Popular mathematics is the presentation of

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

to an aimed general audience. The difference between

recreational mathematics Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...

and popular mathematics is that recreational mathematics intends to be fun for the mathematical community, and popular mathematics intends to make mathematical knowledge known by the general audience. Some popularization methods are mathematical books which require no mathematical background, and in other cases involves

social interaction A social relation or also described as a social interaction or social experience is the fundamental unit of analysis within the social sciences, and describes any voluntary or involuntary interpersonal relationship between two or more individuals ...

raise awareness Consciousness raising (also called awareness raising) is a form of activism popularized by United States feminists in the late 1960s. It often takes the form of a group of people attempting to focus the attention of a wider group on some cause or ...

. There are several

reasons In the most general terms, a reason is a consideration which justifies or explains an action, a belief, an attitude, or a fact. ''Normative reasons'' are what people appeal to when making arguments about what people should do or believe. For exa ...

to popularize mathematics or promote mathematics, but it is indeed the most difficult

academic discipline An academy ( Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary or tertiary higher learning (and generally also research or honorary membership). The name traces back to Plato's school of philosophy ...

to popularize.

History

Research by

historians of mathematics The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments ...

has shown the existence of a tradition of popularization dating back at least to the

Middle Ages In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire a ...

, and we can even consider ''

The Sand Reckoner ''The Sand Reckoner'' ( el, Ψαμμίτης, ''Psammites'') is a work by Archimedes, an Ancient Greek mathematician of the 3rd century BC, in which he set out to determine an upper bound for the number of grains of sand that fit into the unive ...

'', in the 3rd century BC, as the first example of a mathematical text intended for a non-mathematician. The

popularization of science ''Popular Science'' (also known as ''PopSci'') is an American digital magazine carrying popular science content, which refers to articles for the general reader on science and technology subjects. ''Popular Science'' has won over 58 awards, inclu ...

has accompanied the progress of science at least since the 17th century, with Galileo's famous text, ''

The Assayer ''The Assayer'' ( it, Il Saggiatore) was a book published in Rome by Galileo Galilei in October 1623 and is generally considered to be one of the pioneering works of the scientific method, first broaching the idea that the book of nature is to be ...

'' or for example works such as the ''Conférences sur la plurality des mondes'' of Fontenelle or ''

Letters to a German Princess ''Letters to a German Princess, On Different Subjects in Physics and Philosophy'' (French: ''Lettres à une princesse d'Allemagne sur divers sujets de physique et de philosophie'') were a series of 234 letters written by the mathematician Leonhar ...

'' of

Leonhard Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...

, popular mathematical texts are also quite common, thus the

Encyclopedia An encyclopedia (American English) or encyclopædia (British English) is a reference work or compendium providing summaries of knowledge either general or special to a particular field or discipline. Encyclopedias are divided into articles ...

is a vast undertaking of popularization in all kinds of fields and the very numerous Mathematics articles that we owe to

D'Alembert Jean-Baptiste le Rond d'Alembert (; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the ''Encyclopédie ...

are, as far as this disciplinary field is concerned, an obvious illustration. Alongside this, we must mention several important texts of the

18th century The 18th century lasted from January 1, 1701 ( MDCCI) to December 31, 1800 ( MDCCC). During the 18th century, elements of Enlightenment thinking culminated in the American, French, and Haitian Revolutions. During the century, slave trad ...

, the translation of the ''

Philosophiæ Naturalis Principia Mathematica (English: ''Mathematical Principles of Natural Philosophy'') often referred to as simply the (), is a book by Isaac Newton that expounds Newton's laws of motion and his law of universal gravitation. The ''Principia'' is written in Latin and ...

'' by

Émilie du Châtelet Gabrielle Émilie Le Tonnelier de Breteuil, Marquise du Châtelet (; 17 December 1706 – 10 September 1749) was a French natural philosopher and mathematician from the early 1730s until her death due to complications during childbirth in 1749. ...

which makes it possible to make

Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...

