I have a bachelors degree in mathematics from the Technical University of Munich. Which on the one hand I am very proud of, but probably not for the reasons you might imagine.
I’m proud of it, because it was not easy for me to go through it. In university mathematics you are either really good at structural logical thinking, which will definitely reward you with good grades – without you needing to put a lot of effort in it! Or, well, you hustle just to stay afloat.
But I would probably still do it again, why? Well mathematics in university is really not that useful in the sense that outside of academia or insurance. You might find practical use once coupled with biology, informatics, physics, or other fields, but then you’re moving mostly away from mathematics…
Mostly mathematics is about proving things in the highly theoretical setup, so for example is a + b = b + a? Is that correct always? Hint: see Wikipedia for group theory or algebra… If you’re thinking numbers only, you’re thinking not broad enough!
So you’re trying to prove stuff, how does this work… Well you have to start somewhere, right? So you find yourself axioms, which are the fundaments on which you can build everything else. Having these fundamentals you can then use them to start prove new things. Basically everything is routed in those axioms. If you’re now thinking, how do I know that I have enough or whether some of them are exchangeable, then you’re already thinking in the right direction (trait: always ask for the limits!)
Mathematicians have a few traits that I find very useful in the business context:
Find the most elegant & broadest solution
When you’re trying to prove a theorem, you could just give an example of how it will work in this specific case, for instance I can prove that two times two is always greater that two. Can I broaden that theorem? Is two times x always bigger than x? Well, not really if x goes negative my prove goes south.
Also when proving something mathematicians value elegance and simplicity. This is so prevalent that I got minus points for taking a too complicated route!
It’s always the argument that counts
In most negotiation books you will read, separate the person from the problem / topic. As in mathematics the argument is on something so theoretical, it does not matter who you are or what your status is, even a first semester can show a professor a mistake or a more elegant solution, both unlikely, but possible. Also the professor can’t say, oh this is up for interpretation – there is no wiggle room in mathematics. Black or white.
Also as arguments are highly logical, the challenge comes in, how many steps does the professor undertake to make his argument / prove. And a sign of a very good mathematician is that he/she can follow along an argument where the other side only gives the broad picture / main arguments.
Always check the premise!
In my first semester most professors would make jokes about mechanical engineers or economists that they always use mathematical concepts without understanding them and the most common example were where people in other fields used mathematical models where the promise is not met. So if you can use a prove or model only for numbers greater than zero, but it was used for the whole spectrum of numbers, then that would definitely make the model return unintended consequences.
That’s actually so true also in business, everyone is talking about hypotheses and proving them, well every hypotheses has to have premises! And you have to be aware of them and really watch whether the premise of your hypotheses has changed! This night change so many things down the road, and your hypotheses is oftentimes completely useless once a premsis has changed!
Don’t be afraid to ask until you really understand
What I learned really late was that all really good mathematicians were asking ten times more questions than I did. It’s really simple, if you don’t understand something, ask. If you find something not making sense to you, ask. But be prepared, as the most shaming answer is, we talked about exactly that in the last lecture!
Again like in business, i find to many people either think they understand it or don’t understand something but don’t bother to ask. And the funny thing is, of course I can tell if someone hasn’t got it! You cannot pretend to understand something as one follow up question will reveal yourself, if your body language has not already! Also in business, a lot of people are happy with a pseudo answer, which does not really answer the question.. A second question would be so useful here, but most people will be happy to have asked one question and not bother really understanding the matter.
Trust your instinct!
This one might come as a surprise, but mathematicians use their gut feeling and instincts all the time. When searching for a prove your first instinct is usually correct and you always dig in the direction that your instinct goes. As you can’t know beforehand whether your way is the correct one, mathematicians while proving theorems are working under extreme uncertainty, which is not different than in business. I have my premises, a few hypotheses, and have to then follow my instincts, as the right way will only be visible after I have found and went that way. There always might be a better / shorter way… When I don’t succeed, I also don’t know what to blame! Mostly in business, when something fails, everybody blaims external factors and if something successe, it’s internal!
Bonus: remember the broad concept, don’t sweat the details
There are basic concepts in mathematics that should be engraved on your head after six semesters of doing maths, but none are really necessary as remembering stuff is so complicated versus just re-proving a theorem, that you’re almost always better off to prove something than remember the details!
Hope this helps to understand why I would study mathematics again, but would not seek a job where I really have to use mathematics. It’s all about the concepts and the tools, not about the exact treatment…