# Mathematician:Mathematicians/Sorted By Birth/1001 - 1500 CE

For more comprehensive information on the lives and works of mathematicians through the ages, see the MacTutor History of Mathematics archive, created by John J. O'Connor and Edmund F. Robertson.

*The army of those who have made at least one definite contribution to mathematics as we know it soon becomes a mob as we look back over history; 6,000 or 8,000 names press forward for some word from us to preserve them from oblivion, and once the bolder leaders have been recognised it becomes largely a matter of arbitrary, illogical legislation to judge who of the clamouring multitude shall be permitted to survive and who be condemned to be forgotten.*- -- Eric Temple Bell:
*Men of Mathematics*, 1937, Victor Gollancz, London

- -- Eric Temple Bell:

## Contents

- 1 $\text {1001}$ – $\text {1100}$
- 2 $\text {1101}$ – $\text {1200}$
- 3 $\text {1201}$ – $\text {1300}$
- 3.1 Nasir al-Din al-Tusi (1201 – 1274)
- 3.2 Qin Jiushao (c. 1202 – 1261)
- 3.3 Campanus of Novara (c. 1220 – 1296)
- 3.4 Yang Hui (c. 1238 – c. 1298)
- 3.5 Ibn al-Banna' al-Marrakushi (1256 – 1321)
- 3.6 Chu Shih-Chieh (c. 1260 – c. 1320)
- 3.7 William of Ockham (c. 1288 – 1347 or 1348)
- 3.8 Levi ben Gershon (1288 – 1344)

- 4 $\text {1301}$ – $\text {1400}$
- 5 $\text {1401}$ – $\text {1420}$
- 6 $\text {1421}$ – $\text {1440}$
- 7 $\text {1441}$ – $\text {1460}$
- 8 $\text {1461}$ – $\text {1480}$
- 9 $\text {1481}$ – $\text {1490}$
- 10 $\text {1491}$ – $\text {1500}$

## $\text {1001}$ – $\text {1100}$

##### Chia Hsien (c. 1010 – c. 1070)

Chinese mathematician best known for discussing Pascal's Triangle about 500 years before Pascal.
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##### Omar Khayyam (1048 – 1131)

Persian mathematician better known nowadays for his poetry.

Completely solved the problem of the solution of cubic equations using conics.

Noted for being one of the first to discuss in print what is now known as Pascal's Triangle.
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##### Gopala (11th century )

**Gopala** was an Indian mathematician noted for studying the Fibonacci numbers before $1135$.
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##### Acharya Hemachandra (1089 – 1172)

Indian all-rounder who, among other things, investigated the Fibonacci sequence, following Gopala.
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## $\text {1101}$ – $\text {1200}$

##### Robert of Chester (12th century )

English Arabist of the $12$th century who translated several books from Arabic to Latin.

Hence appears to be the first to introduce the Arabic numerals to Europe.

His most immediate legacy was his use of the word sine (as **sinus**, meaning **bay** or **fold**) for the word that in the original Indian meant **bow** or chord.

Some credit Gerard of Cremona for this, but Gerard now appears to have followed Robert.
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##### Bhaskara II Acharya (1114 – 1185)

Indian mathematician and astronomer.

One of the first to identify zero as a number in its own right.
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##### Gerard of Cremona (c. 1114 – 1187)

Italian scholar whose calling was to translate Arabic scientific and mathematical papers into Latin, many of which themselves were translations of works originally written in Greek.

Some sources credit him for the mistranslation that led to the word sine, but this may be more reliably attributed to Robert of Chester, who appears to be earlier.
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##### Leonardo Fibonacci (c. 1170 – c. 1250)

Italian mathematician.

One of the most important figures in the history of the development of mathematics.

Wrote the highly influential and important *Liber Abaci* in which he discussed the Hindu-Arabic number system and its practical applications.

Most famous for the Fibonacci numbers. The number sequence itself was known to Indian mathematicians as early as the $6$th century, but it was Fibonacci's *Liber Abaci* which made them well-known throughout Europe.
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##### Li Ye (1192 – 1279)

Chinese mathematician and writer who published and improved the tian yuan shu method for solving polynomial equations of one variable.
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##### John of Holywood (c. 1195 – 1256)

English mathematician and monk, also (perhaps better) known as **Johannes de Sacrobosco** (his name translated into Italian), best known for his works concerning astronomy and the calendar.

Proposed an amendment to the Julian calendar (at the time ten days adrift). His suggestions were influential on Christopher Clavius's own work to develop the Gregorian calendar.
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## $\text {1201}$ – $\text {1300}$

##### Nasir al-Din al-Tusi (1201 – 1274)

Multi-discipline scientist and prolific writer who pre-empted several later Western scientists:

- Darwin with his ideas on evolution
- Copernicus on his heliocentric view of the solar system
- Galileo with his insight into the nature of the Milky Way.