's work available to French-speaking scientists and the ''Eulogy of Euler'' by

Marquis de Condorcet Marie Jean Antoine Nicolas de Caritat, Marquis of Condorcet (; 17 September 1743 – 29 March 1794), known as Nicolas de Condorcet, was a French philosopher and mathematician. His ideas, including support for a liberal economy, free and equal pu ...

which makes known the production of this great mathematician or the one, by Fontenelle, Isaac Newton and

Gottfried Wilhelm Leibniz Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathema ...

. On the other hand, the ''

Journal des sçavans The ''Journal des sçavans'' (later renamed ''Journal des savans'' and then ''Journal des savants,'' lit. ''Journal of the Learned''), established by Denis de Sallo, is the earliest academic journal published in Europe. It is thought to be the ear ...

'' serves as a support for the popularization of science, particularly mathematics, by announcing recent discoveries and by presenting recent books and works aimed at a wide audience. Alongside this, there are books on recreational mathematics for

didactic Didacticism is a philosophy that emphasizes instructional and informative qualities in literature, art, and design. In art, design, architecture, and landscape, didacticism is an emerging conceptual approach that is driven by the urgent need to ...

purposes, such as the books by Bachet de Méziriac,

Claude Mydorge Claude Mydorge (1585 – July 1647) was a French mathematician. His primary contributions were in geometry and physics. Mydorge served on a scientific committee (whose members included Pierre Hérigone and Étienne Pascal) set up to determine ...

Jacques Ozanam Jacques Ozanam (16 June 1640, in Sainte-Olive, Ain – 3 April 1718, in Paris) was a French mathematician. Biography Jacques Ozanam was born in Sainte-Olive, Ain, France. In 1670, he published trigonometric and logarithmic tables more accu ...

and

Édouard Lucas __NOTOC__ François Édouard Anatole Lucas (; 4 April 1842 – 3 October 1891) was a French mathematician. Lucas is known for his study of the Fibonacci sequence. The related Lucas sequences and Lucas numbers are named after him. Biography Lucas ...

, the eulogies of mathematicians on their death or their jubilee pronounced by one of their collaborators and intended to present their work to their non-mathematician colleagues and friends, and the numerous forms contenting themselves with giving results without demonstration, or having for purpose of teaching calculation techniques. With a more immediately practical objective, the progressive mathematization of physics from the work of Newton frequently leads mathematicians to produce popular texts for the use of other scientists and even beyond; we can particularly cite the publications of Joseph Bertrand in the 19th century, Antoine Cournot tries, meanwhile, to popularize mathematics in the direction of

economists An economist is a professional and practitioner in the social science discipline of economics. The individual may also study, develop, and apply theories and concepts from economics and write about economic policy. Within this field there are ...

. We begin, at the beginning of the 20th century, to find more and more texts addressed to non-specialists, for example by Russell, Poincaré or Borel, and texts really intended for the general public and seeking to communicate the essence of what is the work of the mathematician are, in 1940,

A Mathematician's Apology ''A Mathematician's Apology'' is a 1940 essay by British mathematician G. H. Hardy, which offers a defence of the pursuit of mathematics. Central to Hardy's " apology" — in the sense of a formal justification or defence (as in Plato's '' Ap ...

G. H. Hardy Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of pop ...

, the following year the book by Richard Courant, '' What Is Mathematics?'' and in 1945 George Pólya 's book

How To Solve It ''How to Solve It'' (1945) is a small volume by mathematician George Pólya describing methods of problem solving. Four principles ''How to Solve It'' suggests the following steps when solving a mathematical problem: # First, you have to ''un ...

. Beginning in 1956,

Martin Gardner Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis ...

's regular math games column in ''

Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it i ...

'' pioneered a more mainstream approach to mathematical topics; other similar chronicles appear in numerous popular journals, for example that of Jean-Paul Delahaye in ''Pour la science''.

Christopher Zeeman Sir Erik Christopher Zeeman FRS (4 February 1925 – 13 February 2016), was a British mathematician, known for his work in geometric topology and singularity theory. Overview Zeeman's main contributions to mathematics were in topology, partic ...

was the first mathematician to deliver a lecture at the

Royal Institution Christmas Lectures The Royal Institution Christmas Lectures are a series of lectures on a single topic each, which have been held at the Royal Institution in London each year since 1825, missing 1939–1942 because of the Second World War. The lectures present sc ...

