# How popular is pure math in college

Mathematics has fascinated humans since our earliest intellectual endeavors. Ancient peoples were intrigued by the mathematical relationships between the sun, moon, and stars. This fascination began one of the most fundamental human intellectual endeavors. While mathematicians, philosophers, and scientists debate whether mathematics is a human description of nature or the fundamental structure of reality, there is no question that mathematics has driven most of humanity’s technological and intellectual advancement.

The mathematicians of today examine everything from the complex mathematical relationships found in living organisms to the bizarre, non-Euclidean geometries of extra-dimensional spaces. The schools on this list, many with faculty who have earned Fields Medals (the mathematics equivalent of a Nobel Prize), lead way in the ever-evolving field of mathematics.

Taking the QS ranking as our point of departure, we set their ranking against the ranking for mathematics programs produced by AcademicInfluence.com. Using machine learning and search algorithms to characterize academic influence on the web, AcademicInfluence.com avoids the human bias that infects most academic rankings.

The rankings uncovered by AcademicInfluence.com are based on the influential faculty and alum publications, citations, and references associated with a school, degree programs, departments, or discipline. This ranking by influence approach elevates a school or degree program based on which members of its academic community are objectively influential in a given discipline.

By weighing both the QS Programmatic World Rankings and Academic Influence’s rankings, we not only created a unique ranking of the top 50 mathematics programs, but we reveal why each university mathematics program appears where it does.

## The 50 Best Mathematics Programs in the World

### 1. Massachusetts Institute of Technology (MIT)

Cambridge, Massachusetts

MIT enjoys a reputation as a world-renowned, specialized research institution that focuses on the intersection of science and technology. As such, the study of mathematics plays a key role for most students throughout all the school’s programs. The 60 faculty members, including two MacArthur fellows, are distinguished scholars with a dedication to research and the education of their students. MIT has produced two Fields Medals and numerous Nobel Prize winners.

Divided into pure and applied mathematics, the **Mathematics Department** at MIT is home to approximately 330 undergraduate students and 115 graduate students. Undergraduate students can choose concentration options that include:

- Applied Mathematics
- General Mathematics
- Mathematics With Computer Science
- Theoretical Mathematics

Graduate studies and research areas are divided into the following areas:

- Algebra
- Computational Biology
- Geometry
- Representation theory
- Theoretical Computer Science

Students can find all the academic support they need, from tutoring to scheduling, through MIT’s Math Academic Services team.

### 2. Harvard University

Cambridge, Massachusetts

Harvard University’s Benjamin Peirce, father of Charles Sanders Peirce, was the first American to make original, major contributions to the field of mathematics. In his wake, the department made progress in the areas of topology, algebraic geometry, complex analysis, and number theory.

Comprehensive in nature, Harvard’s **Department of Mathematics** offers a variety of some of the best mathematics and research programs that include bachelor’s degrees, master’s programs, and Ph.D.s. Current faculty members exhibit strong interest in:

- Differential Equations
- Diophantine Geometry
- Lie Groups
- Mathematical Physics
- Modular forms
- Number theory

Most programs require a capstone project or senior thesis before graduation. Seminars, tutoring centers, and peer-led clubs offer additional opportunities for networking and classwork assistance.

Harvard’s math department runs multiple regular conferences such as the Current Developments Conference and the Conference on Geometry and Topology. Harvard, near Boston, also sits at the center of America’s university capital. With schools like MIT, Boston College, Boston University, and Tufts within miles, Harvard provides its faculty and students with a massive network of additional resources.

### 3. Stanford University

Stanford, California

Celebrating 125 years of thriving success and global impact at the heart of California’s Silicon Valley, Stanford University has produced a proud academic tradition and many research achievements. Boasting 16 postdocs/research assistants, six visiting professors, and 59 professors and lecturers, the school’s **Department of Mathematics** offers a diverse range of courses and resources to its students.

Stanford serves as a hub where leaders in mathematics gather to push the field forward. Professors possess specialized expertise in a broad array of subjects, including financial math, number theory, representation theory, and symplectic geometry. Twenty-nine famous competitors in the International Mathematical Olympiad can claim affiliations with Stanford.

