Who Invented Math?

Who invented math? Nobody alone. Mathematics grew over more than 40,000 years in many cultures: people cut tally marks into bones, scribes in Mesopotamia and Egypt calculated for trade and land survey, Indian scholars made zero a number to calculate with, the Greeks introduced the proof and scholars of the Islamic world gave algebra its name. Single signs and ideas can be assigned to named people, but the whole cannot.

Where mathematics comes from

Mathematics arose wherever people had to count, share, measure or predict: stores of grain, fields, taxes, calendars. A single place of origin cannot be named. Even the starting point shows this, since animals and babies have a sense for small quantities. Exact counting beyond that is a cultural achievement that needs language and practice.

Every one of these cultures created parts that others took over or that arose independently again. The Maya reached place value without any contact with India. That knowledge also traveled across borders is shown by the path of our digits from India via Baghdad to Pisa. Declaring the Greeks the inventors of mathematics overlooks that their predecessors in Mesopotamia and Egypt had been calculating for thousands of years. The Greek contribution was above all the proof, not the calculation. For the full story from prehistory to today see the history of mathematics.

Who is the father of mathematics?

Nobody awards the title “father of mathematics,” and there is no election or certificate. Books and websites give the nickname to different people, depending on which part of mathematics they mean. The table shows the most common names and what is behind them.

The nicknames do not contradict each other, because they refer to different fields. For a one-sentence answer: the earliest named Greek mathematician is Thales, the organizer of geometry is Euclid and the namesake of algebra is al-Khwarizmi. An overall ranking would be opinion, not history.

Who was the first mathematician in the world?

The first mathematician cannot be named, because the first calculators left no names. Whoever counted clay tokens in Mesopotamia around 3500 BC, or made arithmetic exercises about field areas in Shuruppak around 2600 BC, remained anonymous. Tally notches on bones cannot be assigned to a person either.

Two names come closest, and both come with restrictions:

• Ahmes was an Egyptian scribe who copied the Rhind papyrus around 1550 BC from a model about 300 years older. His is the oldest known name connected to a mathematical text. We know of no contribution of his own, because he copied.
• Thales of Miletus (about 624 to 546 BC) is called the first known Greek philosopher, scientist and mathematician. The evidence is thin here too: nothing he wrote survives, and later authors liked to credit famous men with discoveries.

The first women with known names appear later. They are introduced in the list of famous female mathematicians.

Who invented numbers?

Numbers were invented by nobody alone. People could count long before writing, number signs arose independently in several cultures, and our present digits 0 to 9 come from India. It helps to separate three things: counting, number words and written number signs.

• Counting without writing: The Lebombo bone from southern Africa (over 40,000 years old) shows tally marks. What was counted is unknown.
• Mesopotamia, from about 3300 BC: Clay tokens for goods became number signs on tablets, later a place value system in base 60 with only two signs. See Babylonian numerals.
• Egypt, from about 3100 BC: There was a separate hieroglyph for 1, 10, 100 up to a million. The mace head of king Narmer already names numbers above a million. Try it with Egyptian numerals.
• Mesoamerica: Dots for ones and bars for fives were in use there in the last centuries BC. The Maya stacked them in base 20 and had a sign for zero. More at Mayan numbers.
• Rome: The symbols I, V, X, L, C, D and M probably go back to Etruscan models and tally notches. The Romans often wrote 4 as IIII. Look them up on the Roman numerals page.
• India: The Brahmi signs on the inscriptions of emperor Ashoka (about 250 BC) are the ancestors of our digits. In the first centuries AD a place value system with ten digits developed.
• The road to Europe: Al-Khwarizmi described calculating with the Indian digits around 825 in Baghdad. They spread after Fibonacci’s Liber abaci of 1202. The full story is on the Hindu-Arabic numerals page.

So there are two honest answers to “Who invented numbers?” Counting is as old as humankind and has no inventor. The digits almost the whole world writes with today were developed by Indian scholars. How different systems compare is shown on number systems.

Who invented zero?

Zero has no inventor, but a history in several steps. First came a sign for “nothing here,” so that 205 could be told from 25. Only later did zero become a number you calculate with. The two steps happened in different places.