1978.

Hannah Fry Hannah Fry (born February 1984) is a British mathematician, author, and radio and television presenter. She is Professor in the Mathematics of Cities at the UCL Centre for Advanced Spatial Analysis. She studies the patterns of human behaviour, ...

was the second in 2019.

Reasons

There are several reasons to popularize mathematics. The first is to increase the number minorities in mathematics. Mathematical communication is an important tool that allows children to demonstrate their mathematical thinking and understanding of the world, and has become ever important in a world with increasing amounts of

math anxiety Mathematical anxiety, also known as math phobia, is anxiety about one's ability to do mathematics. Math Anxiety Mark H. Ashcraft defines math anxiety as "a feeling of tension, apprehension, or fear that interferes with math performance" (2002, p ...

. Sometimes students use semi-proudlythe sentence “not being good at math,” while being ashamed of saying they don't understand Picasso, as Marcelo Viana, mathematician, said. A significant difficulty in popularizing mathematics is the abstract nature of many concepts, and therefore the virtual impossibility of illustrating them. From the 1980s, with the appearance of powerful graphic tools revolutionized certain sectors of mathematics education and their popularization. In 1986, a traveling exhibition by

Heinz-Otto Peitgen Heinz-Otto Peitgen (born April 30, 1945 in Bruch, Nümbrecht near Cologne) is a German mathematician and was President of Jacobs University from January 1, 2013 to December 31, 2013. Peitgen contributed to the study of fractals, chaos theory, an ...

, ''Frontiers of Chaos'', introduced the

general public In public relations and communication science, publics are groups of individual people, and the public (a.k.a. the general public) is the totality of such groupings. This is a different concept to the sociological concept of the ''Öffentlichkei ...

to the beauty of fractal images''.'' In 2005, Erica N. Walker said in an interview with

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

that she was a mathematical activist.

Methods

Popularizers of mathematics follow some methods to popularize mathematics. The creation of

resource Resource refers to all the materials available in our environment which are technologically accessible, economically feasible and culturally sustainable and help us to satisfy our needs and wants. Resources can broadly be classified upon their ...

s such as

book A book is a medium for recording information in the form of writing or images, typically composed of many pages (made of papyrus, parchment, vellum, or paper) bound together and protected by a cover. The technical term for this physical arr ...

s which includes mathematical

literature Literature is any collection of written work, but it is also used more narrowly for writings specifically considered to be an art form, especially prose fiction, drama, and poetry. In recent centuries, the definition has expanded to include ...

museum A museum ( ; plural museums or, rarely, musea) is a building or institution that cares for and displays a collection of artifacts and other objects of artistic, cultural, historical, or scientific importance. Many public museums make these ...

magazine A magazine is a periodical publication, generally published on a regular schedule (often weekly or monthly), containing a variety of content. They are generally financed by advertising, purchase price, prepaid subscriptions, or by a combinatio ...

s, which can be enjoyed by the

public In public relations and communication science, publics are groups of individual people, and the public (a.k.a. the general public) is the totality of such groupings. This is a different concept to the sociological concept of the ''Öffentlichkei ...

, and which vary according to the historical moment, especially to approach

fashion Fashion is a form of self-expression and autonomy at a particular period and place and in a specific context, of clothing, footwear, lifestyle, accessories, makeup, hairstyle, and body posture. The term implies a look defined by the fashion in ...

culture Culture () is an umbrella term which encompasses the social behavior, institutions, and norms found in human societies, as well as the knowledge, beliefs, arts, laws, customs, capabilities, and habits of the individuals in these groups.Tyl ...

s and to have a greater impact and scope.

Education Education is a purposeful activity directed at achieving certain aims, such as transmitting knowledge or fostering skills and character traits. These aims may include the development of understanding, rationality, kindness, and honesty. Va ...

can play a fundamental role in the development of mathematical culture.

