**Popular mathematics** is mathematical presentation aimed at a general audience. Sometimes this is in the form of books which require no mathematical background and in other cases it is in the form of expository articles written by professional mathematicians to reach out to others working in different areas.

- Notable works of popular mathematics
- On zero
- On infinity
- On constants
- On complex numbers
- On the Riemann hypothesis
- On recently solved problems
- On classification of finite simple groups
- On higher dimensions
- On introduction to mathematics for the general reader
- Biographies
- Magazines and journals
- Audio and video
- Museums
- References

Some of the most prolific popularisers of mathematics include Keith Devlin, Rintu Nath, Martin Gardner, and Ian Stewart. Titles by these three authors can be found on their respective pages.

- Charles Seife (2000).
*Zero: The Biography of a Dangerous Idea*. Souvenir Press. ISBN 978-0-285-63594-4. - Robert Kaplan (2000).
*The Nothing That Is: A Natural History of Zero*. Oxford. ISBN 978-0-19-514237-2. - Rintu Nath (2013).
*Moments in Mathematics*. Vigyan Prasar, Department of Science and Technology (India). ISBN 978-81-7480-224-8. Archived from the original on 2015-11-02.^{[ circular reference ]}

- Rózsa Péter (1961).
*Playing with Infinity: Mathematical Explorations and Excursions*. Simon & Schuster. - Rucker, Rudy (1982),
*Infinity and the Mind: The Science and Philosophy of the Infinite*; Princeton, N.J.: Princeton University Press. ISBN 978-0-691-00172-2. - Brian Clegg (2003).
*Brief History of Infinity: The Quest to Think the Unthinkable*. Constable and Robinson. ISBN 978-1-84119-650-3. - Robert Kaplan & Ellen Kaplan (2004).
*The Art of the Infinite: Our Lost Language of Numbers*. Penguin. ISBN 978-0-14-100886-8.

- Petr Beckmann (1976).
*A History of Pi*. Saint Martin's Press. ISBN 978-0-312-38185-1. - Eli Maor (1998).
*"e", The Story of a Number*. Princeton. ISBN 978-0-691-05854-2. - Mario Livio (2003).
*The Golden Ratio*. Headline Review. ISBN 978-0-7472-4988-7. - Julian Havil (2003).
*Gamma*. Princeton. ISBN 978-0-691-09983-5.

- Paul J. Nahin (1998).
*An Imaginary Tale: The Story of*. Princeton. ISBN 978-0691027951. - Paul J. Nahin (2006).
*Dr. Euler's Fabulous Formula*. Princeton. ISBN 978-0-691-11822-2.

- John Derbyshire (2004).
*Prime Obsession*. Plume Books. ISBN 978-0-452-28525-5. - Marcus du Sautoy (2003).
*The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics*. ISBN 0-06-093558-8. - Dan Rockmore (2006).
*Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers*. Vintage. ISBN 0-375-72772-8. - Karl Sabbagh (2002).
*Dr Riemann's Zeros*. Atlantic Books. ISBN 1-84354-100-9.

- Robin J. Wilson (2003).
*Four Colours Suffice*. Penguin. ISBN 978-0-14-100908-7. - Simon Singh (2002).
*Fermat's Last Theorem*. Fourth Estate. ISBN 1-84115-791-0. - Donal O'Shea (2007).
*The Poincaré Conjecture*. Penguin. ISBN 978-1-84614-012-9. - George G. Szpiro (2003).
*Kepler's Conjecture*. Wiley. ISBN 0-471-08601-0. - George G. Szpiro (2007).
*Poincaré's Prize*. Dutton.

- Mario Livio (2006).
*The Equation That Couldn't Be Solved*. Souvenir Press. ISBN 978-0-285-63743-6. - Mark Ronan (2006).
*Symmetry and the Monster*. Oxford. ISBN 0-19-280722-6.

- Rucker, Rudy (1984),
*The Fourth Dimension: Toward a Geometry of Higher Reality*; Houghton Mifflin Harcourt.

- Richard Courant and Herbert Robbins (1941).
*What is Mathematics?: An Elementary Approach to Ideas and Methods*. London: Oxford University Press. ISBN 0-19-502517-2. - Edward C. Titchmarsh (1948).
*Mathematics for the General Reader*. Dover Publications. ISBN 0486813924.

- Paul Hoffman (1998).
*The Man Who Loved Only Numbers*. Fourth Estate. ISBN 1-85702-811-2. - Bruce Schechter (2000).
*My Brain is Open: The Mathematical Journeys of Paul Erdos*. Simon & Schuster. ISBN 0-684-85980-7. - Robert Kanigel (1991).
*The Man Who Knew Infinity: A Life of the Genius Ramanujan*. Washington Square Press. ISBN 0-671-75061-5. - Siobhan Roberts (2006).
*King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry*. Walker Books. ISBN 0-887-84201-1.

- Popular science magazines such as
*New Scientist*and*Scientific American*sometimes carry articles on mathematics. *Plus Magazine*is a free online magazine run under the Millennium Mathematics Project at the University of Cambridge.

The journals listed below can be found in many university libraries.

*American Mathematical Monthly*is designed to be accessible to a wide audience.*The Mathematical Gazette*contains letters, book reviews and expositions of attractive areas of mathematics.*Mathematics Magazine*offers lively, readable, and appealing exposition on a wide range of mathematical topics.*The Mathematical Intelligencer*is a mathematical journal that aims at a conversational and scholarly tone.*Notices of the AMS*- Each issue contains one or two expository articles that describe current developments in mathematical research, written by professional mathematicians. The Notices also carries articles on the history of mathematics, mathematics education, and professional issues facing mathematicians, as well as reviews of books, plays, movies, and other artistic and cultural works involving mathematics.