• Babylon: The scribes used a place value system without zero for over a thousand years. From about 400 BC two wedge signs marked an empty place, mostly in the middle of a number and not at the end.
• Maya: A base 20 system with a zero sign is documented many times in inscriptions and books. Their zero was mostly a placeholder and a sign for a completed cycle.
• Greece: Ptolemy used a round sign for an empty place in astronomical tables around 130 AD, but saw it more as punctuation than as a number.
• India: The placeholder became a number here. The Bakhshali manuscript uses a dot for empty places. Its date is disputed: radiocarbon dating at Oxford in 2017 gave the 3rd or 4th century for one leaf and later times for others.
• 628: Brahmagupta wrote down the first rules for calculating with zero in his Brahmasphutasiddhanta. Almost all agree with today’s, only for division he erred: he set 0 : 0 = 0.
• 876: An inscription in the Chaturbhuj temple in Gwalior contains the oldest undisputed dated Indian zero in circle form, in the numbers 270 and 50.
• 1202: Fibonacci introduced zero to Europe in the Liber abaci but called it only a “sign.” It gained general acceptance in the course of the 17th century.

A short answer to “Who invented zero?” is therefore: as a placeholder, several cultures independently; as a number, Indian scholars; with firm rules, first Brahmagupta. Roman numerals never had one, see the Roman numeral for zero.

Who invented fractions?

Fractions are as old as fair sharing. The oldest calculating texts from Egypt and Mesopotamia contain them. Our notation grew in three stages that do not belong to one person:

1. Egypt: Almost all fractions were unit fractions with numerator 1. Others were written as a sum of different unit fractions, for example 2/5 as 1/3 + 1/15.
2. Babylon: Scribes calculated with sixtieths and tables of reciprocals. Our 60 minutes and 360 degrees come from there.
3. The fraction bar: The horizontal line between numerator and denominator is known from Arabic arithmetic books, and several sources name al-Hassar around 1200. Fibonacci was the first European mathematician to use it in the modern form.

Decimal fractions (0.25 instead of 1/4) are younger. Al-Uqlidisi treated them around 950 in Damascus. In Europe Simon Stevin spread them in his pamphlet De Thiende of 1585, though he did not write a point or comma yet. John Napier popularized the decimal point in 1617. In Germany a comma is written today, in the United States a point.

Who invented the x and the other symbols?

Letter algebra developed in four steps, as the historian Georg Nesselmann described in 1842: first everything in words (rhetorical), then with abbreviations (syncopated), finally with symbols.

1. About 825: Al-Khwarizmi wrote equations completely in words. The unknown was called “root” or “thing.”
2. About 250: Diophantus abbreviated the unknown with a sign and its square with another, but worked with only one unknown.
3. 1591: François Viète was the first to use letters also for known quantities, vowels for unknowns and consonants for knowns. That let him describe a method for all equations of one type at once.
4. 1637: René Descartes introduced a, b, c for known and x, y, z for unknown quantities in La Géométrie. We write the same way today.

Why Descartes chose x is not reliably recorded. Several explanations exist, including an anecdote about a printer, but the scholarly literature considers none of them secure. Other signs have a birth year too:

Who invented algebra?

No single person invented algebra, but one gave it its name and its first order as a subject: al-Khwarizmi, around 825 in Baghdad. The title of his book contains the word al-jabr, “the completing,” from which “algebra” was made. People had solved equations long before, and the modern formula language came much later.

1. Babylon, about 1800 BC: Scribes solved problems that we write as quadratic equations with fixed recipes and area pictures, all in words.
2. About 250 AD: Diophantus abbreviated the unknown and collected hundreds of problems in the Arithmetica.
3. 628: Brahmagupta calculated with negative numbers and zero and gave a general rule for quadratic equations, also in words.
4. About 825: Al-Khwarizmi sorted linear and quadratic equations into six types and justified each rule geometrically.
5. About 1070: Omar Khayyam solved cubic equations with conic sections.
6. 1545: Cardano published the solution formulas for equations of third and fourth degree.
7. 1591 and 1637: Viète and Descartes introduced letter algebra.

