# Mathematician:Mathematicians/Sorted By Birth/1801 - 1850 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 $1801$ – $1810$
- 2 $1811$ – $1820$
- 3 $1821$ – $1830$
- 4 $1831$ – $1840$
- 5 $1841$ – $1850$
- 5.1 1841
- 5.2 1842
- 5.3 1843
- 5.4 1844
- 5.5 1845
- 5.6 1846
- 5.7 1847
- 5.8 1848
- 5.9 1849
- 5.10 1850

## $1801$ – $1810$

### 1801

##### George Biddell Airy (1801 – 1891)

English mathematician and astronomer

Work on planetary orbits.

Measured the mean density of the Earth.

Devised a method of solution of two-dimensional problems in solid mechanics.

Established Greenwich as the location of the prime meridian.
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### 1802

##### Niels Henrik Abel (1802 – 1829)

Norwegian mathematician who died tragically young.

Made significant contributions towards algebra, analysis and group theory.

Best known for proving the impossibility of solving the general quintic in radicals (Abel-Ruffini Theorem).
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##### János Bolyai (1802 – 1860)

Hungarian mathematician who was one of the founders of non-Euclidean geometry.
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### 1803

##### Jacques Charles François Sturm (1803 – 1855)

**Charles Sturm** was a mathematical physicist whose work was mainly in the fields of applied mathematics and physics.
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### 1804

#### October

##### Wilhelm Eduard Weber (1804 – 1891)

German physicist who invented the first electromagnetic telegraph with Carl Friedrich Gauss.
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#### December

##### Carl Gustav Jacob Jacobi (1804 – 1851)

Prolific Prussian mathematician, now most famous for his work with the elliptic functions.
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##### Viktor Yakovlevich Bunyakovsky (1804 – 1889)

Ukrainian mathematician best known for his contribution to the Cauchy-Bunyakovsky-Schwarz Inequality.
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### 1805

##### Johann Peter Gustav Lejeune Dirichlet (1805 – 1859)

Full name: **Johann Peter Gustav Lejeune Dirichlet**.

German mathematician who worked mainly in the field of analysis.

Credited with the first formal definition of a function.
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##### William Rowan Hamilton (1805 – 1865)

Irish mathematician and physicist famous (among other things) for:

- Creating the field of Hamiltonian mechanics;
- The discovery of quaternions;
- Development of aspects of graph theory.

### 1806

##### Augustus De Morgan (1806 – 1871)

British mathematician and logician best known for De Morgan's laws.

Also introduced and made rigorous the Principle of Mathematical Induction.
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### 1807

##### Moritz Abraham Stern (1807 – 1894)

German mathematician known for formulating Stern's diatomic series.

Also known for the Stern-Brocot Tree which he wrote about in $1858$ and which Brocot independently discovered in $1861$.
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### 1808

#### May

##### Carl Anton Bretschneider (1808 – 1878)

German mathematician who worked in geometry, number theory, and history of geometry.

He also worked on logarithmic integrals and mathematical tables.

Probably the first mathematicians to use the symbol $\gamma$ for the Euler-Mascheroni constant, which he published in a paper of $1837$.
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#### July

##### Johann Benedict Listing (1808 – 1882)

German mathematician and physicist who coined the term **topology** in a letter of $1836$.

In $1858$ he invented the Möbius strip at about the same time that August Ferdinand Möbius did.
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#### November

##### Friedrich Julius Richelot (1808 – 1875)

German mathematician best known for his construction of the regular $257$-gon.
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### 1809

##### Joseph Liouville (1809 – 1882)

Active in the fields of number theory, complex analysis, differential geometry, topology, mathematical physics and astronomy.

Proved the existence of transcendental numbers.

Contributed the Sturm-Liouville theory to the field of mathematical physics, in collaboration with Charles Sturm.

Pioneered the study of fractional calculus.

There are several theorems named after him, all in different areas of mathematics and physics.
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##### Benjamin Peirce (1809 – 1880)

American mathematician and logician who has been called "The founding father of modern abstract algebra".

