DPhil in Mathematics
About the course
The DPhil in Mathematics is a research degree in which students pursue original research in areas such as algebra, geometry, number theory, mathematical biology, quantum theory, and data science, and write a thesis contributing to the field.
During your study at Oxford, you can share in the excitement of contributing to research in one or more of the many topics studied by Oxford mathematicians.
To learn more about the research topics you’ll have the opportunity to explore, please refer to the Research areas section on this page.
During your DPhil you will be required to complete some 'broadening training' to broaden your mathematical knowledge beyond your specialist area. Exactly how this happens varies, but usually it is by attending lectures, seminars, and colloquia. You will also gain a wide range of research and other skills.
You will be required to contribute to the teaching work of the department. You will be trained for this at the start of your time as a DPhil student, and the work itself will include marking students’ work and later leading classes of students.
Attendance
The course is full-time and requires attendance in Oxford. Full-time students are subject to the University's Residence requirements.
Undertaking the course is regarded as equivalent to working full-time hours and may also sometimes require some additional hours. The minimum period of registration for the DPhil is six terms but in practice you may need nine terms at least.
Provision exists for students on some courses to undertake their research in a ‘well-founded laboratory’ outside of the University. This may require travel to and attendance at a site that is not located in Oxford. Where known, existing collaborations will be outlined on this page. Please read the course information carefully, including the additional information about course fees and costs.
Resources to support your study
As a graduate student, you will have access to the University's wide range of resources including libraries, museums, galleries, digital resources and IT services.
The Bodleian Libraries is the largest library system in the UK. It includes the main Bodleian Library and libraries across Oxford, including major research libraries and faculty, department and institute libraries. Together, the Libraries hold more than 13 million printed items, provide access to e-journals, and contain outstanding special collections including rare books and manuscripts, classical papyri, maps, music, art and printed ephemera.
The University's IT Services is available to all students to support with core university IT systems and tools, as well as many other services and facilities. IT Services also offers a range of IT learning courses for students to support with learning and research, as well as guidance on what technology to bring with you as a new student at Oxford.
The Mathematical Institute's home is the purpose-built Andrew Wiles Building. This provides ample teaching facilities for lectures, classes and seminars. Each research student is allocated an office in the Andrew Wiles Building that they will share with three or four other students: each student has their own desk, with a computer.
The Mathematical Institute provides IT support, and students can use the department's Whitehead Library, with an extensive range of books and journals.
In addition to the common room, where graduate students regularly gather for coffee and other social occasions, there is also a café in the Andrew Wiles Building.
Supervision
The allocation of graduate supervision for this course is the responsibility of the Mathematical Institute and it is not always possible to accommodate the preferences of incoming graduate students to work with a particular member of staff. Under exceptional circumstances a supervisor may be found outside the Mathematical Institute.
You will be invited to suggest a specific supervisor or supervisors in your application, and your preferences will be considered in allocating you a supervisor (which will be done before your arrival).
You will have the opportunity to meet individually with your supervisor.
Assessment
All students will be initially admitted to the status of Probationer Research Student (PRS). Within four terms of admission as a PRS student you will be expected to apply for transfer of status from Probationer Research Student to DPhil status.
A successful transfer of status from PRS to DPhil status will require satisfactory attendance and the submission of a thesis. Students who are successful at transfer will also be expected to apply for and gain confirmation of DPhil status within nine terms of admission, to verify that their work continues to be on track. Both milestones normally involve an interview with two assessors (other than your supervisor) and therefore provide important experience for the final oral examination.
You will be expected to teach at least two sets of classes before transfer of status and a further three additional sets before confirmation of status. You will be expected to acquire transferable skills as part of your training. This normally involves attendance at workshops, seminars and colloquia.
You will be expected to submit a substantial original thesis which should not exceed 200 pages after three or, at most, four years from the date of admission. To be successfully awarded a Doctor of Philosophy in Mathematics you will need to defend your thesis orally (viva voce) in front of two appointed examiners.
Graduate destinations
The department, working alongside the university’s Careers Service, supports graduate students as they move from the DPhil to the next stage of their career. Many graduate students stay in academia, by taking up a postdoctoral position, and many move into employment in a range of industries and sectors where the expertise and skills developed during the DPhil are highly valued.
