Why ask ex mathematicians math questions?

[chrissbliss]

Skimming around this forum and talking to people it seems that at interviews for quant jobs you get asked quite some general, fairly basic, math/probability questions.
Whilst certainly seeing the point in asking stuff about quantitative finance, C++ and other things that are not standard to non-finance PhD's, I can't immediately see why you'd ask e.g. a PhD in mathematical analysis basic stuff regarding Taylor series expansions or evaluation of integrals. Surely this stuff will be something the candidate knows and understands well, or at least could very easily refresh. The only reasons I can see why he/she would fail giving good answers to such questions, are
a) because they forgot it (but would recall it in a split second by skimming a book), or
b) because they are nervous due to the interview situation and underperforms.

I suppose in a fast paced environment it's often good to know stuff by heart and being able to deliver results rapidly without peeking in books, but would a science PhD ever not learn this very quickly (at least if able to deliver rapid answers to quant finance theory at an interview)?

[mj]

well it's scary how many really basic things some maths phds can't do:

e.g.

integrate log x
write a routine to numerically integrate a function from a to b
generate a random number from a discrete pdf

On the last one, i asked my interviewer (after taking the job) why he'd asked me something so easy and he said that only the two successful candidates got it.

[nablaQuadrat]

(...) I can't immediately see why you'd ask e.g. a PhD in mathematical analysis basic stuff regarding Taylor series expansions or evaluation of integrals.

Well, my HH has just told me that the average annual salary mounts to GBP 25K. The base salary of a (junior) quant can be 2X as much ( not speaking of the more senior positions ). Your selling point for these jobs is that you know (applied) Maths ( reasonably ).
If you paid so much money for somebody who has just walked in from the street, would not you also test upon his qualities ? I think it is quite fair.

( What is NOT reasonable, is to conduct am interview with more than, say, 10 rounds. At MSCI it can easily be 16 rounds. Within 5 hours (i.e., 5 rounds of 1 hour) your maths and product knowledge as well as your attitude can fairly be mapped up. All the rest is just arrogance and/or lacking of organization. )

[chrissbliss]

Well, my HH has just told me that the average annual salary mounts to GBP 25K. The base salary of a (junior) quant can be 2X as much ( not speaking of the more senior positions ). Your selling point for these jobs is that you know (applied) Maths ( reasonably ).
If you paid so much money for somebody who has just walked in from the street, would not you also test upon his qualities ? I think it is quite fair.

If the person walking in from the street had a PhD diploma in math with him I think I'd rather find it insulting to ask stuff they teach you during your first undergrad semester. And in some sense a waste of time; I mean, if they fail to answer it it's because they forgot the technique and/or got nervous.

But OK, it is true that there are two kinds of mathematicians; one type that has a lot really on top of his head and can answer reasonably basic questions in a split second and one type that might not but has a great ability to solve deep problems if given a little bit of time. Responding well to stress and being quick with the basics probably is important for many quant jobs.

[mj]

the real issue is that any semi-competent mathematician should be able to work out how to do these things on the spot.

Give me an algorithm, any algorithm, to do numerical integration.

If you can't work one out on the spot, you are not very good at maths and I can feel secure in rejecting you.

Unfortunately, a phd in maths doesn't always mean what it ought to.

[chrissbliss]

the real issue is that any semi-competent mathematician should be able to work out how to do these things on the spot.

Give me an algorithm, any algorithm, to do numerical integration.

If you can't work one out on the spot, you are not very good at maths and I can feel secure in rejecting you.

Unfortunately, a phd in maths doesn't always mean what it ought to.

Ok that's extremely basic I guess but e.g. questions on diagonalization of matrices I had to briefly look up to recall (hadn't touched those things for 10+ years), and I don't think my thesis in pure math was bad.

[mj]

The paradox lies in that the more basic the question the more useful it is! Getting it right doesn't say much but getting it wrong says heaps.

(Un)fortunately, the really basic questions weed out a lot of candidates.

[chrissbliss]

I see your point but I still think it's a huge difference between failing a basic questions and a) being able to look it up and completely understand how to do it in only a minute or two or b) needing quite some time to grasp and solve it, and I believe a PhD in math should in most cases be a guarentee that the situation is a)

[rajat25690]

Hi Mark,

In the second post on this thread, you say "generate a random number from a discrete pdf". I am not sure what you mean by that. Are you saying that we are given a discrete pdf and we have to generate numbers which follow this distribution or are you saying that we are given a function which generates numbers coming out of a discrete pdf and we have to use that function to generate uniformally distributed random numbers? If you meant the latter, can you tell me the answer please. In any case, what would be the answer to the latter question?

Rajat.

[mj]

it was the former

[rajat25690]

If the question was the latter, what would the answer be?

[stochan]

in the latter case you need to approximate the uniform distribution with a discrete distribution on 0, 1/n, 2/n,..., 1 (which is reasonable because no machine can do otherwise).