Like George Boole, attempted to put logic on a sound mathematical footing.

He also contributed to many other areas of mathematics.

Proved that there is no odd perfect number with fewer than four prime factors.

Introduced the terms idempotence and nilpotence in $1870$, in his work *Linear Associative Algebra*.

Father of Charles Sanders Peirce.
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##### Hermann Günter Grassmann (1809 – 1877)

Prussian mathematician who pioneered the field of linear algebra and vector analysis.

His work was way ahead of its time, and did not receive the recognition it deserved until much later.

During his life he gained more recognition for his study of languages, including Gothic and Sanskrit, than as a mathematician.
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### 1810

##### Ernst Eduard Kummer (1810 – 1893)

German mathematician mostly active in the field of applied mathematics.

Also worked in abstract algebra and field theory.

Related by marriage to Dirichlet.
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## $1811$ – $1820$

### 1811

##### Elias Loomis (1811 – 1889)

American mathematician and physicist best known for his textbooks.

Also known for his thorough investigation into the geomagnetic storm of 1859.
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##### Évariste Galois (1811 – 1832)

French mathematician famous for dying at the age of 20 as the result of a duel.

Despite his total collected works amounting to a mere 60 pages or so, he had a significant influence in the development of the field of group theory. He was in fact the first person to use the word **group** in a technical sense.

His innovative approach to the problem of the insolubility of the quintic led to the field known now as Galois theory.
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### 1812

#### January

##### William Shanks (1812 – 1882)

English amateur mathematician famous for using Machin's Formula for Pi to calculate $\pi$ (pi) to $707$ places in $1873$, a result which was correct only up to the $527$th place.

The error was highlighted in $1944$ by D.F. Ferguson, using a mechanical calculator.

Shanks' approximation was the longest expansion of $\pi$ until the advent of the electronic digital computer about one century later.

Shanks also calculated Euler's number $e$ and the Euler-Mascheroni constant $\gamma$ to many decimal places.

Also published a table of primes up to $60 \ 000$ and found the natural logarithms of $2$, $3$, $5$ and $10$ to $137$ places.

Also calculated the exact powers of $2$ up to $2^{721}$.
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#### April

##### Theodor Schönemann (1812 – 1868)

Also rendered as **Theodor Schoenemann**.

German mathematician who obtained some important results in number theory.

Obtained Hensel's Lemma before Hensel, and formulated Eisenstein's Criterion (also known as the Schönemann-Eisenstein Theorem) before Eisenstein.
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### 1813

##### Pierre Alphonse Laurent (1813 – 1854)

French mathematician and first-rate military and civil engineer best known for his discovery of what is now known as a Laurent series.

Also published works on the theory of light polarization.
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### 1814

##### Daniel da Silva (1814 – 1878)

Portuguese mathematician who was also a marine officer.

Credited with the Inclusion-Exclusion Principle, which he published in 1854.
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##### Eugène Charles Catalan (1814 – 1894)

French and Belgian mathematician who is most famous for his work in combinatorics and number theory.
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##### James Joseph Sylvester (1814 – 1897)

English mathematician who contributed to matrix theory, invariant theory, number theory, partition theory and combinatorics.

First coined the word matrix.

Contributed notably to the growth of mathematics in the USA.

Tutor of Florence Nightingale.
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### 1815

#### October

##### Karl Theodor Wilhelm Weierstrass (1815 – 1897)

German mathematician whose main work concerned the rigorous foundations of calculus.

Known as "the father of modern analysis".
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#### November

##### George Boole (1815 – 1864)

Irish mathematician famous for his work in the mathematization of logic, and the invention of what is now called Boolean algebra.
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#### December

##### Augusta Ada Lovelace (1815 – 1852)

English mathematician and writer, chiefly known for her work on Charles Babbage's Analytical Engine.

Creator of the first algorithm intended to be carried out by a machine.

