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]

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)