in the 1930s.

¬︎

Logical not; the hooked negation sign spread with the formal-logic school of the 1930s.

⇒ ⇔︎

Implies, and if and only if — the double arrows, spread in the mid-twentieth century with Bourbaki among the popularizers.

∈︎

Set membership, “is an element of” — introduced, as a Greek epsilon, by Giuseppe Peano in 1889.

⊂ ⊆︎

The subset signs — contained in, or contained in or equal. The curved cup goes back to Ernst Schröder’s logic of 1890.

∪ ∩︎

Union and intersection — everything in either set, and everything in both — introduced by Giuseppe Peano in 1888.

∅︎

The empty set: the Scandinavian letter Ø, borrowed by André Weil for the Bourbaki group in 1939.

∀︎

The universal quantifier, “for all” — an inverted A, introduced by Gerhard Gentzen in 1935.

∃︎

The existential quantifier, “there exists” — a reversed E, introduced by Giuseppe Peano in 1897.

ℕ ℤ ℚ ℝ ℂ︎
  • The number families in blackboard bold: the naturals, the integers (ℤ, from German Zahlen), the rationals (ℚ, for quotient), the reals, and the complex numbers.
  • The doubled strokes began as lecturers’ chalk imitation of bold type and moved into print in the 1960s.
ℵ₀︎

Aleph-null, the smallest infinity — the count of the counting numbers. Georg Cantor chose the Hebrew aleph for his infinite cardinals in the 1890s.

∎︎

The tombstone, or halmos: end of proof. Paul Halmos borrowed the mark from magazine typography, where it closes an article — mathematicians named it after him, and it has largely retired the old Q.E.D.

Astronomical and zodiac symbols

The classical signs for the Sun, the Moon, the planets, and the asteroids — many of which doubled as alchemical symbols for metals — followed by the twelve signs of the zodiac.

☉︎
  • The astronomical symbol for the Sun.
  • The alchemical symbol for gold.
  • A circle with a central dot — a sun-disc form that dates from the Renaissance.
☽︎
  • The astronomical symbol for the Moon.
  • The alchemical symbol for silver.
  • A crescent — the Moon’s most familiar shape.
⊕︎
  • An astronomical symbol for planet Earth.
  • The globe-and-cross is read as the world split by the equator and a meridian — or as the four points of the compass.
☿︎
  • The astronomical symbol for Mercury.
  • The alchemical symbol for the metal mercury (quicksilver).
  • The figure is read as the winged cap and caduceus — the herald’s staff — of Mercury, messenger of the gods.
♀︎
  • The astronomical symbol for Venus.
  • The alchemical symbol for copper.
  • The symbol for the female sex, used to denote women — a convention introduced by the botanist Carl Linnaeus in the 1750s.
  • Popularly said to depict the hand mirror of Venus, the goddess of love.
♂︎
  • The astronomical symbol for Mars.
  • The alchemical symbol for iron.
  • The symbol for the male sex, used to denote men.
  • Popularly said to depict the shield and spear of Mars, the god of war.
♃︎
  • The astronomical symbol for Jupiter.
  • The alchemical symbol for tin.
  • Said to represent either an eagle, the bird of Jove, or a stylized Greek letter zeta, the initial of Zeus.
♄︎
  • The astronomical symbol for Saturn.
  • The alchemical symbol for lead.
  • Said to represent the scythe or sickle of Saturn, the god of the harvest.
♅︎

An astronomical symbol for Uranus.

♆︎

The astronomical symbol for Neptune.

♇︎

A symbol for Pluto, now classified as a dwarf planet.

⚳︎

The historical astronomical symbol for the dwarf planet Ceres.

⚴︎

The historical astronomical symbol for the asteroid Pallas.

⚵︎

The historical astronomical symbol for the asteroid Juno.

⚶︎

The historical astronomical symbol for the asteroid Vesta.

♈︎

The zodiac sign Aries, the Ram.

♉︎

The zodiac sign Taurus, the Bull.

♊︎

The zodiac sign Gemini, the Twins.

♋︎

The zodiac sign Cancer, the Crab.

♌︎

The zodiac sign Leo, the Lion.

♍︎

The zodiac sign Virgo, the Maiden.

♎︎

The zodiac sign Libra, the Scales.

♏︎

The zodiac sign Scorpio, the Scorpion.

♐︎

The zodiac sign Sagittarius, the Archer.

♑︎

The zodiac sign Capricorn, the Sea-Goat.