Hence she is often regarded as the first computer programmer.
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### 1816

### 1817

##### Angelo Genocchi (1817 – 1889)

Italian mathematician who specialized in number theory.

Worked with Giuseppe Peano.
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### 1818

### 1819

#### April

##### Andrew Hollingworth Frost (1819 – 1907)

English mathematician best known for his discovery of an order $7$ perfect magic cube, accomplished in $1866$.
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#### August

##### George Stokes (1819 – 1903)

Full name and title: **Sir George Gabriel Stokes**.

Mathematician and physicist who made important contributions to fluid dynamics, optics and mathematical physics.

Known for the Navier-Stokes Equations and Stokes' theorem. He was not the pioneer of the latter; it was named after him for his habit of setting its proof as an examination question.
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#### September

##### Claude Séraphin Moret-Blanc (1819 – 1886)

French mathematician who discovered some results in number theory.

Mainly known for the result Positive Integers Equal to Sum of Digits of Cube.
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#### December

##### Pierre Ossian Bonnet (1819 – 1892)

French mathematician who made some important contributions to the differential geometry of surfaces.

Mainly known for the Gauss-Bonnet Theorem.
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### 1820

##### Florence Nightingale (1820 – 1910)

One of the most famous people in British history, she reformed the system of care in military field hospitals.

However, she was also a gifted mathematician, and contributed significantly to the field of statistics.
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##### Isaac Todhunter (1820 – 1884)

English mathematician best known nowadays for his books on mathematics and its history.
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## $1821$ – $1830$

### 1821

##### Heinrich Eduard Heine (1821 – 1881)

German mathematician who worked mainly in analysis.
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##### Pafnuty Lvovich Chebyshev (1821 – 1894)

**Pafnuty Lvovich Chebyshev** (Russian: **Пафну́тий Льво́вич Чебышёв**) was a Russian mathematician.

His work was mainly in the fields of probability, statistics and number theory.

He is best known for proving Bertrand's Postulate in $1850$. It has since been known as the Bertrand-Chebyshev Theorem.
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##### Arthur Cayley (1821 – 1895)

English mathematician most famous for his work in group theory and graph theory.

Also one of the pioneers of matrix algebra, and hence sometimes cited as one of the "fathers" of matrix theory.
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### 1822

##### Léon-François-Antoine Aurifeuille

French mathematician after whom Aurifeuillian factorizations are named.

Also wrote a number of books.
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#### March

##### Joseph Louis François Bertrand (1822 – 1900)

French mathematician working in the fields of number theory, differential geometry, probability theory, economics and thermodynamics.

He conjectured Bertrand's Postulate, in 1845, that there is at least one prime between $n$ and $2n - 2$ for every $n > 3$. This was proved in 1850 by Chebyshev, and hence it is also known as the Bertrand-Chebyshev Theorem.

Also wrote plenty on the history of mathematics.
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#### December

##### Charles Hermite (1822 – 1901)

French mathematician who did research mainly in the fields of number theory and analysis.

The first to prove that e is transcendental.
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### 1823

##### Ferdinand Gotthold Max Eisenstein (1823 – 1852)

German mathematician known both as **Gotthold Eisenstein** and **Ferdinand Eisenstein**, best known for his work in number theory.

Student of Carl Friedrich Gauss.

Died tragically young of tuberculosis.
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##### Leopold Kronecker (1823 – 1891)

German mathematician most notable for his view that all of mathematics ought to be based on integers.

Also a proponent of the mathematical philosophy of finitism, a forerunner of intuitionism and constructivism.

His influence on the mathematical establishment was considerable.