In addition to numerous courses and excellent degree programs, the department also supports and manages the Mathematics Research Center (MRC). Though research is the primary goal, MRC also provides seminars, conferences, and outreach activities to the community and high school students in particular. The Mathematics and Statistics Library and the Stanford University Mathematical Organization function as excellent resources run by the department.

### 4. University of Oxford

Oxford, United Kingdom

One of the oldest universities in the world, Oxford had plenty of time to develop an outstanding reputation in many fields. Along with the university’s science department, **Oxford Mathematics** has been home to historic alumni such as Edwin Hubble, Robert Hooke, and Stephen Hawking.

The natural connection between math and science lends itself towards departmental collaboration through the Mathematical Institute at Oxford. Research is conducted by physicists, medical professionals, engineers, social scientists, and others who contribute to the success of the school’s math department. Students in both the pure and applied mathematics programs attend classes in the same building, which further encourages partnerships and collaboration among students in one of the best mathematics programs in the world.

Approximately 1,200 undergraduate and graduate students participate in the various programs taught by 170 expert faculty members. A total of 16 focus groups and centers on campus conduct most the research, including the Geometry Group, the History of Mathematics Group, and the Oxford Centre for Nonlinear Partial Differential Equations. The department also networks with the Oxford Solid Mechanics initiative and the Clay Mathematical Institute.

### 5. (tie) University of Cambridge

Cambridge, England

Home to Isaac Newton and many other great scientists and mathematicians from history, Cambridge is one of the oldest centers of learning in the world. Today, Cambridge serves students as a large research university that consists of 31 colleges and 150 departments and faculties.

Cambridge separates its **Faculty of Mathematics** into two departments: (1) applied mathematics and theoretical physics, and (2) pure mathematics and mathematical statistics. The applied mathematics department employs 50 academic faculty members who monitor 110 research students. The pure mathematics department hosts 42 academic faculty members who also help manage the faculty’s Statistical Laboratory.

Undergraduate studies in mathematics at Cambridge are known as the “Mathematical Tripos.” Students may complete the program in three or four years and are then eligible for further study at the graduate level.

In addition to providing a broad range of quality degree programs, the math department also manages more than nine centers of research excellence and numerous outreach programs. Maintaining business and industrial partnerships both locally and nationally has served as both a highlight of the department’s success and a key to future endeavors.

### 5. (tie) Princeton University

Princeton, New Jersey

Princeton University has come a long way from its humble beginnings as the College of New Jersey. Under the combined leadership of mathematician Henry Burchard Fine and Woodrow Wilson, Princeton University at large — and its mathematics and physics departments in particular — flourished. The school provided the momentum that propelled American education from obscurity to comparability with European standards in the early 20th century.

Today, Princeton’s historic **Department of Mathematics** carries on this grand tradition with 64 faculty members and 17 researchers who continue to push the boundaries of the field. As is the case with the best mathematics programs, Princeton’s students enjoy engaging and supportive classroom settings that provide the opportunity to develop their own contributions to the field through tutoring options.

At the graduate level, students typically spend two years expanding their background in mathematics before focusing on independent research under professor mentorship. Students are expected to attend several informal seminars to hear peers, professors, and experts present papers on current research topics. The department also rubs shoulders with the renowned Institute for Advanced Study, where such luminaries as Albert Einstein, John von Neumann, and Kurt Gödel conducted research.

### 7. University of California – Berkeley

Berkeley, California

Located in Evans Hall on the scenic University of California – Berkeley campus, the school’s **Mathematics Department** includes 55 faculty members and nearly 1,000 graduate and undergraduate students. UCB’s math department provides students access to an extensive collection of research and scholarship resources in the Mathematics Statistics Library and works closely with the school’s Mathematical Sciences Research Institute to offer workshops, seminars, and colloquia.

