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[PureMath]

Hi guys,

I am a PhD student in Pure Mathematics without a strong background in Probability and no specific knowledge on finance so far.
My university is not ranked in the top 5 in the UK, but it is in the top 10.

Since I got my Master's and my Bachelor's in Italy, I am aware that I can actually get a first class in most of the UK's university course units on Finance, provided I have at least 2 weeks to prepare each one. Unfortunatelly, I plan to do an internship on summer 2022 and I have no time to become as competitive as a Master's student on Finance. I am also aware that not many people trust our transferrability of skills and therefore I cannot use the argument I expressed a few lines above.

Do you have any suggestion? Do you know if there are companies in UK or EU famous for recruiting Pure Mathematicians? (Of course, if they ask me if I know Machine Learning I would answer "no". But I know C++ and I can solve most of the standard questions on probability).

 

[PureMath]

To be more specific, I wish to ask a weird question. Do you have a list of not-very-selective hedge funds? I think I need to start with something where I can compete. I do not want to apply for 10 companies each one as selective as Jane Street. Feel free to send PVTs, if a public thread is not the right place to mention those firms.

 

[CrossGamma]

A master degree in "Finance" would not be very helpful if you aim for a quant career. It gives you some basic background about markets and instruments but very little would be directly applicable to hedge funds or trading firms. With a Ph.D. in pure maths, you would likely be considered for many quant positions. Especially on the buy side, where quant roles are not purely about pricing, typically no explicit finance background is expected and the necessary basics are taught in-house as part of the onboarding. I would rather focus on brushing up on probability and coding (algorithms, data structures, ...) to be more competitive in interviews. Applying for a few places and going through their process will give you a better idea of what skills you should focus on improving.

 

[Daniel Duffy]

what's 'pure mathematics'? e.g. Lie Algebras, Group Theoty or a wee bit more applied?

Out of curiosity

1. How many pure mathemagicians can program in C++?
2. Can pure mathemagicians make the transition to algorithm?

The "software" you learn in university is nothing like what you need later on...

 

[PureMath]

Thank you for your replies.
@CrossGamma do you know if I can try to apply again in the next years? I can solve problems of Probability at Math Olympiad's level (not IMO 3,5,6, of course, especially because it is not a common subject there) but I totaly lack of non-elementary knowledge.

@Daniel Duffy Lie Algebras (and not in characteristic 0 ). Wow, usually the non-applied gold standard is Algebraic Geometry, but this time the first attempt is the right one.
Our programming language depends on our background, in particular on how nerdy we were at High School and on what they taught us in the Bachelor's. I would say that C++ is one of the most common among mathemagicians.
I think I can learn algorithms in a few months (after my PhD, I will), but cannot really reach a competitive level. In the past I learnt some standard patterns from the Informatics Olympiad, but I need to admit I was not fast enough. I can solve combinatorial problems, even some marked as "Hard", but I'm not a sprinter! I also believe that the need of speed is a bit misleading because people who spent months or years in studying those kind of problems can easily notice that the patterns are always the same and it provides a huge specific-advantage. It's like a bias.

 

[CrossGamma]

Apply again where? I am missing some context here. Most companies accept re-applications after a year.

 

[PureMath]

Apply again where? I am missing some context here. Most companies accept re-applications after a year.

Thanks.

Do you know where I can find some less selective companies?
I read this nice article How To Get A Quant Job Once You Have A PhD | QuantStart
...and wish to know where the smaller funds are.

I think I can only find very competitive funds through LinkedIn & co.


____
Btw, if it is really a matter of Math Olympiad, I won a silver medal at italian math olympiad and could arguably compete for a gold medal that year (as I ranked top 25 at some Italian selection stages for international competitions). But... If the author of the article refers to IMO then it's a completely different story. I will never be able to outrun an IMOist...

 

[Daniel Duffy]

Thank you for your replies.
@CrossGamma do you know if I can try to apply again in the next years? I can solve problems of Probability at Math Olympiad's level (not IMO 3,5,6, of course, especially because it is not a common subject there) but I totaly lack of non-elementary knowledge.

