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How difficult is a Ph.D in Math or Fin Math?

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5/23/08
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I don't mean to be a post troll or anything creating multiple threads my first day, but I got the impression that even though lots of quant jobs are now available to those with a professional master's degree, the highest paying quant jobs ($1-2 mil and above) are reserved for those with the highest level of education (Ph.d). So my question is how difficult is a Ph.d in Math or Math Fin? How long do the dissertations have to be? Don't want to sound like an idiot but what percentile of the general population would you say is talented enough to go for a Ph.d, 3%? 1%? Less?
 
So my question is how difficult is a Ph.d in Math or Math Fin? How long do the dissertations have to be? Don't want to sound like an idiot but what percentile of the general population would you say is talented enough to go for a Ph.d, 3%? 1%? Less?

For a math Ph.D., probably the top 1%. Since Mensa takes the top 2%, if you don't qualify for membership, a math Ph.D. is probably out of reach. The dissertations I've seen have been padded -- i.e. include results and discussion already known -- in addition to some "original" material. The "original research" in a doctoral thesis isn't usually that great -- it fulfils part of the requirement for a Ph.D. -- and often the thesis advisor has to hold the student's hand and essentially write his thesis for him (which is not supposed to happen).

The difficulty level of the dissertartion depends on which U you go to, the area you work in (e.g. algebraic topology or group theory), and the stature of your advisor.

If you're contemplating doing a math Ph.D. out of mercenary considerations, don't bother: there are easier ways of making money. A math Ph.D. takes several years and unless you really want to do it for its own sake, you will probably drop out at some stage (attirtion rates for math Ph.D. students vary from 50% to 80%).
 
For a math Ph.D., probably the top 1%. Since Mensa takes the top 2%, if you don't qualify for membership, a math Ph.D. is probably out of reach. The dissertations I've seen have been padded -- i.e. include results and discussion already known -- in addition to some "original" material. The "original research" in a doctoral thesis isn't usually that great -- it fulfils part of the requirement for a Ph.D. -- and often the thesis advisor has to hold the student's hand and essentially write his thesis for him (which is not supposed to happen).

Yes. I have a PhD is pure maths and I have seen this "holding hands" business, which may even continue after the thesis if there is some "bonding" between the student and supervisor. Unfortunately, if the thesis adviser is of high stature, this student who he is helping will probably be far more successful than some other new mathematician who is making an honest contribution.

My thesis was over 150 pages, all of which was original research, but I have seen an award winning thesis where the original result is about 20 pages, and the remainder is just filler.

The difficulty level of the dissertartion depends on which U you go to, the area you work in (e.g. algebraic topology or group theory), and the stature of your advisor.

You seem to know a fair bit, maybe you have a math PhD yourself? :)
 
In other countries, like Russia, Ph.D. is much harder to get. Students need to produce a certain number of papers, and their thesis is not evaluated "in house" but gets sent to a special organization that evaluates it on the basis of quality and originality. Also, depending on advisor's reputation a student may get more or less trouble along the way of writing and defending the thesis.
 
the highest paying quant jobs ($1-2 mil and above) are reserved for those with the highest level of education (Ph.d). So my question is how difficult is a Ph.d in Math or Math Fin? How long do the dissertations have to be? Don't want to sound like an idiot but what percentile of the general population would you say is talented enough to go for a Ph.d, 3%? 1%? Less?
I don't know where you got the idea that quants making 1-2M and above. There are outliers but those certainly are not research quants. The people who earns 7 figures salary are those who make many times that much in profit for the company. Doing research is not profit generating.

Keep that in mind when you want to do a PhD just to make that kind of salary. It's a total wrong way to do things.
My highest respect goes to people who actually finish a PhD in any discipline. I know not all PhD are created equally but the time, drive, sacrifice it takes to stick it out to the end is deserving of the highest respect.
I know some guy who took 10 years to do his Math PhD. By the end, his thesis adviser is literally ignoring his presence, his wife refuses to talk to him for his lack of progress and for not generating income in years. In addition, he is too old for any academia post doc job, or any good job for that matter.
Last I heard of him, he interviewed for some job teaching high school math and they turned him down for his lack of "class room presentation skill". Not sure if he finished his PhD by now.
This may be too dramatic to be used as an example but nonetheless, it serves as a cautionary tale in case someone wants to do PhD just because they think it will lead to huge sum of money.
 
Then do you know what it takes to obtain a job like a Goldman Sachs partner? Isn't the avg pay for a partner like 40-50 million? Do quants have any chance of getting those jobs?
 
If you are at the top Yes but this takes time, ie > 5 to 10 years.

If you are a quant that come up with a money making idea and are able to sell it, yes, you should be able to pull that amount of money.

If you can produce some multiple of that number to the firm, the firm will be extremely happy to pay you that amount.
 
Also, if you think PhD will get you there, go and do a PhD. That's only up to you. It might or might not work out but you will have to do it to find out though.
 
This post assumes, for better or worse, that you are thinking about a Math Ph.D. in an applied field rather than a theoretical one like Abstract Algebra or Geometry and Topology (applied fields can increase your marketability).