His views put him in direct opposition most notably to Georg Cantor, who was exploring the mathematics of the transfinite.
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### 1824

#### March

##### Gustav Robert Kirchhoff (1824 – 1887)

Prussian physicist contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects.
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#### June

##### Johann Martin Zacharias Dase (1824 – 1861)

German mental calculator famous for calculating $\pi$ to $200$ places in $1844$.
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##### William Thomson, 1st Baron Kelvin (1824 – 1907)

**William Thomson, $1$st Baron Kelvin**, was a British mathematical physicist and engineer who did important work in:

- the mathematical analysis of electricity
- formulation of the first and second laws of thermodynamics
- unification of the discipline of modern physics

Received a knighthood from Queen Victoria for his work on the development of the transatlantic electric telegraph project.
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### 1825

##### Edward J. Goodwin (1825 – 1902)

Indiana physician and amateur mathematician who believed he had squared the circle, trisected the angle and doubled the cube.

He proposed a bill to allow for the charging of royalties for the use of the value of $\pi$ (pi) that he had calculated.

It was rejected before the second reading through the efforts of Clarence Abiathar Waldo.
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##### Francesco Faà di Bruno (1825 – 1888)

Italian mathematician and priest, most famous (in mathematics) for Faà di Bruno's Formula on derivatives of composite functions.

Also notable for his beatification on 25th September 1988 by Pope John Paul II.
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##### August Beer (1825 – 1863)

German physicist and mathematician.

Contributed towards the Beer-Lambert-Bouguer Law.
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### 1826

#### January

##### Giuseppe Battaglini (1826 – 1894)

Italian mathematician best known for being the founder of *Giornale di Matematiche*, later known as *Giornale di Matematiche di Battaglini*.

Also did considerable work in the field of non-Euclidean geometry.
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#### March

##### Alphonse Armand Charles Georges Marie de Polignac (1826 – 1862)

French mathematician best known for De Polignac's Formula and Polignac's Conjecture.
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#### May

##### Jean François Théophile Pépin (1826 – 1904)

French mathematician who centred on number theory.
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#### September

##### Georg Friedrich Bernhard Riemann (1826 – 1866)

**Bernhard Riemann** is most famous for the Riemann Hypothesis, which is (at time of writing, early 21st century) one of the most highly sought-after results in mathematics.
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#### November

##### Henry John Stephen Smith (1826 – 1883)

Irish mathematician remembered for his work in elementary divisors, quadratic forms, and the Smith-Minkowski-Siegel Mass Formula in number theory.

Devised the Smith Normal Form of a matrix.
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### 1827

##### Gustavus Frankenstein (1827 – 1893)

German-American clock maker, artist, mathematician and writer.

Best known now for being the first to discover a perfect magic cube of order 8.
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#### January

##### Ivan Mikheevich Pervushin (1827 – 1900)

Full name in Russian: **Иван Михеевич Первушин**.

Russian priest, who worked in number theory in his spare time.

Most famous for demonstrating the primality of the Mersenne number $M_{61}$, which then became known as Pervushin's number.
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### 1828

### 1829

### August

##### Norman Macleod Ferrers (1829 – 1903)

English mathematician and university administrator, best known nowadays for Ferrers diagrams.
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### November

##### Elwin Bruno Christoffel (1829 – 1900)

German mathematician and physicist.

Introduced fundamental concepts of differential geometry, opening the way for the development of tensor calculus.

This later provided the mathematical basis for general relativity.
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### 1830

## $1831$ – $1840$

### 1831

#### January

##### Francis Guthrie (1831 – 1899)

English-born, later South African, mathematician and botanist, who is best known in the field of mathematics for posing the Four Color Theorem in $1852$.
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#### June

##### James Clerk Maxwell (1831 – 1879)

Scottish scientist in the field of mathematical physics.

Most noted for his theory of electromagnetic radiation.

Maxwell's equations for electromagnetism have been called the "second great unification in physics" after the first one realised by Isaac Newton.
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#### October

##### Julius Wilhelm Richard Dedekind (1831 – 1916)

German mathematician, usually referred to as **Richard Dedekind**, who worked in the fields of abstract algebra, and algebraic number theory.

Most noted for his work on the foundations of the real numbers.

Used the thinking behind the resolution of Galileo's Paradox to underpin the definition of an infinite set.
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### 1832

##### Charles Lutwidge Dodgson (1832 – 1898)

Better known as **Lewis Carroll**, **Charles Dodgson** was a logician, and also an Anglican priest and author.

