Before diving into the discourse about Math PhD Rankings, please note. Mathematics, as most people say, is the most basic science.
Also, other people see math as the universal language of science. Therefore, rather than being science itself, it is the means by which science expresses itself.
Either way, it is agreeable that mathematics is essential to the advance of science. However, the impact of it does not end there. Any area which requires measurement and thoroughness requires math.
This is the reason why mathematics is important to various fields including finance, engineering, and psychological testing.
Some Requirements to Study Mathematics
Another important thing is where to study mathematics. A mathematics department requires many things to be successful. Most essentially, it needs a talented academic community where there are innovative professors to guide the students.
Also, an outstanding mathematics department needs to develop and maintain strong connections with other well-established research centers. It must possess the resources to bring in a consistent number of top scholars and conference participants.
Finally, mathematics particularly benefits from cross-disciplinary collaboration with other departments. The universities on this list are renowned for their expertise in many fields.
10 Best Math PhD Rankings by Universities in the World 2021
The 10 Best Mathematics Universities in the world for Math Ph.D. Rankings and mathematics programs include:
1. Princeton University
Princeton University formerly known as the College of New Jersey has come a long way. Under the combined leadership of mathematicians Henry Burchard Fine and Woodrow Wilson, the University, and its mathematics and physics departments, in particular, grew.
Princeton provided the drive that pushed American education from obscurity to comparability with European standards in the early 20th century.
Currently, the university’s historic mathematics department carries on its grand tradition. Its remarkable 64 faculty members and 17 visitors/researchers press on the boundaries of the field.
The classroom settings are engaging and supportive and provide every student with the opportunity to develop their own contributions to the field through tutoring options.
At the graduate level, students spend two years intensifying their background in mathematics before focusing on independent research under the mentorship of a professor.
Students are expected to attend a number of informal seminars to hear peers, professors, and experts present papers on current research topics.
The department also associates with the renowned Institute for Advanced Study where personalities such as Albert Einstein, John von Neumann, and Kurt Gödel once did research. Therefore, there is never a lack of world-class thinkers presenting their ideas in Princeton.
2. University of Michigan
When the University of Michigan was established at the Ann Arbor campus in 1817, one of the first four subjects taught was Mathematics. As the school increased, so did the department, to the current total of 145 academic faculty members.
The departments offer various numbers of programs, research areas, and outreach opportunities.
Undergraduate students have four main paths to choose from: Teaching Mathematics, Actuarial Mathematics, Mathematics of Finance and Risk Management, and Mathematical Sciences, which are subdivided into Pure and Applied Mathematics.
The Master’s program offers three main degrees with multiple subdivisions: Quantitative Finance and Risk Management, Applied and Interdisciplinary Mathematics, and the general Mathematics Master’s Degree.
Doctoral studies at Michigan are based on two-semester courses in algebra, analysis, applied analysis, and geometry/topology.
After establishing a strong foundation in these areas students will then begin developing their own unique contributions to the field as they pursue more specialized work and dissertation writing.
Students benefit from 15 areas of research, as well as a long-term grant program for elite students interested in pursuing groundbreaking topics.
These academic and research areas include Combinatorics, Differential Equations and Geometry, Logic and Foundations, and Number and Probability Theory.
3. Standford University
Talking about Math PhD Rankings? Celebrating 125 years of flourishing success and global impact from the heart of California’s Silicon Valley, Stanford University has produced a proud academic tradition and incisive research achievements.
A department of such size (it currently boasts 16 postdocs/research assistants, six visiting professors, and 59 professors and lecturers) and resources are able to offer a diverse range of courses.
But more prominently, Stanford is a center where the leaders in the field gather to push mathematics forward. Professors have specializations in a broad range of subjects, including Financial Math, Number Theory, Representation Theory, and Symplectic Geometry.
Twenty-nine famous competitors in the internationally renowned Mathematical Olympiad have affiliations with Stanford.
In addition to the 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 specifically high school students.
The Mathematics and Statistics Library is another excellent resource run by the department, as well as SUMO (Stanford University Mathematical Organization).
4. Havard University
Harvard University’s Benjamin Peirce (father of Charles Sanders Peirce) was the first American to produce original, major contributions to the field of mathematics.