YouTube YouTube is a global online video platform, online video sharing and social media, social media platform headquartered in San Bruno, California. It was launched on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim. It is owned by ...

channels about

started, such as

Numberphile ''Numberphile'' is an educational YouTube channel featuring videos that explore topics from a variety of fields of mathematics. In the early days of the channel, each video focused on a specific number, but the channel has since expanded its s ...

3Blue1Brown 3Blue1Brown is a math YouTube channel created and run by Grant Sanderson. The channel focuses on teaching higher mathematics from a visual perspective, and on the process of discovery and inquiry-based learning in mathematics, which Sanderson cal ...

, and are viewed by many people. Several museums aim at enhancing public understanding of mathematics, like

Museum of Mathematics The National Museum of Mathematics or MoMath is a museum dedicated to mathematics in Manhattan, New York City. It opened on December 15, 2012. It is located at 11 East 26th Street between Fifth and Madison Avenues, across from Madison Square P ...

New York City New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the L ...

, and its predecessor, the

Goudreau Museum of Mathematics in Art and Science The Goudreau Museum of Mathematics in Art and Science was a museum of math that was open from 1980–2006 in Long Island, New York. The museum was named after mathematics teacher Bernhard Goudreau, who died in 1985, and featured many of the 3-d ...

, the Haus der Mathematik in

Vienna en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...

, the

Arithmeum The Arithmeum is a mathematics museum owned by the Forschungsinstitut für Diskrete Mathematik (Research Institute for Discrete Mathematics) at the University of Bonn. It was founded in 2008 by the director of the institute, Bernhard Korte, who ...

Bonn The federal city of Bonn ( lat, Bonna) is a city on the banks of the Rhine in the German state of North Rhine-Westphalia, with a population of over 300,000. About south-southeast of Cologne, Bonn is in the southernmost part of the Rhine-Ruhr r ...

, the

Mathematisch-Physikalischer Salon The Mathematisch-Physikalischer Salon (, ''Royal Cabinet of Mathematical and Physical Instruments'') in Dresden, Germany, is a museum of historic clocks and scientific instruments. Its holdings include terrestrial and celestial globes, astronomic ...

Dresden Dresden (, ; Upper Saxon: ''Dräsdn''; wen, label=Upper Sorbian, Drježdźany) is the capital city of the German state of Saxony and its second most populous city, after Leipzig. It is the 12th most populous city of Germany, the fourth larg ...

, the

Mathematikum The Mathematikum is a science museum, located in Gießen, Germany, which offers a huge variety of mathematical hands-on exhibits. It was founded by Albrecht Beutelspacher, a German mathematician. The Mathematikum opened its doors to visitors on ...

Giessen Giessen, spelled Gießen in German (), is a town in the German state (''Bundesland'') of Hesse, capital of both the district of Giessen and the administrative region of Giessen. The population is approximately 90,000, with roughly 37,000 univers ...

, the Experiminta in

Frankfurt Frankfurt, officially Frankfurt am Main (; Hessian: , "Frank ford on the Main"), is the most populous city in the German state of Hesse. Its 791,000 inhabitants as of 2022 make it the fifth-most populous city in Germany. Located on its na ...

, the Virtuelles Freiberger Museum für Mathematik und Kunst in

Freiberg Freiberg is a university and former mining town in Saxony, Germany. It is a so-called ''Große Kreisstadt'' (large county town) and the administrative centre of Mittelsachsen district. Its historic town centre has been placed under heritage c ...

, or the

Garden of Archimedes The Garden of Archimedes (Italian: ''Il Giardino Di Archimede'') is a museum for mathematics in Florence, Italy. It was founded on March 26, 2004 and opened its doors to the public on April 14 of that year. The mission of the museum is to enhan ...

in Firenze, or the Museu de Matemàtiques de Catalunya in

Cornellà de Llobregat Cornellà de Llobregat (; es, Cornellá de Llobregat) is a municipality in the ''comarca'' of the Baix Llobregat in Catalonia, Spain. It is situated on the left bank of the Llobregat River. It is in the south-western part of the Barcelona metr ...

