# List of notable amateur mathematicians

An amateur mathematician is a person who does mathematics research out of their own pure interests and without remuneration. Some people who have written on this topic have confused the meaning of the terms amateur and unqualified. That is a misrepresentation of the accepted definitions and will not be used here.

When asked, most professional mathematicians express the view that amateurs cannot make serious contributions to the subject because of the amount of prior knowledge required to reach the forefront of research. Indeed, Wikipedia defines a mathematician as someone who uses mathematics in their work, which excludes the very concept of an amateur mathematician as understood here.

However, there are areas where amateurs have proven this view to be incorrect by solving problems that professional scholars have failed to make progress on for decades. Often new insights are found today by using computational methods neglected and undervalued by academics. In today's society there are many lucrative employment opportunities outside academia for individuals with strong mathematical abilities. Many of these people maintain their interest in the subject and should be encouraged to contribute to research. It is a misconception that all amateur mathematicians lack knowledge, ability or qualifications.

### Criteria for inclusion[edit]

For the purposes of this list we do include those who made mathematical discoveries as an amateur but who then became professional mathematicians as a result of that work, provided they are well known for their contributions made as an amateur (e.g. George Boole, Srinivasa Ramanujan, Yitang Zhang or the four Cambridge undergraduates who solved the Squaring the square problem). Amateur status does not imply that the person was unqualified, but those who held a professional academic position in research mathematics in the past would not be included here. They may be professional researchers in a different subject matter so long as their mathematics research was not part of their funded academic work. They could also count as amateur if they completed a doctorate in mathematics but later made discoveries in mathematics as an amateur (e.g. Zhang). Collaboration with a professional academic would not exclude someone from the list provided it is clear that the amateur mathematician's contribution was significant. Some early astronomers have not been included despite their contributions to pure mathematics because their occupation would have funded the time for their work and at the time the scope of their research would be less well defined. (e.g. John Machin, Thomas Clausen, and Henry Perigal.) School teachers of mathematics up to secondary level can count as amateur mathematicians because they are not funded to do research. Teachers in higher education would not be included.

To be notable they should have made original discoveries in mathematics that are recognised as significant by the mathematics community. For the purposes of this list we require that their mathematical contribution is cited or credited to their name on a Wikipedia page other than their own biography. They do not necessarily have to have their own biographical page on Wikipedia to qualify. It does not matter whether the work is classified as recreational mathematics or not. This is a high-bar, and many people may rightfully consider themselves as amateur mathematicians without meeting this requirement for notability.

Amateurs have made important discoveries throughout history and for the purposes of this list we begin with works from the 16th century. Before then the distinction between professional and amateur was less clear. Communication is important in enabling amateur mathematicians to work and be recognised. In the 17th century Marin Mersenne (who was himself an accomplished amateur mathematician) corresponded with many of the mathematicians of the time, both professional and amateur. His role inspired the foundation of scientific institutions in several countries such as the Royal Society in the UK. These were initially open to amateurs. Their published transactions were the precursors of today's academic journals but these became more difficult to access by amateurs as publishing bodies needed to monetise them. In the 21stb century the internet has made mathematical research accessible to all-comers once more.

## 16th century[edit]

#### Gerolamo Cardano 1501-1576 (medical doctor)[edit]

#### Federico Commandino 1509-1575 (medical doctor)[edit]

#### John Napier 1550-1617 (land owner)[edit]

## 17th century[edit]

#### Marin Mersenne 1588-1648 (theologian)[edit]

- Mersenne Prime numbers
- Mersenne's laws for harmonics of a vibrating string

#### Bernard Frénicle de Bessy 1604-1674 (lawyer)[edit]

- Magic squares and the Frénicle standard form.
- Sum of cube property for 1729.

#### Pierre de Fermat 1607-1665 (lawyer)[edit]

- Adequality technique in calculus
- Fermat's Last Theorem, Fermat numbers, Fermat's little theorem and numerous other discoveries in number theory
- The problem of points and the foundations of probability (with Pascal)

#### Blaise Pascal 1623-1662 (heir)[edit]

- The problem of points and the foundations of probability (with Fermat)
- Pascal's triangle and combinatorics

#### Giordano Vitale 1633-1711 (soldier)[edit]

- A theorem on Saccheri quadrilaterals

#### Abraham Sharp 1653-1742 (schoolmaster)[edit]

- Calculation of pi to 71 decimal places

## 18th century[edit]

#### Thomas Bayes 1701-1761 (minister)[edit]

- Bayes' theorem in probability and statistics

#### John Landen 1719-1790 (land agent)[edit]

- Landen's transformation for elliptic integrals

#### Caspar Wessel 1745-1818 (lawyer)[edit]

- The complex plane

## 19th century[edit]

#### François Budan de Boislaurent 1761-1840 (medic)[edit]

- Budan's theorem for the numerical solution of polynomials

#### Jean-Robert Argand 1768-1822 (shopkeeper)[edit]

- The Argand diagram of the complex plane.
- The first rigorous proof of the Fundamental theorem of algebra

#### Sophie Germain 1776-1831 (independent)[edit]

#### George Green 1793-1841 (miller)[edit]

- A version of Green's theorem

#### Olinde Rodrigues 1795-1851 (banker)[edit]

- Applications of quaternions to rotations

#### Thomas Kirkman 1806-1895 (rector)[edit]

#### Hermann Grassmann 1809-1877 (school teacher)[edit]

- Foundation of linear algebra
- Formalisation of arithmetic and Peano axioms
- Exterior algebra also known in physics as Grassmann algebra
- The Grassmannian

#### Évariste Galois 1811-1832 (political activist)[edit]

- Galois theory and solubility of polynomials
- Group theory

#### William Shanks 1812-1882 (landlord)[edit]

- Calculation of pi to 527 correct digits
- Calculation of e to 205 digits
- Calculation of Euler's constant to 101 digits