Changes to this course
The University will seek to deliver this course in accordance with the description set out in this course page. However, there may be situations in which it is desirable or necessary for the University to make changes in course provision, either before or after registration. The safety of students, staff and visitors is paramount and major changes to delivery or services may have to be made if a pandemic, epidemic or local health emergency occurs. In addition, in certain circumstances, for example due to visa difficulties or because the health needs of students cannot be met, it may be necessary to make adjustments to course requirements for international study.
Where possible your academic supervisor will not change for the duration of your course. However, it may be necessary to assign a new academic supervisor during the course of study or before registration for reasons which might include illness, sabbatical leave, parental leave or change in employment.
For further information please see our page on changes to courses and the provisions of the student contract regarding changes to courses.
Research areas
You’ll have the opportunity to undertake research within the specialised themes of this course, which include:
- algebra
- combinatorics
- functional analysis
- geometry
- history of mathematics
- logic
- machine learning and data science
- mathematical biology
- mathematical physics
- mathematical and computational finance
- number theory
- numerical analysis
- modelling applied to problems in industry
- partial differential equations
- stochastic analysis
- topology
Further information
You will be asked to outline your research interests in your personal statement when you apply. You will also be invited to listing at least one but no more than three research groups that you would like your application to be seen by.
Information about the Mathematical Institute's research groups can be found on its website, along with information about academic and research staff.
Entry requirements for entry in 2026-27
Proven and potential academic excellence
The requirements described below are specific to this course and apply only in the year of entry that is shown. You can use our guidance to help you evaluate whether your application is likely to be competitive.
We know that contextual factors can make it difficult for candidates to demonstrate their full potential. This course is taking part in an initiative to use contextual data to help us to better understand your achievements in the context of your individual background. For further details, please refer to the information about improving access to graduate study in the How to apply section of this page.
Please be aware that any studentships that are linked to this course may have different or additional requirements and you should read any studentship information carefully before applying. Contextual data may also be used in the assessment of studentships.
Degree-level qualifications
As a minimum, applicants should hold or be predicted to achieve the following UK qualifications or their equivalent:
- a first-class undergraduate degree with honours in mathematics or a related discipline.
A previous master's degree is not required, though the requirement for a first-class undergraduate degree with honours can be alternatively demonstrated by strong performance in a master's degree.
For applicants with a bachelor's degree from the USA, the minimum overall GPA that is normally required to meet the undergraduate-level requirement is 3.7 out of 4.0.
If your degree is not from the UK or another country specified above, visit our International Qualifications page for guidance on the qualifications and grades that would usually be considered to meet the University’s minimum entry requirements.
GRE General Test scores
No Graduate Record Examination (GRE) or GMAT scores are sought.
Other qualifications, evidence of excellence and relevant experience
- Research or working experience in the proposed research area may be an advantage.
- Publications are not expected but may be used as evidence of excellence.
English language proficiency
This course requires proficiency in English at the University's standard level. If your first language is not English, you may need to provide evidence that you meet this requirement. The minimum scores required to meet the University's standard level are detailed in the table below.
| Test | Minimum overall score | Minimum score per component |
|---|---|---|
| IELTS Academic (Institution code: 0713) | 7.0 | 6.5 |
| TOEFL iBT* including the 'Home Edition' (Institution code: 0490) | 100 | Listening: 22 Reading: 24 Speaking: 25 Writing: 24 |
| C1 Advanced† | 185 | 176 |
| C2 Proficiency‡ | 185 | 176 |
| Oxford Test of English Advanced | 155 | 145 |
*Changes to the TOEFL iBT test are being introduced on 21 January 2026. If you are taking a TOEFL test after this date, please note that these changes may affect whether the University is able to accept this test.
†Previously known as the Cambridge Certificate of Advanced English or Cambridge English: Advanced (CAE)
‡Previously known as the Cambridge Certificate of Proficiency in English or Cambridge English: Proficiency (CPE)
Your test must have been taken no more than two years before the start date of your course. Our Application Guide provides further information about the English language test requirement.
Declaring extenuating circumstances
If your ability to meet the entry requirements has been affected by the COVID-19 pandemic (eg you were awarded an unclassified/ungraded degree) or any other exceptional personal circumstance (eg other illness or bereavement), please refer to the guidance on extenuating circumstances in the Application Guide for information about how to declare this so that your application can be considered appropriately.
References
You will need to register three referees who can give an informed view of your academic ability and suitability for the course. The How to apply section of this page provides details of the types of reference that are required in support of your application for this course and how these will be assessed.
Supporting documents
You will be required to supply supporting documents with your application. The How to apply section of this page provides details of the supporting documents that are required as part of your application for this course and how these will be assessed.