I wouldn't necessarily put numbers on one's aptitude for deciding whether or not you could successfully defend a thesis.


My personal measure on how successful one would be in completing a Math Ph.D. is based on the following:
1) Can you do Calc I,II,III? How comfortable are you with Linear Algebra, Real Analysis, and Differential Equations classes? How good were you in applied classes such as Math Econ and Statistics?
2) Is your mind creative? Were you a cookbook homework student? Or did you come up with different ways to solve problems?
3) Do you have the determination to complete a 3-5 year project? Or are you the type of person that gets bored easily and would quit?
4) Believe it or not, there is a little bit of politicking in academia as well. I've seen students fall by the wayside because they simply were not liked. These cases are few and far between, but you have to find an advisor that you can get along with and that is involved in a research area that you like.

You have to be prepared to work between 5 and 7 years on a topic with a guy you may or may not get along with. The 2-3 years you spend taking your qualifying exams can be hell. On the other hand, academia is more relaxed than other places, and the pace is generally slower. And having a doctorate of any sort opens eyes when glazing over resumes.

My dissertation was 110 pages, of which slightly more than half was review and the rest original research. I had my hand held quite a bit, but feel as though I could hold my own on my own if need be. This, again, depends on your advisor.

I'm not sure whether you are married with kids, but I have cases like the aforementioned stories were families were divided because of Ph.D. programs. Theses take lots of time and effort, and the spouse/family must be understanding and patient. The scary thing is sometimes you don't know how it will affect the family until it does. I'm a single guy, so my scope of knowledge on that topic is limited. I guess I should also mention that doctorally funded theses in math and science are paid for and provide a stipend.

I can't answer whether or not it's worth it to go through a Ph.D. program for a quant finance job. The other guys will have to answer you on that one. I'm having trouble finding a job because my research didn't directly involve finance. If you join any research type program and want to do FE, be sure your topic is directly related. Or it can be a waste. Also, if you go to graduate school, be sure to do an internship where you will get QUANT FINANCE EXPERIENCE. Trust me, I'm finding out the hard way.

It isn't necessarily all about whether you are the top 1% on board scores or the like (though I'd be worried if you aren't in the top 15% compared to the average undergraduate student). I've seen geniuses with perfect 2400 GRE's fail to complete Ph.D.'s due to lack of concentration, and people who probably couldn't make it into MIT undergrad, but were excellent researchers. It takes a basal level of intelligence to finish a Math Ph.D., but by and large, the most important factors are how hard you work, your determination, and how well you and your advisor get along (and how flexible he/she is).
 
You seem to know a fair bit, maybe you have a math PhD yourself?

Nope. Tried and failed. Lack of any real ability was one factor; others were family, lack of funds, lack of enough background to attempt a research problem, and an incompetent advisor. Hardly unique. I've known a Fields Medallist who almost didn't complete his doctorate because he was making no headway; he thought of becoming a C programmer.

One should think twice before attempting a math Ph.D. Universities are hardly hiring anyone, and when a prof retires, replace him with one or more adjuncts. The competition for jobs is fiercer than ever. And one should always keep in mind what Courant said sixty years ago: " In the future, the only mathematics that will survive wil be related to physics, biology, and economics."

If one does decide to go for the Ph.D., one should make sure to have taken a whole swathe of first-,second-, and third-year grad level courses at a major university so that one can attempt a thesis in a mainstream area of mathematics (e.g. modular forms or cohomology of groups or algebraic number theory); if one's dissertation is in some peripheral backwater area, with a dissertation title like "Virtual representations of ghost pseudo-loops," it'll be even more difficult to get an academic job, and the area itself may be a dead end. Having completed these courses (and of course having passed the qualifying exams and got through the other bureaucratic requirements), choose an advisor with care. The advisor shouldn't be some old fogey, well past his prime, who has no idea what's actually going on in the world of ideas. Nor should be some never-has-been, who, except for a handful of obscure papers, has nothing to his credit. He should ideally be a mathematician in his prime (say between 30 and 45), and more than just a narrow specialist: he should have a bird's eye view of neighboring disciplines, and have a feel for the way the whole area is developing. He should already have supervised a thesis or two so he has some idea of what a research student is capable of. He should also be able to encourage students (there are first-rank mathematicians who destroy grad students).

The dissertation itself defines the research student in the eyes of the mathematical community. Of the 20-50% of grad students who complete their Ph.D., 90-95% never do any further research. Of the minuscule percentage who do, their subsequent papers are usually related to their doctoral work. So make sure the Ph.D. is in a mainstream area.

Most dissertations are unremarkable. The exceptions would be Serre's thesis, which introduced spectral sequences (thus revolutionising algebraic topology, and earning him a Fields Medal), and Donaldson's thesis (on 4-manifolds, which revolutionised the field (until Seiberg-Witten theory came along) and earnt him not only a Fields Medal but a chair at Oxford at the age of 26).
 