- Simon Singh's
*Fermat's Last Theorem*is available in audio and there is also a*Horizon*television program.

Several museums aim at enhancing public understanding of mathematics:

In the **United States**:

- Museum of Mathematics, New York, and its predecessor, the Goudreau Museum of Mathematics in Art and Science,

In **Austria**:

- Haus der Mathematik , Wien

In **Germany**:

- Arithmeum, Bonn
- Mathematisch-Physikalischer Salon, Dresden
- Mathematikum, Gießen
- Experiminta , Frankfurt on Main
- Virtuelles Freiberger Museum für Mathematik und Kunst , Freiberg
- MiMa Mineralien- und Mathematikmuseum , Oberwolfach

In **Italy**

In mathematics, a **conjecture** is a conclusion or a proposition which is suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found. Some conjectures, such as the Riemann hypothesis or Fermat's Last Theorem, have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.

A **number** is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called *numerals*; for example, "5" is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows for the representation of any number using a combination of ten fundamental numeric symbols, called digits. In addition to their use in counting and measuring, numerals are often used for labels, for ordering, and for codes. In common usage, a *numeral* is not clearly distinguished from the *number* that it represents.

A **prime number** is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.

In mathematics, **Euler's identity** is the equality

**Hermann Klaus Hugo Weyl**, was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski.

In mathematical logic, the theory of infinite sets was first developed by Georg Cantor. Although this work has become a thoroughly standard fixture of classical set theory, it has been criticized in several areas by mathematicians and philosophers.

**Mario Livio** is an Israeli-American astrophysicist and an author of works that popularize science and mathematics. For 24 years (1991-2015) he was an astrophysicist at the Space Telescope Science Institute, which operates the Hubble Space Telescope. He has published more than 400 scientific articles on topics including cosmology, supernova explosions, black holes, extrasolar planets, and the emergence of life in the universe. His book on the irrational number *phi*, *The Golden Ratio: The Story of Phi, the World's Most Astonishing Number* (2002), won the Peano Prize and the International Pythagoras Prize for popular books on mathematics.

**John Willard Morgan** is an American mathematician, with contributions to topology and geometry. He is, as of 2020, Professor Emeritus at Columbia University.

* From Here to Infinity: A Guide to Today's Mathematics*, a 1996 book by mathematician and science popularizer Ian Stewart, is a guide to modern mathematics for the general reader. It aims to answer questions such as "What is mathematics?", "What is it for " and "What are mathematicians doing nowadays?". Author Simon Singh describes it as "An interesting and accessible account of current mathematical topics".

* The Story of Maths* is a four-part British television series outlining aspects of the history of mathematics. It was a co-production between the Open University and the BBC and aired in October 2008 on BBC Four. The material was written and presented by University of Oxford professor Marcus du Sautoy. The consultants were the Open University academics Robin Wilson, professor Jeremy Gray and June Barrow-Green. Kim Duke is credited as series producer.

**Infinity** represents something that is boundless or endless, or else something that is larger than any real or natural number. It is often denoted by the infinity symbol **∞**.

**Barry Charles Mazur** is an American mathematician and the Gerhard Gade University Professor at Harvard University. His contributions to mathematics include his contributions to Wiles's proof of Fermat's Last Theorem in number theory, Mazur's torsion theorem in arithmetic geometry, the Mazur swindle in geometric topology, and the Mazur manifold in differential topology.

**Julius Wilhelm Richard Dedekind** was a German mathematician who made important contributions to abstract algebra , axiomatic foundation for the natural numbers, algebraic number theory and the definition of the real numbers.

**Harold Mortimer Edwards, Jr.** was an American mathematician working in number theory, algebra, and the history and philosophy of mathematics.

The **Millennium Prize Problems** are seven problems in mathematics that were stated by the Clay Mathematics Institute on May 24, 2000. The problems are the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Poincaré conjecture, Riemann hypothesis, and Yang–Mills existence and mass gap. A correct solution to any of the problems results in a US$1 million prize being awarded by the institute to the discoverer(s).

**Eli Maor**, an Israel-born historian of mathematics, is the author of several books about the history of mathematics. Eli Maor received his PhD at the Technion – Israel Institute of Technology. He teaches the history of mathematics at Loyola University Chicago. Maor was the editor of the article on trigonometry for the *Encyclopædia Britannica*.

The **Euler Book Prize** is an award named after Swiss mathematician and physicist Leonhard Euler (1707-1783) and given annually at the Joint Mathematics Meetings by the Mathematical Association of America to an outstanding book in mathematics that is likely to improve the public view of the field.

* Deutsche Mathematik* was a mathematics journal founded in 1936 by Ludwig Bieberbach and Theodor Vahlen. Vahlen was publisher on behalf of the German Research Foundation (DFG), and Bieberbach was chief editor. Other editors were Fritz Kubach, Erich Schönhardt, Werner Weber, Ernst August Weiß, Karl Dörge, Wilhelm Süss, Günther Schulz (de), Erhard Tornier, Georg Feigl, Gerhard Kowalewski, Maximilian Krafft, Willi Rinow, Max Zacharias, and Oswald Teichmüller. In February 1936, the journal was declared the official organ of the German Student Union (DSt) by its

**Colin Rourke** is a British mathematician, who has published papers in PL topology, low-dimensional topology, differential topology, group theory, relativity and cosmology. He is an emeritus professor at the Mathematics Institute of the University of Warwick and a founding editor of the journals *Geometry & Topology* and *Algebraic & Geometric Topology*, published by Mathematical Sciences Publishers, where he is the vice chair of its board of directors.

**George Geza Szpiro** is an Israeli–Swiss author, journalist, and mathematician. He has written articles and books on popular mathematics and related topics.

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