# Mathematician:Mathematicians/Sorted By Birth/1601 - 1700 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 $1601$ – $1610$
- 2 $1611$ – $1620$
- 3 $1621$ – $1630$
- 4 $1631$ – $1640$
- 5 $1641$ – $1650$
- 6 $1651$ – $1660$
- 7 $1661$ – $1670$
- 8 $1671$ – $1680$
- 9 $1681$ – $1690$
- 10 $1691$ – $1700$

## $1601$ – $1610$

### 1602

##### John Greaves (1602 – 1652)

English mathematician, astronomer and antiquarian.

Collected astrolabes and astronomical measuring devices (now in the Museum of the History of Science, Oxford).

Studied weights and measures, and wrote a treatise on the Roman foot and denarius, and was a keen numismatist.

In $1645$ he attempted a reform of the Julian calendar which was not adopted.
**show full page**

#### August

##### Gilles Personne de Roberval (1602 – 1675)

French mathematician whose work was a precursor to calculus.

Worked on the quadrature of surfaces and the cubature of solids.
**show full page**

### 1603

##### Pierre de Carcavi (c. 1603 – 1684)

French mathematician who was also a secretary of the National Library of France under Louis XIV.

Noted for his correspondence with Pierre de Fermat, Blaise Pascal, Christiaan Huygens, Galileo Galilei, Marin Mersenne, Evangelista Torricelli and René Descartes.
**show full page**

### 1604

##### Bernard Frénicle de Bessy (c. 1604 – 1674)

French mathematician who wrote numerous mathematical papers, mainly in number theory and combinatorics.

Described all $880$ essentially different normal magic squares of order $4$.

Invented the Frénicle standard form, a standard representation of magic squares

Solved many problems created by Pierre de Fermat.

Discovered the cube property of the number $1729$ (Ramanujan number), later referred to as a taxicab number.
**show full page**

### 1607

##### Antoine Gombaud (1607 – 1684)

**Antoine Gombaud, Chevalier de Méré** was a French gambler, writer, philosopher and amateur mathematician best known for his work in probability theory.
**show full page**

### 1608

##### Evangelista Torricelli (1608 – 1647)

Italian physicist and mathematician, best known for inventing the barometer.

Disciple of Galileo.

Gave his name to Torricelli's Law.
**show full page**

## $1611$ – $1620$

### 1611

##### John Pell (1611 – 1685)

English mathematician and foreign diplomat most famous for what is now known as Pell's Equation.
**show full page**

### 1612

##### Antoine Arnauld (1612 – 1694)

French Roman Catholic theologian, philosopher and mathematician.
**show full page**

### 1613

##### Claude Perrault (1613 – 1688)

French architect, best known for his participation in the design of the east façade of the Louvre in Paris.

Also achieved success as a physician and anatomist, and as an author.

Wrote treatises on physics and natural history.

The first to investigate the tractrix, which he did in $1670$.
**show full page**

### 1614

##### John Wilkins (1614 – 72)

English Anglican clergyman, natural philosopher and author.

One of the founders of the Royal Society.

Demonstrated the use of mathematics in the design of machines.
**show full page**

### 1615

##### Frans van Schooten (1615 – 1660)

Dutch mathematician who is most known for popularizing the analytic geometry of René Descartes.

His 1659 and 1661 edition of his commentary on *La Géométrie* by René Descartes was highly influential, and used by Isaac Newton and Gottfried Wilhelm von Leibniz.
**show full page**

### 1616

##### John Wallis (1616 – 1703)

English mathematician who made considerable contributions towards the invention of the calculus.

Credited with introducing the symbol $\infty$ for infinity.

One of the first English mathematicians to use the techniques of analytic geometry as defined by Descartes.
**show full page**

### 1617

##### Tito Livio Burattini (1617 – 1681)

Italian inventor, architect, Egyptologist, scientist, instrument-maker, traveller, engineer, and nobleman.

Developed an early system of measurement based on time, similar to today's International System of Units.

Invented the the **metro cattolico** (that is "catholic [i.e. universal] metre"), a unit of length equivalent to the length of a pendulum whose period is $1$ second.

Probably the first to recommend the name **metre** for a unit of length.
**show full page**

### 1618

##### Elisabeth of the Palatinate (1618 – 1680)

Princess of the Electorate of the Palatinate who studied (among other things) mathematics and philosophy with René Descartes.

