What’s the difference between an introverted mathematician and an extroverted mathematician? The extrovert looks at the other person’s shoes. You probably have heard this joke (very funny) many times and might believe that mathematicians work stuck in their offices (and their own heads). It was probably true a couple of centuries ago. However, things have changed after the rapid development of maths, especially applied maths. Why?

Nowadays we have to specialise, at least a little bit. We don’t have Da Vinci’s any more; it’s just impossible to fully understand more than your very narrow area. But while mathematics research narrows more and more, it tries to tackle more and more complex and multidisciplinary problems. What do we do now?!

We, as mathematicians, must get out of our comfort zones and collaborate. We need to accept our lack of understanding of certain aspects of each maths problem while, at the same time, being aware of how we can contribute to the solution. We have to identify what kind of experts we need to ask for help to make some progress. This is how it all begins.

When I started my adventure in maths, I certainly didn’t anticipate this. I was prepared for working alone and talking to colleagues only in my free time. While it could possibly work in pure maths, I would totally fail to succeed in applied fields if I tried to do so.

Examples? Mathematics of Planet Earth Centre for Doctoral Training! Yes, we pursue our individual degrees and work on our own projects. However, we operate as a cohort too. Sharing experience, tips and asking for help are essential for this programme to exist. I can’t even count how many times computer science experts saved my life (or at least my precious laptop) by preventing me from running a code that would destroy the system^{1} . In exchange I could give them a hand when they got lost in abstract multidimensional spaces (although I don’t claim I can visualise anything in more than three dimensions, though it disappoints my first year lecturer!). We all learn from one another.

Recently I realised that it’s not just a fake academic set-up, this is how the “real world mathematics“ works. I spent 5 days at the 116th European Study Group with Industry in Durham, UK (http://www.esgi.org.uk/). This event brought together about hundred mathematicians, physicists and industrial partners. The latter proposed eight problems they wanted to solve in fields as diverse as agriculture, banking and sepsis diagnosis. We divided ourselves into groups according to our interests — I chose the problem proposed by a digital bank. They needed help with marketing their product to the best target audience (of course the ultimate goal was to spend less and earn more). We sat down in a room and…well, and started thinking, talking, brainstorming and arguing. Within 3 days we managed to produce whole models and get some useful results for the industrial partners. Something infeasible for one genius became a reality for a group of people with different backgrounds.

Yes, you might still meet a mathematician staring at her/his own shoes while talking (or avoiding any contact) to you. But this is not a norm anymore. And definitely not the only way to succeed. We can tackle real world problems together because together impossible becomes possible!