Oxford Mathematics interview

The Oxford Mathematics interview is an academic, largely mathematical conversation, run like a short tutorial. You work through an unfamiliar problem out loud, or explore a new definition, while tutors watch how you absorb new ideas, use their hints and explain your thinking. Shortlisted candidates usually have one or two interviews at their first college and at least one at a second, randomly assigned college, each about 25 minutes on Microsoft Teams. For 2027 entry most run from 14 to 17 December 2026.

Key facts

What happens in the interview

Oxford's Mathematical Institute describes its interviews as "largely mathematical". Tutors may ask about an area of maths you've studied, look in detail at a point of technique or a curve sketch, set an unfamiliar problem, or give you a new definition and ask what follows from it.

Tutors run it like a tutorial:

• They start with small cases ("try n = 1, 2, 3, 4"), then ask why the pattern holds.
• They ask for a prediction before the working.
• They give hints when you're stuck. Hints are expected and normal.
• They change the problem once it's solved, for example to a 3 × n grid.
• If a problem is going nowhere, or you've cracked it, they move on.

Small slips don't matter much, and it's very common not to reach a complete solution. In the department's words, "we are not mind-readers", so talk through what you're thinking, including what you're unsure of.

You'll write on a shared Miro whiteboard, so have a touchscreen of at least 8 inches and a basic stylus, plus paper and pens.

What tutors look for

The Mathematical Institute's selection criteria:

• Mathematical aptitude and technical skill: accurate, fluent use of school maths (algebra, curve sketching, calculus) as a tool for the problem.
• Absorbing and using new ideas: picking up a new definition, hint or method and putting it straight to work.
• Thinking independently: making your own progress: trying small cases, spotting patterns, making conjectures and building an argument for them.
• Perseverance and enthusiasm: staying with a hard problem, and enjoying it.
• Explaining your thinking: a running commentary that lets tutors see the thought process, and clear arguments.

How the interview is marked

Oxford doesn't publish a marking scale for Mathematics interviews. Tutors grade each interview from 1 to 9 against agreed descriptors, but the descriptors, and any grade that leads to an offer, aren't public.

The grades are shared with tutors at all the colleges, alongside your admissions test score, UCAS form and contextual information, so no single interview decides the outcome. Tutors care about your thought process, creativity and spotting patterns, not small slips.

Example questions

These are questions published by Oxford and its tutors, in the form Toby asks them. Tutors set their own questions, so yours will differ.

Sliding ladder's middle rung

Published by Oxford: sample interview questions

A ladder leans against a vertical wall, with its feet on the ground. Its middle rung is painted a different colour, so we can see it from the side. As the ladder slides down to the floor, always touching both the wall and the ground, what shape does that middle rung trace out? Sketching a few positions might help.

• Why tutors ask it: it tests whether you can turn a physical picture into coordinates, check guesses against special cases, and notice when a model breaks down.
• A hint a tutor might give: "Try some special positions first. Where is the middle rung when the ladder is upright, when it's flat, and at 45 degrees?"
• A strong answer tests special positions before committing to a guess, then sets up coordinates with the corner at the origin and checks the endpoints of the shape it finds.
• A common slip is guessing a straight line.

Tiling a 2 by n grid

Published by Oxford: sample interview questions

How many ways are there to cover a 2 × n rectangular grid with 2 × 1 tiles? Each tile covers two neighbouring squares, with no gaps or overlaps. Don't worry about the general answer yet: sketch the cases n = 1 to 4 on paper and count them.

• Why tutors ask it: it shows whether you can organise small cases systematically, spot a pattern and then prove it with a clean case split, rather than trusting the first few terms.
• A hint a tutor might give: "Look at the left-most column, the two squares at the left-hand end. In how many different ways can a tile cover the top one?"
• A strong answer lists the small cases by what happens at the left-hand end, not by trial and error, then splits every tiling into cases that don't overlap and proves the pattern rather than just recognising the numbers.
• A common slip is guessing the pattern from four terms and never justifying it.

Moving the last digit

Published by an Oxford tutor on the Computer Science department's website: Interview Question 2

Find the smallest natural number ending in 6, such that if the last 6 is removed and placed in the front, the new number is 4 times the original number. (For example, 26 → 62, and 62 ≠ 4 × 26.)

• Why tutors ask it: it shows whether you can set up a digit problem algebraically or by careful carrying, turn the method into a general procedure, and find the size constraint that rules some cases out.
• A hint a tutor might give: "The original ends in 6, so 4 times it ends in which digit? Which digit of the original is that, once the 6 has moved to the front?"
• A strong answer works from the right one digit at a time, keeping track of every carry, or writes the number algebraically, then checks the result by multiplying by 4.
• A common slip is losing a carry, or stopping at the first 6 that appears in the product.

Practise with Toby

Toby is an AI interviewer that runs practice interviews by voice. The Oxford Mathematics interview is built from Oxford's own guidance and follows the real format:

• First college: first interview. An unfamiliar problem, often opening with a point of technique or a curve sketch, built up from small cases to a general argument.
• First college: second interview. A new definition or problem to explore, testing how quickly you absorb and use a new idea. Some colleges hold only one first-college interview.
• Second college. One interview at a randomly assigned second college, with fresh tutors and a fresh problem.

It draws on 30 problems, each with hints and follow-ups. Fourteen are published questions from Oxford and Cambridge sources, and the rest were written to the same style and level, with every result independently re-derived.

Toby puts the problem on screen, gives you time to think and asks you to talk it through. He gives a hint only when you're stuck, asks why a pattern holds, and changes the problem once you've solved it. Like a real tutor, he doesn't praise every answer.

You can add your personal statement so Toby can ask about it, and choose a 10, 20 or 30-minute interview. Your prep page has the format, the department's criteria and practice problems with hints and worked solutions. Afterwards, your debrief gives you a practice mark out of 10 (6 is acceptable, 7 good, 8 strong), a score against each criterion, notes on every question and the full transcript. A practice mark is a guide, not a prediction.

Frequently asked questions

Sources

Last checked October 2026.

• University of Oxford: Interviews
• University of Oxford: Sample interview questions
• University of Oxford: Mathematics course page
• Oxford Mathematics: Interviews
• Oxford Mathematics: Admissions criteria
• Oxford Mathematics: Prospectus
• Oxford Mathematics: Admissions feedback 2025
• Interview Question 2 (an Oxford tutor's page on the Computer Science department's website)

Related interviews

• Oxford Mathematics and Statistics interview
• Oxford Mathematics and Computer Science interview
• Cambridge Mathematics interview

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