Undergraduate students studying math at UCB can pursue any of three tracks: teaching, applied mathematics, or pure mathematics. The teaching concentration provides learners with coursework on math fundamentals and builds their skills in curriculum development. The applied mathematics track offers core coursework in theory and analysis, plus three cluster classes specific to a field of application. Pure mathematics students focus on math fundamentals and complete elective coursework in geometry, logic, or computing.

The graduate program at UCB includes two doctoral degrees: one in mathematics and one in applied mathematics. Students complete preliminary coursework along with oral and written exams, a seminar, and a dissertation.

Student organizations in the math department include Women in Mathematics at Berkeley, Math Undergraduate Student Association, Mathematics Graduate Student Association. Learners may also join the Noetherian Ring, an organization of women graduate students, postdocs, and professors in UC Berkeley’s mathematics department. This department performs outreach to community groups, schools, and local prisons.

### 8. University of California – Los Angeles

Los Angeles, California

Offering some of the best mathematics programs available today — including bachelor’s degrees, master’s programs, and doctorates — the **Department of Mathematics** at UCLA offers a dynamic and engaging educational approach. Presented with the 2007 Award for an Exemplary Program or Achievement Award from the American Mathematical Society, UCLA’s math department has received high praise for its academic and research successes.

UCLA faculty and students benefit from the school’s Institute for Pure and Applied Mathematics. In addition to hosting numerous world-class mathematicians for public lectures and running various programs and seminars for students, the institute also manages extended, three-month programs with visiting scholars. During these programs, a collection of highly respected thinkers gather for a week of tutorials followed by several workshops that conclude with work at the UCLA Lake Arrowhead Conference Center.

The math-related undergraduate majors available through UCLA’s math department cover a wide range of subjects, including:

- Applied Mathematics
- Financial Actuarial Mathematics
- General Mathematics
- Mathematics for Teaching
- Mathematics of Computation
- Mathematics/Economics

UCLA also emphasizes community outreach via programs aimed at stimulating interest in mathematics in children at a young age. To this end, the school has established both the Philip C. Curtis Jr. Center for Mathematics and Teaching and the Los Angeles Math Circle.

### 9. California Institute of Technology

Pasadena, California

Caltech plays a unique role; it is a very small college with just over 2,000 students, yet it is populated by many of the best scientists and mathematicians in the world. This gives the **Division of Physics, Mathematics, and Astronomy** at Caltech an innovative approach to education.

Enjoying an impressive 3-to-1 student/faculty ratio, students at Caltech might feel like they’re in mentor relationships. At the same time, each student enjoys access to world-class resources like seminars, topics classes, and even a few light-hearted things like a pizza course. The 17 faculty members of the math department serve as excellent resources of knowledge and field-based experience for the 67 undergraduates and 34 graduates participating in some of the best mathematics programs in existence today. Undergraduate students interested in the mathematics major participate in a four-year track ending in a bachelor of science.

After completing required liberal arts classes, junior and senior students should take a minimum of 18 credits per semester for the mathematics major. Caltech encourages senior students to complete a bachelor’s thesis. Throughout the graduate program, master’s and doctoral students are expected to regularly attend seminars and colloquia. The application process requires students to complete a qualifying exam.

### 10. New York University

New York, New York

Sitting at the heart of the economic and business hub of the United States, students at NYU’s **Courant Institute of Mathematical Sciences** enjoy a distinct advantage. With extraordinary networking opportunities and the dedication of 70 faculty members, students can excel in all the school’s degree programs.

NYU’s math department divides its numerous undergraduate math programs into pure and applied mathematics. Undergraduates should declare their intentions for the mathematics major no later than the beginning of their junior year. At the graduate level, students can choose between an MS in mathematics, an MS in scientific computing, and an MS in mathematics in finance. Math students at NYU can also choose to pursue doctoral studies.

The research centers and groups on NYU’s campus have made efforts to combine pure and applied mathematics in order to observe the interaction between the two. Areas of major research include:

- Algebraic Geometry
- Analysis and Partial Differential Equations
- Dynamical Systems and Ergodic theory
- Probability theory
- Scientific Computing

### 11. Columbia University

New York, New York

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