@Daniel Duffy Lie Algebras (and not in characteristic 0 ). Wow, usually the non-applied gold standard is Algebraic Geometry, but this time the first attempt is the right one.
Our programming language depends on our background, in particular on how nerdy we were at High School and on what they taught us in the Bachelor's. I would say that C++ is one of the most common among mathemagicians.
I think I can learn algorithms in a few months (after my PhD, I will), but cannot really reach a competitive level. In the past I learnt some standard patterns from the Informatics Olympiad, but I need to admit I was not fast enough. I can solve combinatorial problems, even some marked as "Hard", but I'm not a sprinter! I also believe that the need of speed is a bit misleading because people who spent months or years in studying those kind of problems can easily notice that the patterns are always the same and it provides a huge specific-advantage. It's like a bias.

Are the Olympiads mostly discrete maths/CS stuff?
Many algos work in continuous space. e.g. PDE, SDE

Just a random sample

Online Courses :: Datasim

www.datasim.nl

Random example: 'pure' maths with applications

Banach fixed-point theorem - Wikipedia

en.wikipedia.org

 

[PureMath]

Are the Olympiads mostly discrete maths/CS stuff?
Many algos work in continuous space. e.g. PDE, SDE

Just a random sample

Online Courses :: Datasim

www.datasim.nl

Yes, unfortunately they are very discrete.

 

[Daniel Duffy]

Yes, unfortunately they are very discrete.

I suppose many people are more comfortable with linear algebra than with Cauchy sequences and real/functional analysis.
This state of affairs is prevalent in current mainstream ML.

 

[PureMath]

I studied a lot of real and functional analysis in my Bachelor's, but cannot directly apply it to other fields.

 

[Daniel Duffy]

I studied a lot of real and functional analysis in my Bachelor's, but cannot directly apply it to other fields.

My favourite subject was FA. It has _many_ applications

. Numerical analysis A-Z
. Finite Element Method (FEM) with Sobolev Spaces etc.
. New advances in ML w.g. RKHS

Reproducing kernel Hilbert space - Wikipedia

en.wikipedia.org

 

[PureMath]

Another question. Do you know how much they care about the result of tests like "Numerical reasoning", "Inductive reasoning", "Verbal reasoning" and similar?
Sometimes I get high results, other times I am just like the comparison group. The reason seems to be that I am not fast enough. Most of those tasks are just a matter of speed, rather than an actual "reasoning".

 

[Daniel Duffy]

Another question. Do you know how much they care about the result of tests like "Numerical reasoning", "Inductive reasoning", "Verbal reasoning" and similar?
Sometimes I get high results, other times I am just like the comparison group. The reason seems to be that I am not fast enough. Most of those tasks are just a matter of speed, rather than an actual "reasoning".

Who is 'they'?

 

[PureMath]

Recruiters, Hiring Team...

_____
(The first question is still open. Where are the less-selective funds?)

 

[PureMath]

Today I got a rejection from IMC because I did not perform well enough in his neurolympics game.
That test was 100% speed+accuracy, 0% creativity and 0% mathematics. To be honest, it looks like a test for Formula 1 pilots rather than a test to select the smartest scientists. Is it possible that my mental speed has always been enough to conduct academic research and to get a full-score on almost all my exams, but suddenly not enough to be a trader?
There is something that I really need to understand. Am I the only one in this forum that is experiencing what I described?

Please, don't be shy, take part in this thread if you have something to add.

I'm also applying for banks and, so far, I have had the feelings that they are much more open-minded compared to hedge funds. They try to evaluate all kinds of abilities, not just "mental speed". Did you have the same feeling?