♒︎

The zodiac sign Aquarius, the Water-Bearer.

♓︎

The zodiac sign Pisces, the Fishes.

Common symbols and currency signs

Everyday punctuation and reference marks, then a selection of national currency signs.

&︎
  • The ampersand, a ligature of the Latin et (“and”).
  • Its name comes from schoolchildren who once recited it as the alphabet’s final character: “and per se and.”
*︎

The asterisk, from the Greek for “little star.”

@︎
  • A commercial sign meaning “at the rate of,” as in “5 @ $2.”
  • Chosen to separate the user from the host in email addresses by Ray Tomlinson in 1971.
^︎

The caret, used to mark an insertion point or to denote exponentiation.

°︎

The degree sign, for angles and for temperature.

!︎
  • The exclamation point, informally called a “bang”; in mathematics it denotes a factorial.
  • The factorial notation n! was introduced by Christian Kramp in 1808.
~︎

The tilde, used to mean “approximately” and as a diacritic over letters such as ñ.

#︎
  • The number sign — also called hash, pound, or octothorpe — and the marker for a hashtag.
  • Its “pound” sense and shape trace to lb, from the Latin libra pondo (“pound by weight”).
$︎
  • The dollar (and peso) sign, used for the US dollar and many other currencies, including the Mexican peso.
  • It most likely evolved from ps, the scribal abbreviation for the Spanish peso, with the s written over the p.
¢︎

The cent sign, one hundredth of a dollar.

€︎
  • The euro, the currency of the eurozone.
  • Its design was inspired by the Greek letter epsilon and the first letter of “Europe,” crossed by two lines for stability.
  • Unveiled by the European Commission in December 1996; uniquely among major currency signs, its designer was never publicly named.
£︎
  • The pound sterling, the currency of the United Kingdom.
  • An ornate letter L, from the Latin libra, a Roman unit of weight.
₹︎
  • The Indian rupee sign, adopted in 2010.
  • Designed by D. Udaya Kumar, it blends the Devanagari letter “ra” with a Latin R.
¥︎
  • The sign shared by the Japanese yen and the Chinese yuan.
  • A letter Y crossed by two strokes; the names “yen” and “yuan” both mean “round,” after the shape of coins.
₪︎

The Israeli new shekel.

₽︎

The Russian ruble.

R︎

The South African rand.

₩︎

The South Korean won.

৳︎

The Bangladeshi taka.

₨︎

The rupee sign (Rs) used by Pakistan, Sri Lanka, Nepal, Mauritius, and others.

R$︎

The Brazilian real.

₱︎

The Philippine peso.

Frequently asked questions

What is the value of pi?

Pi (π) is approximately 3.14159. It is the ratio of a circle’s circumference to its diameter, and it is an irrational number, meaning its decimal expansion never ends and never repeats.

What is the golden ratio?

The golden ratio (φ) is about 1.618. A line is divided in the golden ratio when the whole length is to the longer part as the longer part is to the shorter. It appears throughout art, architecture, and nature.

Who invented the equals sign?

The Welsh mathematician Robert Recorde, in his 1557 algebra book, The Whetstone of Witte. He chose a pair of parallel lines because, he wrote, no two things can be more equal.

Where does the symbol for pi come from?

It is the Greek letter pi, first used for the circle ratio by William Jones in 1706, probably from the Greek word for periphery. Leonhard Euler adopted the letter a generation later, and his influence made it the universal sign.

Which planet has the most moons?

Saturn currently has the most known moons of any planet — well over 270 as of 2026 — having overtaken Jupiter. These tallies keep rising as astronomers confirm new, small satellites, so any exact figure is a snapshot in time. Mercury and Venus have none.

What is the largest known prime number?

As of 2026 it is 2 raised to the power 136,279,841, minus 1 — a Mersenne prime with 41,024,320 digits, discovered through the Great Internet Mersenne Prime Search in October 2024. Because there are infinitely many primes, no prime is ever the largest for long.

How many bones are in the human body?

An adult human body has 206 bones. A newborn has more, around 270, because several bones — such as those of the skull and spine — fuse together during growth.

What does the # symbol mean?

The # sign has several names: number sign, hash, pound sign, and octothorpe. It marks numbers (as in “#1”), is used in programming, and labels a hashtag on social media.

Which languages have the longest and shortest alphabets?

The Khmer alphabet of Cambodia is the longest, with 74 letters. Among the shortest is Rotokas, spoken in Papua New Guinea, with about 12 letters. For comparison, the English alphabet has 26.

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