He is best known nowadays for his *Alice's Adventures in Wonderland* and *Through the Looking-Glass, and What Alice Found There*, not (on the surface) works of mathematics.

His actual mathematical works were idiosyncratic, often focused on making mathematical concepts (in particular, logical syllogisms) accessible to children.

One of the first to treat logical elements with symbols, thus contributing to the birth of symbolic logic.
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##### Rudolf Lipschitz (1832 – 1903)

German mathematician who worked in many areas, including analysis, number theory and differential geometry.
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##### Eugène Rouché (1832 – 1910)

French mathematician best known for his work in complex analysis and calculus.
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##### Peter Ludwig Mejdell Sylow (1832 – 1918)

**Ludwig Sylow** was a Norwegian mathematician who established some important facts on the topic of subgroups of prime order.
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### 1833

### 1834

#### February

##### Hermann Hankel (1834 – 1873)

German mathematician who worked on complex numbers and quaternions.
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#### August

##### John Venn (1834 – 1923)

British mathematician, also an ordained priest, who was active particularly in the fields of probability, statistics, set theory and logic.

Best known for his invention of the Venn diagram.

Later in his career he turned his attention to history.
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### 1835

##### William Stanley Jevons (1835 – 1882)

English economist and logician.

Pioneered the mathematical approach to the study of economics.

Refined and developed George Boole's algebra of classes.
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##### Felice Casorati (1835 – 1890)

Italian mathematician best known for the Casorati-Weierstrass Theorem in complex analysis.
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### 1836

### 1837

### 1838

#### January

##### Marie Ennemond Camille Jordan (1838 – 1922)

**Camille Jordan** was a French mathematician who founded much of the field of group theory.

Also wrote the influential textbook *Cours d'Analyse*.
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#### February

##### Ernst Waldfried Josef Wenzel Mach (1838 – 1916)

Native of the Austrian empire, **Ernst Mach** was a physicist and philosopher.

Noted for his study of shock waves.

Major influence on logical positivism and American pragmatism.

Through his criticism of Isaac Newton, a forerunner of Albert Einstein's Theory of Relativity.
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#### July

##### Georges Pfeffermann (1838 – 1914)

German amateur mathematician who did a lot of work on magic squares and multiplicative magic squares.
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#### October

##### William Carmichael McIntosh (1838 – 1931)

Scottish physician and marine zoologist.

Served as president of the Ray Society, and as vice-president of the Royal Society of Edinburgh.
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#### December

##### Edwin Abbott Abbott (1838 – 1926)

English mathematician and philosopher whose claim to mathematical immortality lies in his speculative fictional work *Flatland: a Romance of Many Dimensions*.
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### 1839

#### February

##### Josiah Willard Gibbs (1839 – 1903)

American scientist who made important theoretical contributions to physics, chemistry, and mathematics.
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#### March

##### Joseph-Émile Barbier (1839 – 1889)

French astronomer and mathematician, best known for Barbier's Theorem on the perimeter of curves of constant width.
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#### June

##### Julius Petersen (1839 – 1910)

Danish mathematician who worked on many areas of mathematics and wrote several textbooks.

Perhaps best known for the Petersen graph.
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#### September

##### Charles Sanders Peirce (1839 – 1914)

American chemist who contributed to the fields of logic and mathematical philosophy, in particular the theory of the use of signs.

Laid some of the groundwork for the mathematical discipline of category theory.

Perceived in $1886$ that the functions of logic can be carried out by electronic circuitry.

Son of Benjamin Peirce.
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#### December

##### Gustav Roch (1839 – 1866)

German mathematician who made significant contributions to the theory of Riemann surfaces.
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### 1840

##### Émile Michel Hyacinthe Lemoine (1840 – 1912)

French mathematician and civil engineer who worked mainly in geometry.

