Giovanna Villani. Maths in real life

21-03-2023 09:09

Last week, we had the pleasure of speaking with Giovanna Villani, a quantitative analyst in banking with over 15 years of experience in modeling and implementing mathematical models for market instruments. Giovanna has a degree in Pure Mathematics, specialising in Mathematical Finance from the Università degli Studi di Padova in Italy and a Master's degree in Mathematics for Financial Instruments from the UAB Universitat Autónoma de Barcelona. She currently works at CaixaBank and is a member of the control commission for the CaixaBank employees' pension plan.

 

Second year Baccalaureate and International Baccalaureate students had the opportunity to talk to Giovanna during Maths Week and ask her questions about her studies, her experience in the world of mathematics, and how they apply in general and in the financial sector. Giovanna kindly answered all the doubts and questions that the students raised during this series of transcribed questions. Let's begin!

 

Would you say that mathematics is even more important today than it was 20 years ago due to advances in technology?

I don't think that mathematics is more important now than before; it has always been important. However, we are at an evolutionary moment focused on technology, and some aspects of mathematics, such as big data, optimisation algorithms, prediction algorithms, and computational mathematics in general, are very important.

 

How does mathematics intersect with other fields, such as engineering, technology, or in your case finance, and why is it important to have a solid foundation in mathematics to succeed in these fields?

Mathematics does not relate to engineering, finance, or computer science; it the basis upon which these disciplines are built. Without mathematics, none of these disciplines would exist. Even human language would not exist without mathematics, as it depends on logic, which is mathematics. Therefore, it can be said that mathematics is fundamental to understanding these disciplines rather than simply interacting with them. It's like when we analyse the grammar of a sentence - without logic, it would be impossible to do so. This is the importance of having a broad mathematical knowledge to understand how various aspects of life work.

 

And does the mathematics studied at university by researchers include pure mathematics, which is very abstract and not necessarily programming-based?

In the mathematics programme, there are exams in computer science (programming). They were included 20 years ago, and they are even more important now, both in mathematics and in any other scientific career. Additionally, many university jobs include a part of computational development of the abstract work done. This also applies to research jobs.

 

On the contrary, is the mathematics used in companies mainly related to programming? Is this the case?

From my experience, programming in jobs is a tool for the practical implementation of the previous mathematical study that has been done. That is, first, a mathematical model is thought out and developed, and then it is implemented so that people can use it. There are companies in which the roles of model development and implementation are separated into different departments and companies in which the same people perform both jobs. Personally, I prefer to implement the models that I develop since someone who has not developed the model may not understand it in depth and implement it incorrectly, unoptimised, slow, or incomplete. It is always more valued from the employer's point of view to have a complete education and to be able to develop the model from start to finish.

 

I imagine that the mathematics used by companies is mainly used for testing purposes (for example, calculations in engineering) or modeling, used for making predictions, such as with COVID, or big data analysis. Are there other applications? Can you tell us about some of them?

Cryptography for security (focused on computing but uses very abstract algorithms based on algebra), logistics, i.e. optimisation of routes, transportation, spaces, etc. (graph theory and discrete mathematics, i.e. focused on integers since it is not the same to transport 10 people as it is to transport 11, and the algorithms are much more complex). Big data is used for many applications, such as image recognition (AI, when the iPhone unlocks because it sees your face), and in general, applications of machine learning, which is how the computer accumulates information to then "learn" from it, with very complicated algorithms and still in the development phase today (a very popular branch in terms of research mathematics).

 

Are there many job opportunities?

Yes, graduates in mathematics are highly sought after. Although they do not have specific training, companies know that they possess strategic ability, a lot of logical reasoning, adaptability, and learning ability. According to statistics, almost all mathematics graduates obtain stable employment within three years of graduation.

 

What are the career paths?

In addition to teaching and advanced university research (PhDs), the most frequent job opportunities are found in financial institutions, insurance companies, general computing, big data (AI), and consulting.

 

What are the mathematical areas used most when studying Artificial Intelligence?

The algorithms used in AI require knowledge from a wide range of mathematical areas, such as calculus (integrals, limits, etc), probability, and linear algebra (matrices and their properties).

 

When studying Artificial Intelligence, do you typically work with practical applications or is it all theory without any practice?

I can't speak from personal experience about a Master's degree in AI, but the course I took a few years ago was quite abstract, although some real-world application examples were provided. The theory of AI is complex, which is why AI experts are in high demand.

 

What is your favorite maths problem?

My favorite math problem is the problem of the 5 pirates and the 100 coins. Here's a link if you want to look it up: https://www.psicoactiva.com/puzzleclopedia/el-tesoro-de-los-piratas/. It involves some very ruthless pirates who prefer to throw a crewmate overboard if they have the opportunity to get another proposal in which they obtain the same number of coins. I like it because it was given to me by my boss in a job interview, and he was given it by his boss in a job interview. All three of us, being mathematicians, ended up publishing a research article in mathematical finance together.