Cambridge Mathematics Interview

Aerial View of Centre for Mathematical Sciences
Aerial View of Centre for Mathematical Sciences

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My interview session was held in Taylor’s College (where I did A-level), and was one- on-one. I forgot who my interviewer was, but I remember he was a math professor at Cambridge and had Erdos number 4 (whoa). The interview was scheduled for half an hour, and he pretty much cut me off at the mark. He started out asking me some questions about my family background, e.g. siblings, parents’ occupation, probably as ice-breaker.

Then we moved on to the fun part. He scanned my personal statement and realized I’ve done a lot of Olympiad math and chose a problem he thought was appropriately challenging for me. I don’t remember exactly what the problem was, but I remember it was something like proving that for any real polynomial, there is a root that has a certain property. The problem statement called for familiarity with polynomials and complex numbers, and the proof required some ‘well-known’ fact about real polynomials. Don’t fret if you are not too comfortable with those yet, as the interviewer should ask if you are familiar with them.

Solving the problem wasn’t straightforward, as it very well shouldn’t have been. The interviewer first asked if I preferred for him to give hints and guidance along the way or keep silent. I opted for silence. I started out working with a few test polynomials, e.g. X^2 + 1, just to poke around and see what I might find. The interviewer offered to give hints (perhaps I was slow), but I declined again. I looked at what was to be proved: some condition on some root… I tried to visualize the locus of complex numbers satisfying that condition, and of course drew it out so the interviewer can see my thought process.

After about ten minutes, clearly behind time, I asked for one of the two hints. The first hint was a fact I had no trouble proving, but didn’t really see where it fit into my progress so far. Then after a little while longer, I asked for the second hint. It was the ‘well-known’ fact that every real polynomial can be written as the product of real polynomials of degree at most two. I knew this fact, but didn’t think to use it until then. But once he said it I basically saw the rest of the proof and just blurted it out.

I asked the interviewer what was the shortest time someone took to solve it. He said five minutes.

My initial approaches were pretty much useless in solving the problem, way off mark from the intended solution, but maybe the interviewer saw something in my method that was intriguing. So write down and draw out and say everything you are thinking. And don’t be embarrassed to ask for hints. If the interviewer thinks the problem is challenging for you, then you should expect to need help.

Towards the end, the interviewer rushed through some questions not related to math and then basically shooed me out the door (because we were running a little late, me being quite slow on the problem).


Erdos number:


Ying Hong Tham is pursuing a Computer Science degree at Stanford University under Astro scholarship. You can find him sneaking into lecture halls at night to use the chalkboards for math scratch work and random doodling.

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