He is best known for defining the Lemoine point of a triangle.
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## $1841$ – $1850$

### 1841

#### January

##### Samuel Loyd (1841 – 1911)

American chess player, chess composer, puzzle author, and recreational mathematician.
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#### August

##### Leo August Pochhammer (1841 – 1920)

German mathematician known for his work on special functions.

Also known for the Pochhammer symbol.
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#### November

##### Charles-Ange Laisant (1841 – 1920)

French politician and mathematician who published some books and founded some journals.

Determined the number of digits in $9^{9^9}$.
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##### Ernst Schröder (1841 – 1902)

**Friedrich Wilhelm Karl Ernst Schröder** (or **Schroeder**) was a German mathematician active mainly in the field of algebraic logic.

He is best known for his contribution to what is now known as the Cantor-Bernstein-Schröder Theorem.
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### 1842

##### Allan Joseph Champneys Cunningham (1842 – 1928)

English military man who studied number theory after leaving the army.

Used his expertise to find factors in numbers such as Mersenne numbers and Fermat numbers.
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#### April

##### Édouard Lucas (1842 – 1891)

French mathematician best known for his study of the Fibonacci numbers. As a result of his researches, discovered what are now known as the Lucas numbers.

In $1876$, proved that the Mersenne number $M_{127}$ is prime, and discovered that $M_{67}$ is actually composite.
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#### May

##### Heinrich Martin Weber (1842 – 1913)

German mathematician who worked in algebra, number theory, analysis and applications of analysis to mathematical physics.

Formulated the ring axioms.
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#### July

##### Otto Stolz (1842 – 1905)

Austrian mathematician working mainly in analysis and the theory of infinitesimals.

Corresponded with Felix Klein on the subject of the Erlangen program, among other subjects.
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#### August

##### Jean-Gaston Darboux (1842 – 1917)

French mathematician who contributed to to geometry and mathematical analysis.

Did considerable important work on linear partial differential equations.
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#### September

##### Alexander Wilhelm von Brill (1842 – 1935)

German mathematician best known for his involvement with Felix Klein in the reform of the teaching of mathematics.

Made significant contributions to the field of algebraic geometry.
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#### November

##### John William Strutt (1842 – 1919)

**John William Strutt, $3$rd Baron Rayleigh**, was an English physicist.

Won the $1904$ Nobel Prize in Physics with William Ramsay for the discovery of argon.

Discovered the phenomenon now called Rayleigh Scattering, which explains why the sky is blue.

Predicted the existence of Rayleigh waves.
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#### December

##### Marius Sophus Lie (1842 – 1899)

**Sophus Lie** (pronounced **Lee**) was a Norwegian mathematician famous for his study of continuous transformation groups.

Such objects are now called Lie groups.
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### 1843

##### Karl Hermann Amandus Schwarz (1843 – 1921)

More usually known as: **Hermann Amandus Schwarz**.

German mathematician known for his work in the field of complex analysis.

Often misspelt **Schwartz**.

Student of Weierstrass.

Best known for his contribution to the Cauchy-Bunyakovsky-Schwarz Inequality.
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##### Moritz Pasch (1843 – 1930)

German mathematician who specialized in the foundations of geometry.

His work served as the inspiration for work by Giuseppe Peano and David Hilbert in their work to re-axiomise the field of geometry.

Best known for his formulation of what is now known as Pasch's Axiom.
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##### Paul Tannery (1843 – 1904)

French mathematician and historian best known for his work on the history of Greek mathematics.

Edited the works of Diophantus, Fermat and Descartes.
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### 1844

##### Max Noether (1844 – 1921)

German mathematician (also occasionally rendered **Nöther**) notable for his work in algebraic geometry and algebraic functions.

Father of Emmy Noether.
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### 1845

#### March

##### Georg Ferdinand Ludwig Philipp Cantor (1845 – 1918)

**Georg Cantor** is the creator of set theory.

He established the importance of correspondence between sets and helped to define the concepts of infinity and well-ordered sets.