Later branches have their own names. Boolean algebra, calculating with true and false, was founded by George Boole in 1847 and 1854. Linear algebra with vectors and matrices arose in the 19th century, among others with Hermann Grassmann (1844) and Arthur Cayley (1858).

Did the Arabs invent math?

No, but they preserved, passed on and extended a great deal. The term “Arabic mathematics” is imprecise, because the scholars wrote in Arabic but came from many regions and religions. Three things we owe to this time in particular:

• The digits: Our ten digits come from India. They reached Europe through Arabic texts, hence the name “Arabic numerals.” More exactly they are Hindu-Arabic or Indo-Arabic numerals.
• Algebra: The word comes from the title of al-Khwarizmi’s book (about 825). His name lives on in the word “algorithm.”
• Transmission: In the House of Wisdom in Baghdad, Greek and Indian works were translated and commented, many of which would otherwise have been lost.

Was math invented or discovered?

This is an open question of philosophy, and experts disagree. The Stanford Encyclopedia of Philosophy sorts the three big answers like this:

• Platonism: Mathematical objects such as numbers and circles exist independently of humans. We discover them, like an explorer finds a new country. Kurt Gödel held this view.
• Formalism: Mathematics is a game with symbols according to fixed rules. The question of a “real” object hardly arises. David Hilbert is seen as a representative.
• Intuitionism and constructivism: Mathematics is a construction of the human mind. L. E. J. Brouwer stood for this. From this view it is more invented.

One distinction helps in everyday life. Invented are signs and language: the digits 0 to 9, the plus sign and the x could have looked different, and about a dozen counting systems existed side by side. Discovered seem relationships: that there are infinitely many primes was proved by Euclid without him choosing it, and the Pythagorean theorem holds in every right triangle, also in Babylonian ones. Geometry also shows how open the question is: in the 19th century non-Euclidean geometries arose that are equally consistent, and physics decides which one describes real space.

“God made the integers, all else is the work of man.”

The sentence is attributed to Kronecker after a lecture of 1886. The earliest known print is in Weber’s obituary; no matching wording is known from Kronecker’s own publications. It shows what the debate is about, but is no proof for a particular doctrine.

Timeline: who contributed what and when

1. 43,000 years ago The Lebombo bone from South Africa with 29 notches, one of the oldest known counting objects.
2. about 3500 to 3200 BC In Mesopotamia the first number signs on clay tablets arise from counting tokens.
3. about 1800 to 1600 BC The tablets Plimpton 322 and YBC 7289 show highly developed Babylonian calculation.
4. about 1550 BC The scribe Ahmes copies the Rhind papyrus with 84 problems.
5. about 300 BC Euclid arranges geometry into axioms and proofs in the Elements.
6. 628 Brahmagupta states rules for zero and negative numbers.
7. about 825 Al-Khwarizmi writes the book on algebra and a text on calculating with Indian digits.
8. 1202 Fibonacci’s Liber abaci brings the digits to Europe.
9. 1489 Johannes Widmann prints + and − in an arithmetic book in Leipzig.
10. 1557 Robert Recorde introduces the equals sign.
11. 1585 Simon Stevin spreads decimal fractions.
12. 1591 and 1637 Viète calculates with letters, Descartes picks x, y and z.

Frequently asked questions

Sources and further reading

• MacTutor History of Mathematics: A history of Zero
• MacTutor History of Mathematics: Thales of Miletus
• Bodleian Libraries: Carbon dating finds Bakhshali manuscript contains oldest recorded origins of the symbol ‘zero’ (14 September 2017)
• Jeff Miller: Earliest Uses of Symbols for Variables and Earliest Uses of Symbols for Fractions and Decimals (on MacTutor)
• Stanford Encyclopedia of Philosophy: Philosophy of Mathematics
• MacTutor: Quotations by Leopold Kronecker, with the reference to Heinrich Weber’s obituary
• Wikipedia: Vedic Mathematics
• Hans Wußing: 6000 Jahre Mathematik. Eine kulturgeschichtliche Zeitreise, Band 1, Springer, Berlin 2008 (in German).