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.
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.
The journals listed below can be found in many university libraries.
Several museums aim at enhancing public understanding of mathematics:
In the United States:
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 Reichsführer, and all local DSt mathematics departments were requested to subscribe and actively contribute. In the 1940s, issues appeared increasingly delayed and bunched; the journal ended with a triple issue in June 1944.
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.