Her correspondence with Descartes survives as a record of the nature of philosophical and religious debates in that period.

Renowned for her intelligence and humanism.
**show full page**

### 1619

##### Prince Rupert of the Rhine (1619 – 1682)

Prince of the lines of both the Electorate of the Palatinate and the House of Stuart, who later in life turned to science and mathematics.

Known for posing the question which is now known as Prince Rupert's Cube.

Renowned for his military flair, but also notorious for his heavy-handed treatment of defeated enemies.
**show full page**

### 1620

##### Nicholas Mercator (c. 1620 – 1687)

German mathematician who designed a marine chronometer for Charles $\text {II}$ of England, and designed and constructed the fountains at the Palace of Versailles.

Known for the Newton-Mercator Series.
**show full page**

##### William Brouncker (c. 1620 – 1684)

English mathematician best known for Brouncker's Formula, an expansion for pi in the form of a generalized continued fraction.

Popularly believed to have been the first European to provide the solution to what is known as Pell's Equation, but the supposition that its name was a misattribution by Euler is disputed.

Improved on William Neile's computation of the arc length of the semicubical parabola $a y^2 = x^3$.
**show full page**

#### April

##### John Graunt (1620 – 1674)

English merchant whose influence on mathematics consists of the first statistical analysis of life expectancy, population estimation and the ratio between the sexes.
**show full page**

## $1621$ – $1630$

### 1622

#### March

##### Johann Heinrich Rahn (1622 – 1676)

Swiss mathematician credited with the first use of the division symbol, $\div$, also known as the obelus, and the therefore sign, $\therefore$.
**show full page**

#### April

##### Vincenzo Viviani (1622 – 1703)

Italian mathematician and scientist.

Pupil of Evangelista Torricelli and a disciple of Galileo.
**show full page**

### 1623

##### Blaise Pascal (1623 – 1662)

French mathematician and philosopher who explored probability theory and projective geometry.

Most famous for the construction now commonly known as Pascal's Triangle.
**show full page**

### 1625

##### John Collins (1625 – 1683)

English mathematician whose principal influence consisted of a copious correspondence with the other leading minds of his day.

Mainly worked as a teacher and an accountant, and authored some books.
**show full page**

##### Giovanni Domenico Cassini (1625 – 1712)

Italian/French mathematician, astronomer, engineer, and astrologer.

Most of his important discoveries were in the field of astronomy.

Not to be confused with his son, also called **Jean-Dominique Cassini**.
**show full page**

### 1626

##### Pietro Mengoli (1626 – 1686)

Italian mathematician who spent most of his working life as a professor at the University of Bologna.

Also ordained into the Priesthood.

Occupies the philosophical transitional ground between the work of Bonaventura Francesco Cavalieri and that of Isaac Newton and Gottfried von Leibniz.
**show full page**

### 1627

##### Joseph Moxon (1627 – 1691)

English printer specialising in mathematical books and maps, a maker of globes and mathematical instruments, and mathematical lexicographer.

Produced the first English language dictionary devoted to mathematics, and the first detailed instructional manual for printers.
**show full page**

### 1628

##### Johannes van Waveren Hudde (1628 – 1704)

Dutch mathematician, who was also at one time the mayor of Amsterdam and governor of the Dutch East India Company.

Organised the regulation of the waterways of Amsterdam, in the process making major steps towards improvements in sanitation.

Collaborated on a translation into Latin of *La Géométrie* by René Descartes.
**show full page**

### 1629

##### Christiaan Huygens (1629 – 1695)

Dutch mathematician, astronomer, physicist and horologist.

Studied the rings of Saturn and discovered its moon Titan.

Invented the pendulum clock.

Believed that light travels in waves, hence the Huygens-Fresnel Principle.
**show full page**

### 1630

##### Isaac Barrow (1630 – 1677)

English Christian theologian and mathematician who had a hand in the development of calculus.

Often cited as being the discoverer of the Fundamental Theorem of Calculus.

Concentrated on the properties of the tangent.

The first to calculate the tangents of the kappa curve.

Famously stood down from his position as Lucasian Professor of Mathematics in favour of Isaac Newton.
**show full page**

## $1631$ – $1640$

### 1631

##### Edward Cocker (1631 – 1676)

English engraver, who also taught writing and arithmetic.