Performance at interview
Technical interviews are normally held as part of the admissions process.
If invited you can expect to be interviewed by at least two people and for the interview to last around 30 minutes. The interview will take place online.
It is expected that interviews will take place around three to five weeks after an application deadline.
Offer conditions for successful applications
If you receive an offer of a place at Oxford, your offer will outline any conditions that you need to satisfy and any actions you need to take, together with any associated deadlines. These may include academic conditions, such as achieving a specific final grade in your current degree course. These conditions will usually depend on your individual academic circumstances and may vary between applicants. Our 'After you apply' pages provide more information about offers and conditions.
In addition to any academic conditions which are set, you will also be required to meet the following requirements:
Financial Declaration
If you are offered a place, you will be required to complete a Financial Declaration in order to meet your financial condition of admission.
Disclosure of criminal convictions
In accordance with the University’s obligations towards students and staff, we will ask you to declare any relevant, unspent criminal convictions before you can take up a place at Oxford.
Academic Technology Approval Scheme (ATAS)
This course may require you to obtain an ATAS certificate before you can apply for a visa/immigration permission. If you are offered a place, the academic department will confirm whether an ATAS certificate is required. If so, they will also send you the information you need to apply for one. You can apply for ATAS whilst your offer is conditional and before the Confirmation of Acceptance for Studies (CAS) is issued. Further information about ATAS is available on the student visa webpages.
Other factors governing whether places can be offered
The following factors will also govern whether candidates can be offered places:
- the ability of the University to provide the appropriate supervision for your studies, as outlined under the 'Supervision' heading in the About section of this page;
- the ability of the University to provide appropriate support for your studies (eg through the provision of facilities, resources, teaching and/or research opportunities); and
- minimum and maximum limits to the numbers of students who may be admitted to the University's taught and research programmes.
Funding
For entry in the 2026-27 academic year, the collegiate University expects to offer over 1,100 full or partial graduate scholarships across a wide range of graduate courses.
If you apply by the January deadline shown on this page and receive a course offer, your application will then be considered for Oxford scholarships. For the majority of Oxford scholarships, your application will automatically be assessed against the eligibility criteria, without needing to make a separate application. There are further Oxford scholarships available which have additional eligibility criteria and where you are required to submit a separate application. Most scholarships are awarded on the basis of academic merit and/or potential.
To ensure that you are considered for Oxford scholarships that require a separate application, for which you may be eligible, use our fees, funding and scholarship search tool to identify these opportunities and find out how to apply. Alongside Oxford scholarships, you should also consider other opportunities for which you may be eligible including a range of external funding, loan schemes for postgraduate study and any other scholarships which may also still be available after the January deadline as listed on our fees, funding and scholarship search tool.
Details of college-specific funding opportunities can also be found on individual college websites:
Please refer to the College preference section of this page to identify which of the colleges listed above accept students for this course.
For the majority of college scholarships, it doesn’t matter which college, if any, you state a preference for in your application. If another college is able to offer you a scholarship, your application can be moved to that college if you accept the scholarship. Some college scholarships may require you to state a preference for that college when you apply, so check the eligibility requirements carefully.
Costs
Annual course fees
The fees for this course are charged on an annual basis.
Fees for the 2026-27 academic year at the University of Oxford
What do course fees cover?
Course fees cover your teaching as well as other academic services and facilities provided to support your studies. Unless specified in the additional information section below, course fees do not cover your accommodation, residential costs or other living costs. They also don’t cover any additional costs and charges that are outlined in the additional costs information below.
How long do I need to pay course fees?
Course fees are payable each year, for the duration of your fee liability (your fee liability is the length of time for which you are required to pay course fees). For courses lasting longer than one year fees will usually increase annually, as explained in the University’s Terms and Conditions.
Graduate students who have reached the end of their standard period of fee liability will be required to pay a University continuation charge and/or a college continuation charge.
The University continuation charge, per term for entry in 2026-27 is £656, please be aware that this will increase annually. For part-time students, the termly charge will be half of the termly rate payable by full-time students.
If a college continuation charge applies (not applicable for non-matriculated courses) it will be between £150 and £500, as explained in our information about continuation charges. Please contact your college for more details, including information about whether your college's continuation charge is applied at a different rate for part-time study.
Where can I find more information about fees?
Our fees and other charges pages provide further information, including details about:
- course fees and fee liability;
- how your fee status is determined;
- changes to fees and other charges; and
- continuation charges.
