# Mathematician:Mathematicians/Sorted By Birth/1501 - 1600 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:

## $\text {1501}$ – $\text {1510}$

### 1501

##### Gerolamo Cardano $($$\text {1501}$ – $\text {1576}$$)$

Italian mathematician, physician, inventor, astrologer and gambler.

- Published systematic methods for solving cubic and quartic equations. Neither were supposedly discovered by him:
- The formula for solving the cubic was passed to him by Tartaglia, but (as he discovered later) was in fact originally discovered by Scipione del Ferro.
- The formula for solving the quartic was discovered by his student Ferrari (and bears Ferrari's name).

- Wrote the first systematic treatment of probability.

### 1510

##### Robert Recorde $($$\text {1510}$ – $\text {1558}$$)$

Welsh physician and mathematician.

Best known for inventing the equals sign. This was just part of his contribution towards the development and systematization of mathematical notation.
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## $\text {1511}$ – $\text {1520}$

### 1511

##### Erasmus Reinhold $($$\text {1511}$ – $\text {1553}$$)$

German astronomer and mathematician, considered to be the most influential astronomical pedagogue of his generation.
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### 1512

##### Gerardus Mercator $($$\text {1512}$ – $\text {1594}$$)$

Flemish geographer, cosmographer and cartographer.

Best known for the $1569$ world map based on a new projection now referred to as Mercator's projection.
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### 1514

##### Georg Joachim Rhaeticus $($$\text {1514}$ – $\text {1574}$$)$

Austrian mathematician who was the sole pupil of Nicolaus Copernicus.

Calculated a table of sines accurate to $10$ decimals.
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### 1515

##### Peter Ramus $($$\text {1515}$ – $\text {1572}$$)$

French logician, humanist and political reformer who fell victim to religious war.
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### 1520

##### Joan Francés Fulcònis $($$\text {c. 1520}$ – $\text {?}$$)$

Mathematician from the area of southern France referred to informally nowadays as Occitania.

Notable for writing one of the earliest mathematics books printed in one of the Occitan dialects, a linguistic group which at the time was subject to political pressure.
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## $\text {1521}$ – $\text {1530}$

### 1522

##### Lodovico Ferrari $($$\text {1522}$ – $\text {1565}$$)$

Italian mathematician who was a student of Gerolamo Cardano.

First one to devise a solution to the general quartic equation, which was later published by Cardano and is now known as Ferrari's Method.
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### 1526

##### Rafael Bombelli $($$\text {1526}$ – $\text {1572}$$)$

Italian mathematician whose influence may have been greater than is currently recognised.

- Documented the rules for multiplication involving negative numbers.

- Pioneered the work on the understanding of imaginary numbers, using as a springboard Cardano's Formula for the solution of the cubic.

- Developed a method of solving square roots by an approach related to continued fractions.

## $\text {1531}$ – $\text {1540}$

##### Hudalrichus Regius $($$\text {fl. 1530s}$$)$

Dutch mathematician who showed that not all numbers of the form $2^n - 1$ for odd $n$ are prime.

He showed in $1536$ that $2^9 - 1 = 511 = 7 \times 73$, and also that $2^{11} - 1 = 2047 = 23 \times 89$.
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### 1532

##### Wilhelm Xylander $($$\text {1532}$ – $\text {1576}$$)$

German classical scholar and humanist who translated the *Arithmetica* of Diophantus.
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### 1538

##### Christopher Clavius $($$\text {1538}$ – $\text {1612}$$)$

German jesuit and logician.

Best known for:

- Clavius's Law (also written as
**Clavius' Law**), otherwise known as the**Consequentia Mirabilis**, which states that if by assuming the negation of a proposition you can prove its truth, then that proposition is true. - Being instrumental in the development of the Gregorian calendar.
- Writing highly-acclaimed and well-received text-books.

### 1540

##### François Viète $($$\text {1540}$ – $\text {1603}$$)$

French amateur mathematician, trained in law, who became a privy councillor under Henry IV of France.

Contributed to many of the early developments of trigonometry and algebra.

Pioneered the use of letters in algebraic equations.

One of the first to use decimal fractions as a matter of course in his published works.
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#### January

##### Ludolph van Ceulen $($$\text {1540}$ – $\text {1610}$$)$

German-Dutch mathematician best known for his calculation of the the value of $\pi$.

The **Ludolphine number** is the expression of the value of $\pi$ to $35$ decimal places:

- $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \ldots$

#### August

##### Joseph Justus Scaliger $($$\text {1540}$ – $\text {1609}$$)$

French religious leader and scholar

Expanding the notion of classical history from Greek and ancient Roman history to include Persian, Babylonian, Jewish and ancient Egyptian history.

Also had the ambition to be a mathematician, and made a failed attempt to square the circle.
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## $\text {1541}$ – $\text {1550}$

### 1546

##### Tycho Brahe $($$\text {1546}$ – $\text {1601}$$)$

Danish nobleman famous for his contributions to the science of astronomy.

Refuted the Aristotelian view that the heavens were unchanging, by interpreting observations of supernovae and comets.