Supposedly the author of the famous and highly popular *Arithmetick*, although it is disputed as to whether he actually was the author.
**show full page**

### 1632

##### Christopher Michael Wren (1632 – 1723)

English mathematician, anatomist, astronomer, geometer and physicist, as well as being Britain's most famous architect.

One of the founders of the Royal Society, and was its president from $1680$ to $1682$.
**show full page**

### 1635

##### Robert Hooke (1635 – 1703)

English scientist who worked in many fields and investigated a great deal of stuff.

In the field of applied mathematics he is best known for Hooke's Law.

Made the essental suggestion to Isaac Newton that planetary orbits have two components: towards the central body, and tangential to the orbit.

Invented the conical pendulum.
**show full page**

### 1637

##### Jacob Marcelis (1637 – ?)

Dutch soap merchant and amateur mathematician who gave an approximation to $\pi$ (pi): $3 + \dfrac {1 \, 008 \, 449 \, 087 \, 377 \, 541 \, 679 \, 894 \, 282 \, 184 \, 894} {6 \, 997 \, 183 \, 637 \, 540 \, 819 \, 440 \, 035 \, 239 \, 271 \, 702}$ which he mistakenly claimed was exact.
**show full page**

##### William Neile (1637 – 1670)

English mathematician whose most important work was on the rectification of the semicubical parabola, which was an important stage in the development of calculus.
**show full page**

### 1638

##### James Gregory (1638 – 1675)

Scottish mathematician and astronomer best known for designing the Gregorian telescope.

Made advances in trigonometry, discovering infinite series representations for several trigonometric functions.
**show full page**

### 1640

#### April

##### Georg Mohr (1640 – 1697)

Danish mathematician and geometer now famous for proving in $1672$ that any geometrical construction that can be made with compasses and straightedge can also be achieved by using only compasses. This result was overlooked at the time. Lorenzo Mascheroni made the same discovery in $1797$. However, it was only in $1928$ that Mohr's priority came to light.

Other books of his are rumoured but none have come to direct light.
**show full page**

#### June

##### Jacques Ozanam (1640 – 1718)

French mathematician renowned for the books he wrote, and for his philanthropy.

Published a set of trigonometric and logarithmic tables more accurate than any of the existing ones.

Identified three pairs of triangular numbers whose sum and difference are also triangular.
**show full page**

## $1641$ – $1650$

### 1642

##### Isaac Newton (1642 – 1727)

Hugely influential English all-rounder famous for:

- Inventing calculus, independently of Leibniz
- Successfully providing a mathematical model for the force of gravity
- Formulating the Principle of Conservation of Momentum and Principle of Conservation of Angular Momentum
- Building the first practical optical reflecting telescope
- Developing a theory of colour based on the splitting of light with a prism

and much more.
**show full page**

### 1646

##### Gottfried Wilhelm von Leibniz (1646 – 1716)

German mathematician and philosopher who is best known for being the co-inventor (independently of Isaac Newton) of calculus.

Took some of the first philosophical steps towards a system of symbolic logic, but his works failed to have much influence on the development of logic, and these ideas were not developed to any significant extent.

Invented the system of binary notation.
**show full page**

### 1647

##### Giovanni Benedetto Ceva (1647 – 1734)

Italian mathematician best known for Ceva's Theorem, a result in geometry.

Also rediscovered and published Menelaus's Theorem.
**show full page**

## $1651$ – $1660$

### 1651

##### Ehrenfried Walther von Tschirnhaus (1651 – 1708)

German mathematician more famous for inventing a brand of porcelain.

Worked on techniques in algebra, and also investigated catacaustic curves.

Published what he thought was a solution to the quintic equation in $1683$, but Gottfried Wilhelm von Leibniz pointed out that it was fallacious.
**show full page**

### 1652

##### Michel Rolle (1652 – 1719)

French mathematician best known for Rolle's Theorem.

Also noted for popularising the $n$th root sign.
**show full page**

### 1654

##### Pierre Varignon (1654 – 1722)

French mathematician whose principal contributions were to graphic statics and mechanics.

Friend of Isaac Newton, Gottfried Wilhelm von Leibniz, and the Bernoulli family.

One of the earliest and strongest French advocate of infinitesimal calculus.

Exposed the errors in Michel Rolle's critique thereof.
**show full page**

#### December

##### Jacob Bernoulli (1654 – 1705)

Swiss mathematician best known for his work on probability theory, analytic geometry and development of the calculus.

