Math

What Is Mathematics?

Mathematics is the study of numbers, shapes, and their relationships. Graduates with a degree in mathematics can pursue careers as financial analysts, statisticians, and auditors. Math students study subjects such as complex variables, number theory, applied mathematics, calculus, and more.

The Best Colleges and Universities for Mathematics Degrees

To view the entire list of top math schools, including schools offering online degrees and a breakdown of the best math colleges and universities in your state, visit our look at the Best Colleges and Universities for Math Degrees.

For a dynamic, real-time listing of the most influential math schools in the world, use our Custom College Ranking.

Did you know that a job in mathematics is a versatile and future-proof career? This degree can prepare you to compete for jobs in tomorrow’s workplace. A degree in mathematics is a versatile one and has a projected growth rate of at least 33% between 2020 and 2030! A career as a mathematician can be complimentary to the rise of automation. Find out more about this versatile degree.

Many college students struggle to nail down what to major in. Our guide to the most popular college majors and programs can help.

Math Degrees

What Will I Study as a Math Major?

As a math major, you’ll study topics like complex variables, number theory, and vector calculus. Additionally, students may have the option to choose a concentration, like statistics or applied mathematics.

What Can I Do With a Degree in Math?

With a degree in math, you could qualify for a position in fields such as data science, teaching, actuarial science, financial analysis, and statistics, among others. A bachelor’s degree can also serve as a stepping stone into graduate school, which may be required for some professions.

If you’re ready to earn your degree at one of the most prestigious schools in the world, get started with a look at the Most Influential Schools in Mathematics

If you’d like to learn more, check out our extensive list of resources for math students, graduates, and professionals...

How To Get a Degree in Mathematics

• Find out How to Major in Mathematics
• Find out what you can do with a Master’s Degree in Mathematics

The Best Online Math Degrees

Math is among the most popular disciplines at both the undergraduate and graduate levels. A growing number of reputable colleges and universities are satisfying demand for this degree by providing an array of high-quality online mathematics degree options. Using our InfluenceRanking engine, we’ve identified the best among them. Check out our growing set of rankings for online math degree programs at every level of education.

• Best Online Bachelor’s in Mathematics Degree

History of the Mathematics Discipline

The Pythagoreans and Ancient Greeks began a systematic study of mathematics in the 6th century B.C., but there are written examples of mathematics from as early as 3000 B.C. The discipline has continued to evolve throughout the ages, but the 20th century proved to be an exciting time as major mathematical studies came to light. We showcase some of the key developments in a brief but comprehensive history of the discipline of mathematics. Below are a few highlights from our 2-part series A Brief History of Mathematics:

1. Claude Shannon developed his information theory.
2. Alan Turing developed his theory of computation.
3. French mathematician Benoit Mandelbrot developed his theory of fractals.
4. Edward Norton Lorenz developed Chaos Theory in Mathematics.
5. John Forbes Nash Jr. developed his Games Theory, which has been used in economics, accounting, military theory, computer science, and Artificial Intelligence.
6. Paul Cohen developed his Continuum Hypothesis. In it, Cohen proved that 19th century mathematician G. Cantor’s Continuum Hypothesis about the possible sizes of infinite sets had not one but two solutions.
7. Stephen Cook posed his famous “P = NP” problem, which remains an important and unsolved problem in mathematics.
8. Andrew Wiles proved that Fermat’s Last Theorem was true.
9. Manindra Agrawal , Nitin Saxena , and Neeraj Kayal developed the AKS primality test, a procedure for determining whether a given number is prime (divisible only by 1 and itself). This was a remarkable development because the algorithm was in the field of computer science research, rather than strictly mathematics.
10. Despite the trend of mathematical principles and theorems using computer science as a tool for research, the early 2000s also saw some remarkable advances in pure mathematics. As an example, Grigori Perelman proved famous mathematician Henri Poincaré ’s 1904 conjecture about the “3-sphere”.
11. In the last twenty years, several other very important long-standing puzzles and theories were solved using pure mathematics, proving that the use of computer science in math, while important, will not not replace the human mathematician. Some of the most important developments included:
    • Preda Mihăilescu proved true the 158 year old Catalan’s conjecture
    • Ben Green and Terence Tao proved the Green-Tao Theorem
    • Ngô Bảo Châu solved the “fundamental lemma”
    • Yitang Zhang proved an important property about primes
    • Kepler’s Conjecture, named after the 17th century mathematician and astronomer Johannes Kepler , was solved

Who Are the Current Top Mathematicians?

The following are the top mathematicians in the field today according to our machine-powered Influence Rankings, which are drawn from a numerical score of academic achievements, merits, and citations across Wikipedia/data, Crossref, and an ever-growing body of data.