#### Ada Lovelace 1815-1852 (countess)[edit]

- Algorithms for computer processing

#### Achille Brocot 1817-1879 (clockmaker)[edit]

#### James Cockle 1819-1895 (judge)[edit]

#### Ivan Pervushin 1827-1900 (priest)[edit]

- Found the ninth Mersenne prime
- Factorisation of Fermat numbers

#### Henri Delannoy 1833-1915 (army officer)[edit]

#### Artemas Martin 1835-1918 (farmer, schoolteacher)[edit]

- Nearly Isosceles Pythagorean triangles

#### Gaston Tarry 1843-1913 (civil servant)[edit]

- Thirty-six officers problem has no solution
- Tarry point for a triangle
- Prouhet–Tarry–Escott problem

#### Jørgen Pedersen Gram 1850-1916 (actuary)[edit]

- Gram–Schmidt process for othogonalisation of vectors
- Gram series for prime number counting
- The Gram matrix, Controllability Gramian, and Observability Gramian in control theory
- Gram's theorem
- Gram–Charlier A series

#### B. Nicolò I. Paganini 1851- (schoolboy)[edit]

- The second amicable pair

#### François Proth 1852-1879 (farmer)[edit]

- Proth's theorem tests for a Proth prime
- Anticipated Gilbreath's conjecture

#### Alfred Kempe 1849-1922 (lawyer)[edit]

- Prior discovery of the Petersen graph
- Kempe's universality theorem
- The Quadruplanar inversor
- Kempe chains for the Four color theorem

#### Thorold Gosset 1869-1962 (lawyer)[edit]

- semi-regular polytopes
- Gosset–Elte figures

## 20th century[edit]

#### Henry Dudeney 1857-1930 (civil servant)[edit]

- Complete set of Pentominos
- Hinged dissection solution to the Haberdasher's Puzzle
- No-three-in-line problem

#### Johan Jensen 1859-1925 (telephone engineer)[edit]

#### James Cullen 1867-1933 (priest, school teacher)[edit]

- Primality of Cullen numbers
- Factorisation of Fermat numbers
- Pierpont prime

#### Henry Cabourn Pocklington 1870-1952 (schoolmaster)[edit]

- Pocklington primality test
- Pocklington's algorithm for inverting quadratic residues

#### Alfred Western 1873-1961 (solicitor)[edit]

- Factorisation of Fermat numbers

#### Ralph Ernest Powers 1875-1852 (railroad employee)[edit]

- Discovery of two Mersenne primes
- Continued fraction factorization

#### Laurence Monroe Klauber 1883-1968 (herpetologist)[edit]

- Prime number arrangement related to the Ulam spiral

#### Srinivasa Ramanujan 1887-1920 (accounting clerk)[edit]

- Extensive work on number theory

#### Kurt Heegner 1893-1965 (independent scholar)[edit]

#### Edouard Zeckendorf 1901-1983 (army medic)[edit]

- Zeckendorf's theorem on Fibonacci numbers

#### Eugène Ehrhart 1906-2000 (school teacher)[edit]

- Ehrhart polynomial for higher-dimensional generalisation of Pick's theorem

#### Leon Bankoff 1908-1997 (dentist)[edit]

- An elementary proof of the Erdős–Mordell inequality
- Bankoff circle

#### David Champernowne 1912-2000 (economist)[edit]

- Champernowne constant as an example of a Normal number

#### Harry Lindgren 1912-1992 (patent officer)[edit]

#### Theophilus Willcocks 1912-2014 (banker)[edit]

- Least squares solution for Squaring the square

#### John Ernest 1922-1994 (artist)[edit]

#### Marjorie Rice 1923-2017 (homemaker)[edit]

#### Harvey Dubner 1928-2019 (engineer)[edit]

- Dubner's conjecture based on Goldbach's conjecture
- Repunit primes
- A Pierpont prime
- Belphegor's prime

#### John Hendricks 1929-2007 (meteorologist)[edit]

- Magic Squares and high-dimensions
- Multimagic cubes

#### Anthony Hill 1930-2020 (artist)[edit]

- Crossing number problem

#### Lee Sallows 1944 (electronics engineer)[edit]

#### George Phillips Odom 1941-2010 (artist)[edit]

- Odom's construction and the golden ratio

#### Lu Jiaxi 1935-1983 (school teacher)[edit]

- Kirkman's schoolgirl problem and Steiner triple systems

#### Robert Ammann 1946-1994 (programmer and postal worker)[edit]

#### Joan Taylor 1957[edit]

#### George Woltman 1957 (programmer)[edit]

#### Kenneth Perko[edit]

- Perko pair of equivalent knots

#### Andrew Beal 1952 (banker)[edit]

#### Marivin Ray Burns[edit]

- The MRB constant

## 21st century[edit]

#### Scott I Chase (director)[edit]

- Edge case for Lander, Parkin, and Selfridge conjecture at 8th powers

#### Yitang Zhang 1955 (lecturer)[edit]

- Existence of infinite prime 2-tuples

#### Philip Gibbs 1960 (software engineer)[edit]

- First rational Diophantine sextuples
- Algorithm and calculation of Ulam numbers up to 1 trillion
- Best known cover for Lebesgue's universal covering problem

#### Greg Egan 1961 (author)[edit]

#### Matt Parker 1980 (comedian)[edit]

- grafting numbers
- Parker magic square

#### Aubrey de Grey 1963 (biologist)[edit]

#### David Smith (print technician)[edit]

- Solutions to the Einstein problem

#### Daniel Larsen 2003 (student)[edit]

- Proof of Bertrand's postulate for Carmichael numbers