Plus Magazine ''Plus Magazine'' is an online popular mathematics magazine run under the Millennium Mathematics Project at the University of Cambridge. ''Plus'' contains: * feature articles on all aspects of mathematics; * reviews of popular maths books and ...

is a free online magazine run under the

Millennium Mathematics Project The Millennium Mathematics Project (MMP) was set up within the University of Cambridge in England as a joint project between the Faculties of Mathematics and Education in 1999. The MMP aims to support maths education for pupils of all abilities fr ...

at the

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

. In 2012, the appearance of ''

Quanta Magazine ''Quanta Magazine'' is an editorially independent online publication of the Simons Foundation covering developments in physics, mathematics, biology and computer science. ''Undark Magazine'' described ''Quanta Magazine'' as "highly regarded for ...

'' contributed to mathematical journalism. Several novels, films and books are centered on mathematical subjects and also aim to popularize them, like

mathematical fiction Mathematical fiction is a genre of creative fictional work in which mathematics and mathematicians play important roles. The form and the medium of the works are not important. The genre may include poems, short stories, novels or plays; comic book ...

. Arguably the first of these is ''

Flatland ''Flatland: A Romance of Many Dimensions'' is a satirical novella by the English schoolmaster Edwin Abbott Abbott, first published in 1884 by Seeley & Co. of London. Written pseudonymously by "A Square", the book used the fictional two-dim ...

'', an 1884 novel intended to introduce the reader to the then-recent concepts of the geometry of

four-dimensional space A four-dimensional space (4D) is a mathematical extension of the concept of three-dimensional or 3D space. Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called ''dimensions'', ...

; subsequently, authors like Denis Guedj or Apóstolos Doxiádis build some of their plots around

Fermat's last theorem In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2. The cases and have been k ...

Goldbach's conjecture Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers. The conjecture has been shown to hold ...

Simon Singh Simon Lehna Singh, (born 19 September 1964) is a British popular science author, theoretical and particle physicist. His written works include ''Fermat's Last Theorem'' (in the United States titled ''Fermat's Enigma: The Epic Quest to Solve th ...

wrote

Fermat's Last Theorem In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2. The cases and have been k ...

book,

Charles Seife Charles Seife is an American author and journalist, and a professor at New York University. He has written extensively on scientific and mathematical topics. Career Seife holds a mathematics degree from Princeton University (1993),Greenwood, Kath ...

wrote Zero: The Biography of a Dangerous Idea,

Rózsa Péter Rózsa Péter, born Rózsa Politzer, (17 February 1905 – 16 February 1977) was a Hungarian mathematician and logician. She is best known as the "founding mother of recursion theory". Early life and education Péter was born in Budapest, ...

wrote

Playing with Infinity ''Playing with Infinity: Mathematical Explorations and Excursions'' is a book in popular mathematics by Hungarian mathematician Rózsa Péter, published in German in 1955 and in English in 1961. Publication history and translations ''Playing with ...

. In 2008, the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

and the Institute of Mathematics and its Applications created the Christopher Zeeman Medal to recognise and acknowledge the contributions of mathematicians involved in promoting mathematics to the public.{{Cite web , title=News from the world of maths: Christopher Zeeman Medal for Maths Communication , url=https://plus.maths.org/content/news-world-maths-christopher-zeeman-medal-maths-communication , access-date=2022-12-18 , website=Plus Maths , language=en In 2010, the

International Mathematical Union The International Mathematical Union (IMU) is an international non-governmental organization devoted to international cooperation in the field of mathematics across the world. It is a member of the International Science Council (ISC) and supports ...

created the

Leelavati Award The Leelavati Award is an award for outstanding contribution to public outreach in mathematics. It is named after the 12th-century mathematical treatise " Lilavati" devoted to arithmetic and algebra written by the Indian mathematician Bhāskara II, ...

for outstanding contribution to public outreach in mathematics.

References

Mathematics and culture Mathematics literature Recreational mathematics

Mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...