Information about how much fees and other costs will usually increase each academic year is set out in the University's Terms and Conditions.
Additional costs
Living costs
In addition to your course fees and any additional course-specific costs, you will need to ensure that you have adequate funds to support your living costs for the duration of your course.
Living costs for full-time study
For the 2026-27 academic year, the range of likely living costs for a single, full-time student is between £1,405 and £2,105 for each month spent in Oxford. We provide the cost per month so you can multiply up by the number of months you expect to live in Oxford. Depending on your circumstances, you may also need to budget for the costs of a student visa and immigration health surcharge and/or living costs for family members or other dependants that you plan to bring with you to Oxford (if dependant visa eligibility criteria are met).
Further information about living costs
The current economic climate and periods of high national inflation in recent years make it harder to estimate potential changes to the cost of living over the next few years. For study in Oxford beyond the 2026-27 academic year, it is suggested that you budget for potential increases in living expenses of around 4% each year – although this rate may vary depending on the national economic situation.
A breakdown of likely living costs for one month during the 2026-27 academic year are shown below. These costs are based on a single, full-time graduate student, with no dependants, living in Oxford.
| Lower range | Upper range | |
|---|---|---|
| Food | £315 | £545 |
| Accommodation | £825 | £990 |
| Personal items | £160 | £310 |
| Social activities | £50 | £130 |
| Study costs | £35 | £90 |
| Other | £20 | £40 |
| Total | £1,405 | £2,105 |
For information about how these figures have been calculated as well as tables showing the likely living costs for nine and twelve months, please refer to the living costs page of our website.
College preference
Students enrolled on this course will belong to both a department/faculty and a college. Please note that ‘college’ and ‘colleges’ refers to all 43 of the University’s colleges, including those designated as societies and permanent private halls (PPHs).
If you apply for a place on this course you will have the option to express a preference for one of the colleges listed below, or you can ask us to find a college for you. Before deciding, we suggest that you read our brief introduction to the college system at Oxford and our advice about expressing a college preference.
If you are a current Oxford student and you would like to remain at your current Oxford college, you should check whether it is listed below. If it is, you should indicate this preference when you apply. If not, you should contact your college office to ask whether they would be willing to make an exception. Further information about staying at your current college can be found in our Application Guide.
The following colleges accept students on the DPhil in Mathematics:
Before you apply
Our guide to getting started provides general advice on how to prepare for and start your application, including advice to help you evaluate whether your application is likely to be competitive.
If it is important for you to have your application considered under a particular deadline – eg under the January deadline in order to be considered for Oxford scholarships – we recommend that you aim to complete and submit your application at least two weeks in advance. Check the deadlines on this page and the information about deadlines and when to apply in our Application Guide.
Application fee waivers
An application fee of £20 is payable for each application to this course. Application fee waivers are available for the following applicants who meet the eligibility criteria:
- applicants from low-income countries;
- refugees and displaced persons;
- UK applicants from low-income backgrounds; and
- applicants who applied for our Graduate Access Programmes in the past two years and met the eligibility criteria.
You are encouraged to check whether you're eligible for an application fee waiver before you apply.
Readmission for current Oxford graduate taught students
If you're currently studying for an Oxford graduate taught course and apply to this course with no break in your studies, you may be eligible to apply to this course as a readmission applicant. The application fee will be waived for an eligible application of this type. Check whether you're eligible to apply for readmission.
Application fee waivers for eligible associated courses
If you apply to this course and are considering applying (or have already applied) to any of the associated courses listed below, you can request an application fee waiver so that you only need to pay one application fee. We recommend that you use your application fee waiver to apply only for eligible courses that are closely related in research area to this one.
For full details about how to request an application fee waiver, please select the course you are interested in from the list below and refer to the equivalent section of its course page.