Pointed out inaccuracies in the astronomical model proposed by Nicolaus Copernicus, preferring to adhere to the geocentric model of Claudius Ptolemy.
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### 1547

##### Abu al-Faiz ibn Mubarak $($$\text {1547}$ – $\text {1595}$$)$

Indian-born Arab poet and scholar of late medieval India.

Known in the mathematical world for his translation of *Lilavati* into Persian.
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### 1548

##### Simon Stevin $($$\text {1548}$ – $\text {1620}$$)$

Flemish mathematician, engineer and writer most famous for inventing the decimal notation for the rendering of fractions.

Recommended the use of a decimal system be used for weights and measures, coinage and for measurement of angles.

Wrote most of his work in Dutch, believing it the best language for communication of scientific and mathematical ideas.
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#### April

##### Pietro Antonio Cataldi $($$\text {1548}$ – $\text {1626}$$)$

Italian mathematician and philanthropist who taught mathematics and astronomy.

Founded in Bologna the most ancient known academy of mathematics.

Worked on the development of perfect numbers and continued fractions.

Attempted in vain (as so many before and since) to prove Euclid's fifth postulate.

Supposed to have discovered the $6$th and $7$th Mersenne primes $M_{17}$ and $M_{19}$ in $1588$.
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### 1550

##### John Napier $($$\text {1550}$ – $\text {1617}$$)$

Scots mathematician famous for his development of natural logarithms.
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## $\text {1551}$ – $\text {1560}$

### 1552

##### Jost Bürgi $($$\text {1552}$ – $\text {1632}$$)$

Swiss clockmaker, maker of astronomical instruments and mathematician most famous for publishing a book on logarithms in 1620.

Believed to have invented his own version of logarithms as early as $1588$, but as he failed to publish, John Napier received the credit for the invention.
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### 1560

##### Thomas Harriot $($$\text {c. 1560}$ – $\text {1621}$$)$

English astronomer, mathematician, ethnographer and translator.

His name is variously reported as **Harriott**, **Hariot**, or **Heriot**.

Made great advances in algebra, recognising all roots of equations even whether they be negative or complex.

Had less influence than he might have done, as no mathematical writings of his were ever published in his lifetime.

Was at one point credited with the invention of $>$ and $<$ for greater than and less than, but it appears that they were in fact invented by somebody else.
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## $\text {1561}$ – $\text {1570}$

### 1561

##### John Blagrave $($$\text {c. 1561}$ – $\text {1611}$$)$

English mathematician whose main work was in the field of horology.

Designed and made instruments, including sundials and astrolabes.
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##### Edward Wright $($$\text {c. 1561}$ – $\text {1615}$$)$

English mathematician noted for his contributions to the science of cartography.
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### 1564

#### February

##### Henry Briggs $($$\text {1561}$ – $\text {1630}$$)$

English mathematician most famous for converting Napierian logarithms into Briggsian (common) logarithms.
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### 1564

##### Galileo Galilei $($$\text {1564}$ – $\text {1642}$$)$

Italian mathematician and scientist usually known as just **Galileo**.

At the forefront of a revolution in the understanding of physics. One of the most influential thinkers in history.
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## $\text {1571}$ – $\text {1580}$

### 1571

#### December

##### Adriaan Metius $($$\text {1571}$ – $\text {1635}$$)$

Dutch geometer and astronomer.

Best known now for his approximation $\dfrac {355} {113}$ for $\pi$ (pi), known to the Chinese and Arabic mathematical traditions centuries earlier.
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##### Johannes Kepler $($$\text {1571}$ – $\text {1630}$$)$

German mathematician and astronomer best known nowadays for Kepler's Laws of Planetary Motion.

Inherited the papers of Tycho Brahe and spent many years analysing his observations, looking for patterns.

His most significant contribution to scientific thought was his deduction that the orbits of the planets are elliptical.

Also pre-empted the methods of integral calculus to find the volume of a solid of revolution by slicing it into thin disks, calculating the volume of each, and then adding those volumes together.
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### 1574

##### William Oughtred $($$\text {1574}$ – $\text {1660}$$)$

English mathematician credited with the invention of the slide rule.

Also credited with inventing a circular version although precedence for this was disputed with his student Richard Delamain.

Experimented with notations in his famously compact writings, inventing some new symbology which stuck, notably $\times$, $\sin$ and $\cos$.

Among others, he may have been influential in the introduction of the symbol $\pi$ for pi, using an abbreviation for the Greek word for **periphery** (that is, **περιφέρεια**).
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### 1580

##### Pierre Hérigone $($$\text {1580}$ – $\text {1643}$$)$

French mathematician and astronomer of Basque origin.

Taught in Paris for most of his life.

His greatest influence was his invention of notation.
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#### May

##### Johann Faulhaber $($$\text {1580}$ – $\text {1635}$$)$

German surveyor and engineer who was also a mathematician of the cossist tradition.

A significant influence on several mathematicians, including René Descartes, Jacob Bernoulli and Carl Jacobi.