Also developed the field of calculus of variations.

Developed the technique of Separation of Variables, and in $1696$ solved what is now known as Bernoulli's (Differential) Equation.

Invented polar coordinates.

Elder brother of Johann Bernoulli, with whom he famously quarrelled.
**show full page**

### 1656

##### Edmund Halley (1656 – 1742)

English astronomer, geophysicist, mathematician, meteorologist, and physicist best known for computing the orbit of Halley's Comet.

He was the second Astronomer Royal in Britain, succeeding John Flamsteed.
**show full page**

### 1659

##### David Gregory (1659 – 1708)

Scottish mathematician and astronomer.

Professor of mathematics at the University of Edinburgh, Savilian Professor of Astronomy at the University of Oxford.

Commentator on Isaac Newton's *Principia*.
**show full page**

## $1661$ – $1670$

### 1661

##### Guillaume de l'Hôpital (1661 – 1704)

French mathematician best known for L'Hôpital's Rule, although this was in fact discovered by Johann Bernoulli.
**show full page**

### 1662

##### Nicolaus Bernoulli (1662 – 1716)

Brother of Jacob Bernoulli and Johann Bernoulli, and father of Nicolaus I Bernoulli.

It is unclear exactly what, if anything, **Nicolaus Bernoulli** contributed to mathematics.

The accepted report is that he was a painter, and an alderman of Basel.

However, some sources, notably 1937: Eric Temple Bell: *Men of Mathematics*, appear to conflate him with Nicolaus II Bernoulli.
**show full page**

### 1667

#### May

##### Abraham de Moivre (1667 – 1754)

French mathematician best known for De Moivre's Formula.

Also noted for his work on the normal distribution and probability theory.
**show full page**

#### July

##### Johann Bernoulli (1667 – 1748)

Swiss mathematician best known for his work on development of the calculus.

Taught Guillaume de l'Hôpital, who then went ahead and published his lecture notes without crediting him.

Pioneered the technique of Integration by Parts.

Younger brother of Jacob Bernoulli, with whom he did not always see eye to eye.
**show full page**

#### September

##### Giovanni Girolamo Saccheri (1667 – 1733)

Italian Jesuit priest, scholastic philosopher, and mathematician.

Attempted (but failed) to prove Euclid's fifth postulate by means of Reductio ad Absurdum, and in the process narrowly missed discovering a non-Euclidean geometry.
**show full page**

## $1671$ – $1680$

### 1671

##### Luigi Guido Grandi (1671 – 1742)

Italian mathematician, engineer, priest and philosopher, best known for his study of the rhodonea (rose) curve.

Contributed to *Note on the Treatise of Galileo Concerning Natural Motion* in the first Florentine edition of Galileo Galilei's works.

Helped introduce Gottfried Leibniz's ideas on calculus to Italy.

Also known for Grandi's Series.
**show full page**

### 1675

##### William Jones (1675 – 1749)

Welsh mathematician who has recently come to notice for being the first to use the symbol $\pi$ (pi) in print to represent the ratio of the circumference of a circle to its diameter.

Close friend of Isaac Newton and Edmund Halley.

On his death, left behind him a library of about $15 \, 000$ books, which was probably the most valuable library of mathematics in England. This has only recently been fully dispersed.
**show full page**

### 1676

##### Jacopo Francesco Riccati (1676 – 1754)

Count **Jacopo Francesco Riccati** was an aristocratic Italian mathematician and jurist from Venice.

Chiefly responsible for introducing Isaac Newton's ideas to Italy.

Best known for having founded the equation which bears his name.

Contributed towards Maria Gaëtana Agnesi's 1748 work *Instituzioni analitiche ad uso della gioventù italiana*.
**show full page**

### 1678

##### Pierre Raymond de Montmort (1678 – 1719)

French mathematician (also known as **Pierre Rémond de Montmort**) who worked in probability theory.

The first to introduce the combinatorial study of derangements.

Also known for naming Pascal's triangle after Blaise Pascal, calling it "Table de M. Pascal pour les combinaisons."
**show full page**

## $1681$ – $1690$

### 1682

#### April

##### John Hadley (1682 – 1744)

English mathematician who invented the sextant, independently of Thomas Godfrey.

Constructed the first practical working reflecting telescope.
**show full page**

#### July

##### Roger Cotes (1682 – 1716)

English mathematician, who worked closely with Isaac Newton by proofreading the second edition of *Principia* before publication.