 

[CrossGamma]

You probably applied at IMC as an option trader as opposed to a quantitative researcher. This process for this role (and to a lesser degree even the quantitative researcher role) is indeed not about finding “the smartest scientists”. While the systems of companies like IMC and Optiver are highly automated, the trader roles still involve a decent amount of operations and human decision making. In particular these types of tests are trying to assess your ability to make quick decisions under uncertainty, adapt to changing situations, ability to memorize large amounts of information as it is presented to you, mental maths, statistical intuition, … Optiver for example is famous for having a fairly hard mental maths test as one of their first early round filters. Later rounds would focus on assessing your maths and probability skills through some puzzles and trading games. Even there a focus would still be on speed, intuition and pragmatism - e.g. are you able to make reasonable estimates when appropriate instead of formally working through a difficult problem.

And yes - being the best mathematician does not necessarily (I would even say typically not) translate into being the best trader. In trading it is often not about finding the best or theoretically neatest solution to a problem but finding something that gets you 90% there and you monetize on it while the opportunity exists. Many theoreticians can find this unsatisfactory.

I see “finite difference methods” and “C++” mentioned here a lot as core skills for quants. While this is maybe still true for quants working on pricing libraries, the vast majority of buy side quants even at options trading firms will not work on the options pricer itself but focus more on market making algorithms, signal analysis, predictions, … While the production implementation is often in C++ and written by developers, prototyping is typically done in Python.

 

[Daniel Duffy]

While the production implementation is often in C++ and written by developers, prototyping is typically done in Python.

Each organisation is different but some scenarios are (let's take a pricing library)

A
Quant 1 creates prototype in Python
Quant 2 creates production version in C++

B
Quant 1 creates prototype in Python
Quant 2 creates production version in C++

C
Quant 1 creates prototype in "no-frills" C/C++ (get it working)
Quant 2 creates production version in C++

Scenario C is optimal when Quant 1 == Quant 2 and less mismatch. Due to real life, I suspect scenario is usual when Quant 1 != Quant 2

A production pricing library in Python is a non-starter IMHO, It would probable be a a maintenance nightmare, not to mention performance and reliability of code.

People code in Python but more accurately they write scripts (nothing wrong with that!) that use Python libraries with C++ and Fortran inside.

At some stage, what do you do if you find that a TensorFlow library doesn't work in your application? You will need a guy or gal who knows C++, numerics and C++<->Python interfacing.

//

Don't put all your eggs in one basket.
Don't throw out baby with the bath water.

​

 

[CrossGamma]

While the production implementation is often in C++ and written by developers, prototyping is typically done in Python.

Each organisation is different but some scenarios are (let's take a pricing library)

A
Quant 1 creates prototype in Python
Quant 2 creates production version in C++

B
Quant 1 creates prototype in Python
Quant 2 creates production version in C++

C
Quant 1 creates prototype in "no-frills" C/C++ (get it working)
Quant 2 creates production version in C++

Scenario C is optimal when Quant 1 == Quant 2 and less mismatch. Due to real life, I suspect scenario is usual when Quant 1 != Quant 2

A production pricing library in Python is a non-starter IMHO, It would probable be a a maintenance nightmare, not to mention performance and reliability of code.

People code in Python but more accurately they write scripts (nothing wrong with that!) that use Python libraries with C++ and Fortran inside.

At some stage, what do you do if you find that a TensorFlow library doesn't work in your application? You will need a guy or gal who knows C++, numerics and C++<->Python interfacing.

Again, you are very focused on pricing which is these days not the main focus of front many office quants even in the options space. The section you are quoting is referring to the tasks other than pricing which are mentioned in the sentence before. And yes, pricing libraries are still typically in C++ - I have not claimed anything different.

 

[Daniel Duffy]

Again, you are very focused on pricing which is these days not the main focus of front many office quants even in the options space. The section you are quoting is referring to the tasks other than pricing which are mentioned in the sentence before. And yes, pricing libraries are still typically in C++ - I have not claimed anything different.

Yes, I know.
From a career viewpoint, knowing just Python may not be enough; it is a very useful tool, like Matlab. C++ is a skill and will be here forever.
If you know C++ you can get the hang of Python in a few weeks, but not the other way around.
Just saying.