Best known for his work on series of powers.
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#### June

##### Willebrord van Royen Snell $($$\text {1580}$ – $\text {1626}$$)$

Dutch applied mathematician and astronomer who founded the modern science of geodesy, by pioneering the technique of triangulation.

Developed an improved method for determining the value of $\pi$ (pi) using polygons.

Discovered the Sine Law.

Known today for rediscovering the Snell-Descartes Law in 1621, governing the refraction of light. He did not publish himself. It first appeared in 1703 when it was published in Christiaan Huygens' *Dioptrica*.
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## $\text {1581}$ – $\text {1590}$

### 1581

##### Edmund Gunter $($$\text {1581}$ – $\text {1626}$$)$

British clergyman, mathematician, geometer and astronomer.

Best remembered for his contributions toward land surveying: Gunter's chain, the Gunter's quadrant and the Gunter's scale.

Credited with the first ever publication, in $1620$, of logarithms of trigonometric functions.

Invented the terms cosine and cotangent.
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#### October

##### Claude Gaspard Bachet de Méziriac $($$\text {1581}$ – $\text {1638}$$)$

First to discuss the solution of indeterminate equations by means of continued fractions.

First member to hold Seat 13 of the Académie Française.
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### 1584

##### Grégoire de Saint-Vincent $($$\text {1584}$ – $\text {1667}$$)$

Flemish Jesuit and mathematician, best remembered for his work on quadrature of the hyperbola.

Gave an early account of the summation of geometric series

Resolved Zeno's paradox by showing that the time intervals involved formed a geometric progression and thus had a finite sum.
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### 1588

##### André Jumeau $($$\text {1588}$ – $\text {1651}$$)$

French amateur mathematician and prior who found the third triperfect number $523 \, 776$.
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#### April

##### Thomas Hobbes $($$\text {1588}$ – $\text {1679}$$)$

English thinker better known for being an astute political philosopher than as a mathematician.

Best known in mathematical circles for believing that he had solved the problem of Squaring the Circle.

Generally considered a mathematical ignoramus, his influence was perhaps of greater importance than generally considered, if only because of the stimulating controversy and discussion he raised.
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#### May

##### Étienne Pascal $($$\text {1588}$ – $\text {1679}$$)$

French tax official and lawyer who also had an interest in science and mathematics.

Noted, and respected, for being unusually honest and honourable in his demanding professional position.

Investigated what is now known as the Limaçon of Pascal.

Most famous, however, for being the father of Blaise Pascal.
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#### September

##### Marin Mersenne $($$\text {1588}$ – $\text {1648}$$)$

French theologian, philosopher, mathematician and music theorist.

Most famous for his work with Mersenne primes.

Claimed in $1644$ that the only primes $p \le 257$ for which $2^p - 1$ is prime are $2, 3, 5, 7, 13, 17, 19, 31, 67, 127$ and $257$. Considering the tools he had at his disposal, he was uncannily accurate.

The first to determine the speed of sound through air.
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## $\text {1591}$ – $\text {1600}$

### 1591

#### February

##### Girard Desargues $($$\text {1591}$ – $\text {1661}$$)$

French mathematician who is considered to be one of the founders of projective geometry.
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#### May

##### Jean Leurechon $($$\text {1591}$ – $\text {1670}$$)$

French Jesuit priest, astronomer and mathematician, known for inventing the Pigeonhole Principle and naming the thermometer.
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### 1595

##### Albert Girard $($$\text {1595}$ – $\text {1632}$$)$

Professional French lutenist who also studied mathematics, working in the fields of algebra, trigonometry and arithmetic.

Gave an inductive formula for the Fibonacci numbers.

First stated in $1632$ that every prime of the form $4 k + 1$ is the sum of two squares in only one way.
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### 1596

#### March

##### René Descartes $($$\text {1596}$ – $\text {1650}$$)$

French mathematician and philosopher who is supposed to have invented the Cartesian coordinate system, and thence the field of analytic geometry.
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#### November

##### Jean Appier Hanzelet $($$\text {1596}$ – $\text {1647}$$)$

French printer and engraver who is believed by some to be the actual author of *Récréations Mathématiques* of $1624$, supposedly by H. van Etten.
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### 1598

Italian mathematician who worked on optics and motion.

His approach to geometry was a precursor to integral calculus.

Introduced the logarithm to Italy.

A disciple of Galileo.
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### 1600

##### Richard Delamain $($$\text {1600}$ – $\text {1644}$$)$

English mathematician credited with the invention of a circular slide rule although precedence for this was disputed with his tutor William Oughtred.

At one time was mathematics tutor to Charles I of England.
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##### John Speidell $($$\text {fl. 1600}$ – $\text {1634}$$)$

English mathematician known for his early work on the calculation of logarithms.
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##### Pierre de Fermat $($$\text {c. 1600}$ – $\text {1665}$$)$

French lawyer, also an amateur mathematician famous for lots of things. Especially:

- Fermat's Little Theorem
- Claimed to have found a proof for what became known as Fermat's Last Theorem, but it has since been doubted that this is in fact the case (he may have been mistaken).

Although he claimed to have found proofs of many theorems, few of these have survived.
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