Invented the quadrature formulas known as Newton-Cotes Formulas.

First introduced what is known today as Euler's Formula, in the form $\map \ln {\cos \theta + i \sin \theta} = i \theta$.

Introduced the concept of the radian.
**show full page**

### 1685

##### George Berkeley (1685 – 1753)

Also known under the name **Bishop Berkeley**.

Anglo-Irish mathematician and philosopher best known nowadays for his critique of the philosophical underpinnings of calculus as it had been developed by Gottfried Wilhelm von Leibniz and Isaac Newton.

Incisive intellectual, noted humanitarian, and, by all accounts, all-round good guy.
**show full page**

##### Brook Taylor (1685 – 1731)

English mathematician noted for Taylor's Theorem, but he was not the only one to have been exploring it.

Also made progress in the mathematics of perspective and the foundations of projective geometry.
**show full page**

### 1686

##### John Machin (c. 1686 – 1751)

English professor of astronomy, best known for developing a quickly converging series for $\pi$ (pi) in $1706$ and using it to compute $\pi$ to $100$ decimal places.
**show full page**

##### Daniel Gabriel Fahrenheit (1686 – 1736)

Dutch-German-Polish physicist, engineer, and glass blower.

Best known for inventing the mercury-in-glass thermometer.

Developed the Fahrenheit temperature scale.
**show full page**

### 1687

#### October

##### Robert Simson (1687 – 1768)

Scots mathematician notable for having produced a translation of Euclid's *The Elements* which was long used as the standard text.
**show full page**

##### Nicolaus I Bernoulli (1687 – 1759)

Swiss mathematician who worked on probability theory, geometry and differential equations.

Most of his important work can be found in his correspondence, particularly with Pierre Raymond de Montmort, in which he introduced the St. Petersburg Paradox.

He also corresponded with Leonhard Paul Euler and Gottfried Wilhelm von Leibniz.

Son of Nicolaus Bernoulli and so nephew of Jacob Bernoulli and Johann Bernoulli.
**show full page**

### 1690

##### Christian Goldbach (1690 – 1764)

Prussian amateur mathematician who also studied law and medicine.

Best known for posing the Goldbach Conjecture, which also appears as Goldbach's Marginal Conjecture, and a similar weaker conjecture known as Goldbach's Weak Conjecture.
**show full page**

## $1691$ – $1700$

### 1692

##### James Stirling (1692 – 1770)

Scottish mathematician best known for Stirling's Formula.

One of the first to study what is now known as the Gamma function.
**show full page**

### 1695

##### Nicolaus II Bernoulli (1695 – 1726)

Swiss mathematician who worked mostly on curves, differential equations and probability theory. He also contributed to fluid dynamics.

Studied as a lawyer, and became involved in the priority dispute between Newton and Leibniz, and also the one between Johann Bernoulli and Brook Taylor.

Posed the problem of reciprocal orthogonal trajectories in $1720$.

Son of Johann Bernoulli and the elder brother of Daniel Bernoulli and Johann II Bernoulli.
**show full page**

### 1698

#### February

##### Colin Maclaurin (1698 – 1746)

Held the record for almost 300 years as the youngest professor in history.

Worked extensively on elliptic functions.

Best known nowadays for Maclaurin Series.
**show full page**

##### Pierre Bouguer (1698 – 1758)

French mathematician, geophysicist, geodesist and astronomer.

The first known discoverer of what is now generally known as the Beer-Lambert-Bouguer Law.

Measured the acceleration of free-fall using a pendulum.

Was the first to notice that the period of a pendulum could be affected by the gravitational force exerted by a high mountain.
**show full page**

#### September

##### Pierre Louis Moreau de Maupertuis (1698 – 1759)

French mathematician, philosopher and man of letters.

Credited with having invented the principle of least action.
**show full page**

### 1700

##### Daniel Bernoulli (1700 – 1782)

Dutch / Swiss mathematician who worked mostly on fluid dynamics, probability theory and statistics.

Considered by many to be the first mathematical physicist.

Son of Johann Bernoulli and the brother of Nicolaus II Bernoulli and Johann II Bernoulli.

Famously suffered from the jealousy and bad temper of his father Johann Bernoulli who, among other unpleasantnesses, tried to steal his *Hydrodynamica* and pass it off as his own, naming it *Hydraulica*.
**show full page**