The following associated courses are taking part in this application fee waiver scheme:
- Autonomous Intelligent Machines and Systems, EPSRC CDT
- Biomedical and Clinical Sciences (Oxford-GSK), DPhil
- Cancer Science (Biological background), CDT
- Cancer Science (Clinician), DPhil
- Cancer Science (Intercalation), DPhil
- Cancer Science (Maths/Physics background), CDT
- Chemical Synthesis for a Healthy Planet, CDT
- Engineering Biology, BBSRC and EPSRC CDT
- Fundamentals of AI, EIT CDT
- Fusion Power, EPSRC CDT
- Genomic Medicine and Statistics, DPhil
- Healthcare Data Science, EPSRC CDT
- Inflammatory and Musculoskeletal Disease, DPhil
- Inorganic Materials for Advanced Manufacturing, EPSRC CDT
- Intelligent Earth, UKRI CDT in AI for the Environment
- Interdisciplinary Life and Environmental Science, DPhil
- Materials 4.0, EPSRC CDT
- Mathematics of Random Systems: Analysis, Modelling and Algorithms, CDT
- Neuroscience (1+3), DPhil
- Quantum Informatics, EPSRC CDT (expected to open soon)
- Robotics and AI for Net Zero, EPSRC CDT (expected to open soon)
- Statistics and Machine Learning, EPSRC CDT
- Superconductivity: Enabling Transformative Technologies, EPSRC CDT
Do I need to contact anyone before I apply?
You do not need to contact the department before you apply but you are encouraged to visit the relevant departmental webpages to read any further information about your chosen course.
However, if you would like to speak to an academic member of staff involved in your preferred area of research, you may get in touch with them directly using the contact details on the Mathematical Institute's webpages.
Improving access to graduate study
This course is taking part in initiatives to improve the selection procedure for graduate applications, to ensure that all candidates are assessed fairly. It is taking part in the 'Close the Gap' project which aims to improve access to doctoral study.
Contextual data (where it has been provided in the application form) and your contextual statement (if you choose to provide one) will be used as part of an initiative to contextualise applications at the different stages of the selection process.
Completing your application
You should refer to the information below when completing the application form, paying attention to the specific requirements for the supporting documents.
For this course, the application form will include questions that collect information that would usually be included in a CV/résumé. You should not upload a separate document. If a separate CV/résumé is uploaded, it will be removed from your application.
If any document does not meet the specification, including the stipulated word count, your application may be considered incomplete and not assessed by the academic department. Expand each section to show further details.
Proposed field and title of research project
Under the section titled 'Field and title of research project', you are strongly encouraged to name at least one but no more than three research groups that you would like your application to be seen by. More information about the research groups in the Mathematical Institute can be found on the department's website.
You should not use this field to type out a full research proposal. You will be able to upload your research supporting materials separately if they are required (as described below).
Proposed supervisor
If known, under 'Proposed supervisor name' enter the name of the academic(s) whom you would like to supervise your research. Otherwise, leave this field blank.
You can enter up to three names and you should list them in order of preference or indicate equal preference.
Referees:
Three overall, academic preferred
Whilst you must register three referees, the department may start the assessment of your application if two of the three references are submitted by the course deadline and your application is otherwise complete. Please note that you may still be required to ensure your third referee supplies a reference for consideration.
Your references should generally be academic, though up to one professional reference will be accepted.
Your references should describe your intellectual ability, academic achievement, motivation, and aptitude for advanced research.
Official transcript(s)
Your transcripts should give detailed information of the individual grades received in your university-level qualifications to date. You should only upload official documents issued by your institution and any transcript not in English should be accompanied by a certified translation.
More information about the transcript requirement is available in the Application Guide.
Contextual statement
If you wish to provide a contextual statement with your application, you may also submit an additional statement to provide contextual information on your socio-economic background or personal circumstances in support of your application.
It is not necessary to anonymise this document, as we recognise that it may be necessary for you to disclose certain information in your statement. This statement will not be used as part of the initial academic assessment of applications at shortlisting, but may be used in combination with socio-economic data to provide contextual information during decision-making processes.
Please note, this statement is in addition to completing the 'Extenuating circumstances’ section of the standard application form.
You can find more information about the contextual statement on our page that provides details of the continuing pilot programme to improve the assessment procedure for graduate applications.
Statement of purpose:
A maximum of 800 words
Your statement should be written in English and explain your reasons for applying for the course at Oxford, your relevant experience and education, and the specific areas that interest you and/or you intend to specialise in. This will be assessed for evidence of motivation for and understanding of the proposed area of study and whether a suitable supervisor can be found.
If possible, please ensure that the word count is clearly displayed on the document.
Start or continue your application
You can start or return to an application using the relevant link below. As you complete the form, please refer to the requirements above and consult our Application Guide for advice.
After you've submitted your application
Your application (including the supporting documents outlined above) will be assessed against the entry requirements detailed on this course page. Whether or not you have secured funding will not be taken into consideration when your application is assessed. You can find out more about our shortlisting and selection process in our detailed guide to what happens next.
Find out how to manage your application after submission, using our Applicant Self-Service tool.