• Keith Devlin is a prolific writer about mathematics and related scientific disciplines, writing both for specialists and a general readership. He has authored over 30 books during his storied career as a mathematician, and 80 research articles! No wonder, then, that in 2007 Devlin was awarded the Carl Sagan Prize for Science Popularization.
• Terence Tao is arguably the greatest living mathematician, and has been called the greatest mathematician of his generation. Tao was a child prodigy, the youngest person ever to win a medal in the International Mathematical Olympiad. He has since won the Field Medal
• Ian Stewart is a gifted mathematician who is also a writer of popular science and science fiction. A fertile mind, his primary focus in mathematics is a subfield of the study of dynamic systems known as catastrophe theory. He has also published widely on diverse topics in mathematics
• John Stillwell is best known as a source of knowledge and education in mathematics. He has been influential as the author of numerous books on subjects in mathematics, including the history of math in the last two centuries, the foundations of mathematics, algebra, number theory, and geometry
• Bruce C. Berndt is world-famous as one of the greatest analytic number theorists, a core area in mathematics exploring the properties of number systems, such as the integers.
• Timothy Gowers ′ work has been primarily in functional analysis, and in particular in the vector construct known as a Banach space. He has also performed fundamental work in combinatorics and number theory (of combinatorial number theory), proving a number of important lemmas and results, as well as introducing the concept of a quasi random group in 2005.
• Peter Sarnak works on problems in analytic number theory, and his contributions have had important applications to other scientific areas like physics and computer science. Sarnak also invented a field known as “arithmetical quantum chaos.”
• Martin Hairer is known as the leading name in stochastic partial differential equations, with significant implications for areas including quantum field theory and spatial modeling.
• Ingrid Daubechies is one of the most widely cited mathematicians, and is world renowned for her work on the mathematics of image compression, known as wavelets (an area of relevance to computer science and other disciplines in addition to mathematics).
• Andrew Wiles became an overnight sensation when he proved one of the most famous conjectures in all of mathematics, known as Fermat’s Last Theorem, after the 17th century mathematician Pierre Fermat.

Learn about other influential mathematicians.

Interviews with Top Mathematicians

• Dr. Ian Stewart discusses real-world applications for math, the joys of mentoring students, and “things that go boing,” in our interview, How mathematicians partner with other experts to find solutions.
• Dr. Keith Devlin discusses the battle between academic research and popularization, the importance of making math both fun and informative, inspiring math books, and much more in our interview, How to make mathematics popular and exciting.
• Dr. Ken Ono discusses Indiana Jones, Olympic swim teams, and unsolvable math problems in our interview, Using Math to Win the Olympics.

Great Books About Mathematics

The following are the most influential books in the field of mathematics today according to our backstage Ranking Analytics tool, which calculates the influence of various sources in both academics and popular culture using a numerical scoring of citations across Wikipedia/data, Crossref, and an ever-growing body of data.

1. Our Mathematical Universe: My Quest for the Ultimate Nature of Reality by Max Tegmark is a popular guide to the author’s vision of the mathematical structure that he believes underlies the ultimate reality of the physical universe.
2. The Signal and the Noise: Why So Many Predictions Fail-But Some Don’t by Nate Silver explains the basics of Bayesian probability theory for a popular audience, and then in a dozen or so chapters, he demonstrates how to think rationally in the light of that theory about a range of physical and social phenomena. In a nutshell, the book is about the best way to use statistical data to make predictions.
3. The Man Who Knew Infinity: A Life of the Genius Ramanujan by Robert Kanigel is a biography of a singular figure in the history of mathematics, Srinivasa Ramanujan (1887–1920), who made substantial contributions to advanced number theory despite being born into modest circumstances in the Indian state of Tamil Nadu and having received almost no formal education in higher mathematics.
4. Concrete Mathematics: A Foundation for Computer Science by Ronald Graham lays out the fundamental mathematics underlying the scientific theory and practice of computation.
5. A Mathematician’s Apology by G. H. Hardy aims to share with its readers a sense of the profound beauty and spiritual elevation of pure mathematics. The author combines fascinating autobiographical material with a stylistic gift for the exposition of difficult abstract concepts.
6. The Mathematics of Life by Ian Stewart outlines the numerous ways in which mathematics now helps us to understand living systems at all levels, from the whole organism in its environment down to the molecular level.
7. A Mathematician’s Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form by Paul Lockhart is concerned that the way we are teaching mathematics today fails to convey to students its most significant and appealing features.
8. Flatland: A Romance of Many Dimensions by Edwin Abbott Abbott is a brilliant introduction to the mathematical idea of dimensionality. Part of its great public success was due to the discussions of time as a fourth dimension that were occurring during the last quarter of the nineteenth century.
9. How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics by Eugenia Cheng is an intriguing effort to make some highly abstract mathematics—notably, category theory—more palatable (no pun intended!) to lay readers by means of teasing mathematical principles out of the tempting recipes in an ordinary cookbook.
10. The Princeton Companion to Mathematics by Timothy Gowers is the most comprehensive survey of pure mathematics as it is being pursued in the world today. Covering all the most active and interesting branches of the field, the individual articles by over 150 distinguished authors are written to be accessible to a general reader, as well as specialists.

Learn more about other influential math books.

Find additional math resources online, with an emphasis on BIPOC student needs.