He is also famous for stating and proving Cantor's Theorem.
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#### May

##### William Kingdon Clifford (1845 – 1879)

English mathematician and philosopher best known for his work on what is now known as Clifford algebra.

Did much of the intellectual groundwork for the General Theory of Relativity.

Died prematurely as a result of tuberculosis probably brought on through overwork.
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##### Pierre René Jean Baptiste Henri Brocard (1845 – 1922)

French meteorologist and mathematician, in particular a geometer.

Best known for the Brocard points, the Brocard circle and the Brocard triangle.

Also known for the still unsolved Brocard's Problem.
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#### November

##### Ulisse Dini (1845 – 1918)

Italian mathematician and politician, best known for his contributions to real analysis.
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### 1846

#### March

##### Magnus Gustaf Mittag-Leffler (1846 – 1927)

Swedish mathematician whose mathematical contributions are connected chiefly with the theory of functions.
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#### June

##### Johann Gustav Hermes (1846 – 1912)

German mathematician best known for his attempted construction of the regular $65 \, 537$-gon.

Recent research suggests that there may be mistakes in this construction.
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### 1847

##### Andrew Gray (1847 – 1925)

Scots mathematician and physicist who worked on electromagnetism, dynamics and Bessel functions.
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##### Achille Marie Gaston Floquet (1847 – 1920)

**Gaston Floquet** was a French mathematician best known for his work in analysis, especially in theory of differential equations.
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### 1848

##### Georges Fontené (1848 – 1928)

French mathematician who worked in geometry, analytic geometry, linear algebra, elliptic functions and elliptic integrals.

Also studied hyperspaces and "courbes gauches".
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#### July

##### Vilfredo Federico Damaso Pareto (1848 – 1923)

Italian engineer, sociologist, economist, political scientist, and philosopher.
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#### November

##### Friedrich Ludwig Gottlob Frege (1848 – 1925)

German philosopher, logician, and mathematician, one of the founders of modern logic.

Made major contributions to the foundations of mathematics.
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### 1849

#### April

##### Felix Christian Klein (1849 – 1925)

German mathematician best known for his work establishing the connections between geometry and group theory.

Architect of the Erlangen program, which classifies geometries according to their symmetry groups.

Noted for the Klein bottle and Klein four-group.
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#### July

##### Alfred Bray Kempe (1849 – 1922)

English mathematician best known for his work on linkages and the Four Color Theorem.
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#### October

##### Ferdinand Georg Frobenius (1849 – 1917)

German mathematician best known for his work on differential equations and group theory.

Gave the first full proof of the Cayley-Hamilton Theorem.
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#### December

##### Gyula Kőnig (1849 – 1913)

Hungarian mathematician best known nowadays for his work in the embryonic field of set theory.

Was opposed to the work of Cantor and spent much effort trying to disprove his work.

Father of Dénes Kőnig.
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### 1850

##### B. Nicolò I. Paganini (c. 1850 – ?)

Italian amateur mathematician known now only for his discovery of the $2$nd amicable pair $1184$ and $1210$.
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#### January

##### Sofia Vasilyevna Kovalevskaya (1850 – 1891)

In Russian: **Со́фья Васи́льевна Ковале́вская**.

The first female Russian mathematician of record.

Made contributions to analysis, differential equations and mechanics.
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#### May

##### Oliver Heaviside (1850 – 1925)

Largely self-taught English mathematician and physicist who was one of the pioneers in the field of electrical engineering.

Invented a considerable amount of the mathematics and terminology used in electromagnetism.

Significantly developed the theory of Operational Calculus, which are still used in modern-day mathematics in the context of Laplace transforms.
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##### Wooster Woodruff Beman (1850 – 1922)

American mathematician best known for his text books and translations.
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#### June

##### Jørgen Pedersen Gram (1850 – 1916)

Danish actuary and mathematician working mostly in the field of statistics.
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#### August

##### Walter William Rouse Ball (1850 – 1925)

English mathematician, lawyer, and amateur magician.

Best known for his accounts of the history of mathematics.
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