I don't mean to be a post troll or anything creating multiple threads my first day, but I got the impression that even though lots of quant jobs are now available to those with a professional master's degree, the highest paying quant jobs ($1-2 mil and above) are reserved for those with the highest level of education (Ph.d). So my question is how difficult is a Ph.d in Math or Math Fin? How long do the dissertations have to be? Don't want to sound like an idiot but what percentile of the general population would you say is talented enough to go for a Ph.d, 3%? 1%? Less?

PhDs can be very frustrating... you need real determination to stick to a handful of projects and get the job done. Most people are really sick of their dissertation topics by the time they finish... My advice is to do a masters degree if possible, and if you enjoy the courses and problem sets it means you're probably capable of doing a PhD, at least in terms of intellect.
 
My Multivariable Calculus course taken at Pierce Community College in Woodland Hills is taught by a Math PhD from UCLA.

I guess the guy just loves math and likes to teach. I think he makes maybe 80K a year.

Dunno about this fascination with money. Seems to be coming from most people in college or not far from having graduated college.

In the real world, you either make things and sell things or become a small cog in a big wheel that makes things and sells things.

Not all cogs are created equally, but some cogs definitely make more money than other cogs.

If one believes they are in the top 2% or 1% they should just try to become a cog in that wheel (trying hard to become a bigger cog definitely doesn't hurt) until they can start making and selling their own thing rather than be just a cog in a wheel.

That way, one stands a far greater chance of making way more than 1 or 2 million a year, which is pretty much as good as its gonna realistically get for most cogs, if that.
 
I agree also with most of the posts here.

From my own experience (and many other that I know), you should be 110% that you love doing research in that specific field. I have started a PhD in C.S., stopped at MS in the end, because I was not convinced about research.
I enjoyed it sometimes, other times it was frustrating, overall I was not excited about doing same thing another 4 years after masters. It was a solitary research, speaking to a few people including advisor, but still a solitary work. Results were unconvincing at best a lot of times, basically you would end up with a thesis that only 5-10 other people in the world can asses the exact value. It is very specialized.

In the end, after you get the PhD, ideally you would work a similar field. This means again that you don't move away far from your academic research. If you do move away, then your specialization might not help much.
Overall, a PhD will not guarantee you a higher income then an M.S. or M.F.E. If you look at different profiles for successful traders, very few have a PhD, and they earn significantly more than a PhD research expert.
 
Overall, a PhD will not guarantee you a higher income then an M.S. or M.F.E. If you look at different profiles for successful traders, very few have a PhD, and they earn significantly more than a PhD research expert.

I think it is hard to make an argument based on "successful trader" outliers. If a PhD can come into the business at $150K, that is pretty good compared to most of the world. If that's all you ever wished for, that's one thing, and there's not a lot to discuss here. Financial jobs pay well.

But to get to the "successful trader" level of pulling in $500K+ per year, well, you need some talent and practice, which you will never learn in school (by definition). Ultimately, you need to get in the door to prove your worth; a PhD is a pretty good ticket in, although not necessarily the best risk-return.
 
Assuming following:
- you can start at $150K with a PhD
- free PhD funded by university

still PhD is not profitable only from financial perspective.
You are "losing" 4 years at least after masters. Also, in those 4 years, the person with masters, has grown in wage. Starting from 100K, in 4 years, with 10% per annum, you get around 145K.

However, these are just details. The baseline is that PhD is not something to pursue only for financial reasons.
 
I'm with the people who sensibly point out that a PhD as a purely finance career move sucks.

Yes, there is on average higher lifetime earnings, even allowing for the lost earnings years.

In my guide I go on at length about using your math and finance skills to model how to run your life. This greater return is clearly at the expense of greater risk expressed as variance of outcome.

That variance does include "outliers" of people who make extreme returns from this investment.
It also includes a larger outlier group who make negative returns.

Another risk term is that you are trying to model the finance markets 5 years in the future. If you're that smart then you don't need a PhD, just some henchmen and a hollowed out vocano for your gang to take over the world.

Of course the risk term is complex since any relevant education gives you options that help you survive the screwups that are inevitable in any career that's 30-50 years long. Failure to maintain and upgrade your skills is a common reason for your career being rather shorter.
 
As someone who is flirting 50-50 with the ideas of trying to head out and get something finance-programming-ish, versus going on to do a quantitative finance/maths phd, I am curious.

My main question is: Who here actually has a phd, and, I think more interestingly, who enjoyed it and or/would recommend the experience?

I ask this just as much in regards to the "chance to study and get a solid quantitative skillset" as I do "purely as a job-prospect-enhancement".

I've several years of programming experience, am a couple months off finishing a Masters of Science in Financial Mathematics, and I see lots of other people on this forum seem to be heading down the Masters route, presumably largely purely for the implied career benefits. The thing is, if I am going to sign up for another 3+ years of study, I'm just as interested in how those three years will be. I find the research element of my masters both frustrating and thoroughly enjoyable, but I don't want to complete a phd "just to show employers that I can finish something", which is a rather scary quote I keep coming across..

So, first-hand experiences/witty anecdotes/furious venting of phd-related fustrations anyone?
 
I'm thinking about a PhD too. From a $$$ perspective it doesn't make sense, but it's just something I want to do.

You only live once, so make the most of it.
 
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