Mathematics Overview

St John's has a large and diverse Mathematics community, with about 15 undergraduates in each year group, drawn from across the UK and overseas. The College's Fellows have a corresponding breadth of expertise, from the most abstract areas of pure mathematics and the statistical analysis of big data, to the fundamental theories of particle physics and the mathematics of ocean dynamics. We encourage applications from bright students of all backgrounds, and award an annual Pythagoras Prize of £10,000 to a first year home undergraduate in Mathematics, based on academic excellence and financial need.  We also provide tailored STEP support to our offer holders from UK state schools.

The College has an active mathematical society, the Adams Society, which was founded in 1923 and organises regular talks and social events. The society is named after John Couch Adams, a Mathematics graduate of the College from the 19th Century, who correctly predicted the existence of Neptune. He is just one of many distinguished alumni, alongside Brook Taylor (of Taylor's Theorem), pioneers of quantum mechanics Paul Dirac and Abdus Salam, and 2020 Nobel Prize winner Sir Roger Penrose.

A short introduction to Mathematics at St John's College from Dr Matthias Dörrzapf and Dr Jack Smith.

Entry Details

UCAS Code: G100

Typical Minimum Entry Requirements

A Level: A*A*A

International Baccalaureate: 42 points, with 776 at Higher Level

STEP (Sixth Term Examination Paper): At least Grades 1 in STEP II and STEP III. 

We strongly encourage applicants to start preparing early for STEP, ideally over the summer between Years 12 and 13, and we provide tailored STEP support to our offer holders at state schools with no or little access to STEP preparation.  A good starting point, with links to many free online resources, is  The questions are designed to be challenging for all applicants, so do not worry if they seem difficult at first: you will improve significantly with practice.

STEP does not require any special knowledge or training, beyond A-level Maths and Further Maths, and is a very good indicator of suitability to study Mathematics at Cambridge.  Working through STEP questions is also an excellent way to prepare for Cambridge maths interviews, to see whether you enjoy university-style mathematical thinking and to prepare for the Cambridge course.

Essential Subjects: A Level Mathematics and Further Mathematics. IB Higher Level Mathematics: Analysis and Approaches (preferred) or IB Higher Level Mathematics: Applications and Interpretation.

We will consider applications from A-level students whose school does not offer Further Mathematics, but it is essential that they be familiar with the content of the Further Mathematics syllabus before starting the Cambridge course. The AMSP (Advanced Mathematics Support Programme) provides resources for independent study, and we are happy to offer guidance to potential applicants in this situation.

Desirable Subjects: None

Submitted Work: None

Admissions Assessment: None


Typical Successful Applicant Profile

In recent years, successful maths applicants to St John's from UK school/college backgrounds have typically had the following characteristics:

  • Among the strongest GCSEs in their GCSE-school cohort, usually across a range of subjects
  • Predicted, and subsequently achieving, three or four A*s at A-level
  • Very high marks (95%+) in Maths A-level
  • Gold in UKMT Maths Challenges if they have had the opportunity to sit these (not having had the opportunity to sit them will certainly not count against you!)
  • Deeply curious about mathematics, excited to dig into the hows and whys of the subject and to tackle challenging non-routine problems, and happy to think beyond the application of standard techniques and formulae.


These characteristics are not all necessary and are only intended to illustrate the level at which our successful applicants are often performing.  We look carefully at each application on an individual basis, recognise the important role that personal and educational circumstances play, and use contextual data to help us better understand your application.

Admissions Interviews

Those invited for interview normally have two subject interviews with subject experts, each of around 25 minutes duration. At least one of these interviews will be with a Director of Studies in Mathematics.

Almost all of the interview time will be spent talking through maths problems. The problems will cover a range of topics but are designed to test how you think, rather than what you know. We are more interested in how you approach unfamiliar concepts, and in how you make or follow suggestions, than in whether you simply know the right answer. You don’t need any special knowledge and it is not a memory test, so there is no need to try to prepare lots of answers or memorise many things. What is most important is that you describe your thoughts to the interviewers. There are no trick questions or puzzles. Please find the Pure Mathematics interviewers for 2022 here

Admissions to Part III Mathematics

Admission into Part III leading to the M.Math, degree normally requires a First Class result at Part II Mathematics. For more information, please see here.  

Student Views

What makes maths at John’s really special is the community we have here.

The upside of being a relatively large maths cohort is that you are likely to find other mathematicians who are on a similar wavelength. We all support each other a tremendous amount and, because of the collegiate system, you can seek advice from people in older years; there’s a real sense of mentorship, which is so invaluable. Supervisions are another unique aspect of Cambridge, they’re an opportunity to really consolidate your learning, often with prominent academics in that field.

I have found that having teaching in such small groups has given me the confidence to ask any questions I want, and clarify parts of the course without feeling shy or nervous.

 - Anusha


St John's has a very welcoming maths community. There’s plenty of individualised support from college, so you can make the most of what is a challenging and rewarding course. I really like the sense of belonging you get from being in a large group of mathematicians; it’s always nice to spot a fellow mathematician walking around in college!

One particular highlight is a student run mathematics society. They regularly organise mathematical talks – one of my favourites is about the distributions of primes, which linked in nicely with the 1A Probability course we had just finished in Lent term. There’s social events as well, from board games to formal dinners, and it’s a great opportunity to unwind.

 - Sae


In my (unbiased) opinion, St John’s is the best college for maths. We have expert teaching staff, who are also very friendly.  We get extra support in the form of example classes in first and second year – which I found really helpful.  And we are ideally situated between the centre of town and the CMS.  John’s is the best college for student life too!

Excellent facilities. Kind and skilled staff. Beautiful buildings. Vibrant clubs and societies.  Lovely people. I have been able to get involved with Ultimate Frisbee, Jazz, Ballroom Dancing, a choir, Fives, and even Comic Opera!

 - Lennie 


I've absolutely loved my first two years doing maths at St John's.  I feel the maths community here is a lot more relaxed and family-like than at other colleges, with fellows and students alike happy to socialise when we get a break from example sheets!  I think we have just the right number of mathematicians at John's too - enough so you can make friends easily, but it is still a very personal experience.

Away from maths, I'm captain of the college hockey team, which is an excellent distraction from working.  John's is also very generous - they paid for me to go on a trip to Marrakesh at the end of my first year, and I should be heading out soon to Nagoya, in Japan, for the return leg of a cultural exchange!

 - Connor