Calculated the value of $51'$ for the precession of the equinoxes.

The first to separate the science of trigonometry, particularly spherical trigonometry, from that of astronomy.
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##### Qin Jiushao (c. 1202 – 1261)

Chinese mathematician, meteorologist, inventor, politician, and writer.

Credited with the discovery of the Ruffini-Horner Method.

Also credited with inventing the Tianchi basin, a type of rain gauge instrument used to gather meteorological data.
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##### Campanus of Novara (c. 1220 – 1296)

Italian mathematician, astronomer, astrologer, and physician who is best known for his work on Euclid's *The Elements*.
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##### Yang Hui (c. 1238 – c. 1298)

Simplified Chinese: 杨辉; traditional Chinese: 楊輝; pinyin: **Yáng Huī**, courtesy name **Qianguang** (谦光).

Chinese mathematician who is best known for an early treatment of Pascal's Triangle (also known as Yang Hui's Triangle), although acknowledging that it was given an earlier treatment by Chia Hsien in a work which is now lost.
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##### Ibn al-Banna' al-Marrakushi (1256 – 1321)

Moroccan mathematician, astronomer, Islamic scholar, Sufi, and a one-time astrologer.

Rediscovered the Thabit pair $\left({17 \,296, 18 \, 416}\right)$.
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##### Chu Shih-Chieh (c. 1260 – c. 1320)

Acknowledged as one of the greatest Chinese mathematicians of his era, he spent 20 years travelling around China teaching mathematics.

**Chu** was his family name, **Shih-chieh** his given name.
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##### William of Ockham (c. 1288 – 1347 or 1348)

English philosopher-monk whose main contribution towards philosophical thought was what is now known as Occam's Razor.

Also wrote down (in words) what are now known as De Morgan's laws.
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##### Levi ben Gershon (1288 – 1344)

French Jewish philosopher, Talmudist, mathematician, physician and astronomer/astrologer.

Notable for publishing an early proof using the principle of mathematical induction.

Anticipated Galileo's error theory.

One of the first astronomers to estimate the distance of the fixed stars to a reasonable degree of accuracy (of the order of $100$ light years).

Refuted Claudius Ptolemy's model of astronomy by direct observation, paving the way for the new model of Nicolaus Copernicus more than $2$ centuries later.

Was involved in a lively debate about Euclid's $5$th postulate, and whether it could be derived from the other $4$.
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## $\text {1301}$ – $\text {1400}$

##### Nicole Oresme (c. 1323 – 1382)

French philosopher and mathematician best known for his many writings.

Known for being critical of the writings of Aristotle, an unusual philosophical position for his day.

Defined the power of a number to a non-integral exponent.
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##### Narayana Pandit (c. 1340 – c. 1400)

Indian mathematician who made considerable contributions to several areas of Indian mathematics.
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##### Madhava of Sangamagrama (c. 1350 – c. 1425)

Indian mathematician who made pioneering contributions to the study of infinite series, calculus, trigonometry, geometry and algebra.

It has been suggested that his works made their way to Europe and had an influence on the later European development of calculus.
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##### Jamshīd al-Kāshī (c. 1380 – 1429)

Prominent mathematician of the newly-founded Samarkand Institute.

Best known for calculating the value of pi ($\pi$) to $16$ decimal places.
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## $\text {1401}$ – $\text {1420}$

##### Nicholas of Cusa (1401 – 1464)

German philosopher, theologian, jurist, and astronomer.

Believed he had calculated $\pi$ exactly, as $3 \cdotp 1423$, but then also gave a good trigonometrical approximation later used by Willebrord van Royen Snell
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##### Antonio Maria del Fiore (15th century – 16th century)

Italian Renaissance mathematician.

A student of Scipione del Ferro, learned from him the formula for the resolution of the particular cubic equation $x^3 + p x = q$, and boasted that he was the only one who could solve such equations.

Challenged Niccolò Fontana Tartaglia to a contest in $1535$ to solve cubics, but was outclassed.

Some sources suggest that it was **del Fiore** who revealed to Gerolamo Cardano that the solution originated from del Ferro and not Tartaglia.
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##### Piero Della Francesca (1412 – 1492)

Italian painter and mathematician.

Recognized as one of the most important Renaissance painters, but was also a creditable mathematician.

His surviving mathematical works concern such subjects as: the abacus; the five Platonic solids, and perspective in painting.
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## $\text {1421}$ – $\text {1440}$

##### Georg von Peuerbach (1423 – 1461)

Austrian astronomer, mathematician and instrument maker, best known for his streamlined presentation of Ptolemaic Astronomy in the *Theoricae Novae Planetarum*.
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##### Johannes Müller von Königsberg (1436 – 1476)

Better known under his Latinized name (**Johannes Müller**) **Regiomontanus**: both surnames mean **King's mountain**.