During his time, the department especially made progress in the areas of topology, algebraic geometry, complex analysis, and number theory.
Being comprehensive in nature, the Mathematics Department offers a variety of programs and research areas, from bachelor to Ph.D. levels.
Current faculty members have a strong interest in Number Theory, Diophantine Geometry, Modular Forms, Differential Equations, Lie Groups, and Mathematical Physics.
The majority of 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.
The Harvard department runs multiple regular conferences such as the Current Developments Conference and the Conference on Geometry and Topology.
Harvard, being near Boston, is also at the center of America’s university capital. With schools like MIT, Boston College, Boston University, and Tufts within miles, Harvard affords its faculty and students a massive network of additional resources and people to work with.
5. University of California, Berkeley
Overlooking the idyllic San Francisco Bay, the Mathematics Department at Berkeley has been recognized for its outstanding faculty members and revolutionary research.
The 55 full-time professors represent most major fields of study and have research experience in Algebra, Mathematical Analysis, Applied Mathematics, Geometry/Topology, Mathematical Logic, and Probability. They are assisted by 25–30 post-doctoral candidates.
The 180 graduate students and 500 undergraduate students can expect a personalized educational experience with support from the dedicated admissions staff, stellar tutoring centers, experienced professors, and knowledgeable peers.
Depending on the chosen degree program, students may be asked to complete the Calculus Placement Exam and/or the Advanced Placement Exam.
The comprehensive Mathematical Library and the Mathematical Sciences Research Institute are both sponsored by the department. The latter attracts about 1,700 mathematicians from around the world annually.
Other affiliated research centers include the Mathematics Department at Lawrence Berkeley National Laboratory and the Adolf C. and Mary Sprague Miller Institute for Basic Research in Science. Berkeley’s Math department has two National Science Foundation founded as research training groups.
6. King Abdulaziz University
King Faisal bin Abdulaziz of Saudi Arabia approved the building of a University bearing his name in 1967. Opening in 1968 with just under 100 students, the University has made great strides to spread higher education to the surrounding area and made tremendous progress as a public research institution.
Established in conjunction with the Faculty of Science in 1973, the Mathematics Department of King Abdulaziz University is the leading academic and research program in the Middle East.
The school has made considerable efforts to attract first-class, international talent, who join the department as visiting faculty.
This attempt to integrate the school into the larger arena of academic scholarship has rapidly pushed it from obscurity to a reputable worldwide presence.
Students have a variety of degree paths and research areas from which to choose. Areas of specialization include Analysis, Differential Equations, Algebra, Topology, Differential Geometry, Numerical Analysis, and Applied Mathematics.
The typical undergraduate degree will require 128 credit hours for completion. Master’s and Doctoral level studies are also available.
7. University of Oxford
Talking about Math PhD Rankings? As one of the oldest universities in the world, Oxford has had plenty of time to develop an outstanding reputation in many fields. The Mathematics and Science Departments at Oxford were home to historic alumni such as Edwin Hubble, Robert Hooke, and Stephen Hawking.
This naturally lends itself towards departmental collaboration through the Mathematical Institute at Oxford. Research is performed together with physicists, medical professionals, engineers, social scientists, and others who contribute to the success of the department.
Both the Pure and Applied Mathematics programs are held in the same building, further encouraging student partnerships.
Approximately 1,200 undergraduate and graduate students are enrolled in the various programs taught by 170 expert faculty members. A total of 16 focus groups and centers on campus conduct the majority of the research.
Areas include the Geometry Group, History of Mathematics Group, and the Oxford Center for Nonlinear PDE. The department also networks with the Oxford Solid Mechanics group and the Clay Mathematical Institute.
8. University of California Los Angeles (UCLA)
Offering a variety of degree programs from Bachelor’s to Doctoral level, the Department of Mathematics at UCLA is dynamic and engaging in its educational approach.
Presented with the Exemplary Program or Achievement Award from the American Mathematical Society in 2007, the department has been given high praise for its academic and research success.
UCLA faculty and students benefit from the Institute for Pure and Applied Mathematics. Besides bringing in numerous world-class mathematicians for the public.