German mathematician, astronomer, astrologer, translator, instrument maker and Catholic bishop.

Pupil of Georg von Peuerbach, whose uncompleted work he continued.

Set up a printing press at Nuremberg in $\text {1471}$ – $\text {1472}$ for printing scientific works.

First publisher of such scientific literature.

Became internationally famous within his own lifetime.
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## $\text {1441}$ – $\text {1460}$

##### Nicolas Chuquet (1445 or 1455 – 1488 or c. 1500)

French mathematician who first treated powers of unknowns systematically.

Inventor of the words billion for $10^{12}$, trillion for $10^{18}$, and so on.
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##### Luca Bartolomeo de Pacioli (1447 – 1517)

Italian mathematician and Franciscan friar who was a pioneer in the field of accounting.

Sometimes referred to as "The Father of Accounting and Bookkeeping".

The first person to publish a work on the double-entry system of book-keeping.

Published a compilation of the mathematics of his day, the first such work since Leonardo Fibonacci's *Liber Abaci* of $1202$.
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##### Leonardo da Vinci (1452 – 1519)

Italian polymath whose areas of interest included invention, painting, sculpting, architecture, science, music, mathematics, engineering, literature, anatomy, geology, astronomy, botany, writing, history, and cartography.

Variously called the father of palaeontology, ichnology, and architecture.

Widely considered one of the greatest painters of all time.

Sometimes credited with the inventions of the parachute, helicopter and tank.
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## $\text {1461}$ – $\text {1480}$

### 1465

##### Jakob Köbel (1462 – 1533)

German mathematician and state official about whom little can be found on the internet.
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##### Scipione del Ferro (1465 – 1525)

Italian mathematician.

First one to come up with a solution to the general cubic equation, which was later published by Cardano and is now known as Cardano's Formula.

Contributed towards the rationalization of fractions.
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### 1471

#### May

##### Albrecht Dürer (1471 – 1528)

German painter, printmaker and theorist whose theoretical treatises involve principles of mathematics, perspective and ideal proportions.
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### 1473

##### Nicolaus Copernicus (1473 – 1543)

Polish mathematician and astronomer who modelled the universe with the Sun at the center, not the Earth.

His book *De Revolutionibus Orbium Coelestium* (On the Revolutions of the Celestial Spheres) sparked a revolution in scientific thought.
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### 1475

##### Charles de Bouvelles (c. 1475 – c. 1567)

French mathematician and philosopher who introduced the hypotrochoid as a technique for Squaring the Circle.

It is suggested by some sources that he was also the first to investigate the cycloid.

Credited with finding the first odd abundant number to be discovered: $45 \, 045$.
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## $\text {1481}$ – $\text {1490}$

### 1487

##### Michael Stifel (1487 – 1567)

German monk and mathematician who made significant advances in mathematical notation, including the juxtaposition technique for indicating multiplication.

The first to use the term exponent. Published rules for calculation of powers.

The first to use a standard method to solve quadratic equations.

Also an early adopter of negative and irrational numbers.
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## $\text {1491}$ – $\text {1500}$

### 1492

##### Adam Ries (1492 – 1559)

Influential German mathematician who wrote some important instructional works, including sets of tables for calculations.
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### 1494

#### August

##### Johannes Scheubel (1494 – 1570)

German mathematician noted for his work in popularising the use of algebra throughout Europe.

Also published an edition of the first six books of Euclid's *The Elements*.
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#### September

##### Francesco Maurolico (1494 – 1575)

Mathematician and astronomer from Sicily, notable for being the first on record to use the Principle of Mathematical Induction.

Contributed to the fields of geometry, optics, conics, mechanics, music, and astronomy.

Edited the works of classical authors including Archimedes, Apollonius, Autolycus, Theodosius and Serenus.

Composed treatises of his own on mathematics and mathematical science.
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#### December

##### Oronce Finé (1494 – 1555)

French mathematician and cartographer who was mainly a populariser and teacher.
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### 1495

##### Petrus Apianus (1495 – 1552)

German humanist and mathematician.

One of his books significantly appears in the painting *The Ambassadors* by Hans Holbein the Younger.
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### 1499

##### Niccolò Fontana Tartaglia (1499/1500 – 1557)

Italian mathematician, engineer and surveyor.

- Published first Italian translations of Archimedes and Euclid.
- Devised a solution to the general cubic equation independently of Scipione del Ferro, later published by Gerolamo Cardano and now known as Cardano's Formula.
- Challenged in $1535$ by Antonio Maria del Fiore to a public contest to solve cubics, and won convincingly.

### 1500

##### Simon Jacob (c. 1500 – 1564)

German reckoner about whom little is known.

Published a book demonstrating that he understood some facts about the Fibonacci numbers that were not rediscovered until centuries later.
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