It has been 15 years since I left math school for the wider world.
Though I have never been asked to integrate by parts, my decision to study math at the university level has been a useful one.
The idea of studying math after high school was not a longstanding dream when I chose to apply.
In my mind’s eye, I could see working in “business” but did not know what that meant in the short-term. A well-timed conversation with my guidance counsellor put math on my radar and it proved to be fortuitous.
For those people supporting students at the post-secondary level or thinking of continuing their own education, here are some surprising lessons you might find by studying math.
Practicing first-principles thinking
In math, one concept leads to another.
For example, multiplication and division are just abstractions of addition and subtraction, and subtraction is just addition with negative numbers.
Even those gnarly math equations full of greek symbols and foreign notations can be traced back to this reality.
A well-trained mind might intuit how to approach a problem, but you could always try another approach by reconfiguring it into something more familiar.
In my first "real" job, I joined a startup in an industry that did not exist at the start of my university studies. First principles thinking helped me understand where to be useful by understanding the nature of the game we were playing.
Whenever I'm met with a novel situation, I tend to figure out what the structure of the problem is and its component parts. That always helps.
Elon Musk is a proponent of this type of thinking and he has used it to disrupt entire industries.
Acknowledging the limit of reason
I suspect that many who are drawn to study math are looking for ultimate truths in their lives.
In my teenage years, I reduced the role of emotionality when rationality existed - it didn't make sense to use something subjective when objectivity was available.
Years after my graduation, I bumped into a masters of math who shared the same early desire and told me that even after studying and researching in the field for many years longer than had I committed, she hit a wall in discerning useful truths for life.
Over time, you come to realise that you have described a conveniently contrived space well though its applicability with humans and other natural systems is limited.
It is obvious to me now that we are an emotional lot and my pursuit of rationality in my teenage years sprung from my emotions at that time.
Perhaps this is why if you didn't know that Albert Einstein was a transformational physicist you might think he was a profound philosopher. Even he could not enroll reality into models that were broad and all-encompassing.
Relishing hard problems together
Math finals were no joke, and of course, the instructors would not make it easy.
The weight of a final exam on the course grade was 70-80%!
In 3 hours, you could either come out a hero or fail the course because your preparation was ill-suited to the challenge. These were high stakes games.
For weeks leading up to finals, my peers and I would go through the mental gymnastics of trying to project the coverage of the final while reminding ourselves of everything we had covered to that point.
This type of training has proven to be useful for the real world. After you’ve had your mind bludgeoned for a few years with what seem like impossible problems, all real-world situations shrink in relation.
It also helps to work with the smartest people you know who share an interest in growing together.
One final note:
Don't believe the tropes about how eccentric mathematicians are - life has taught me that there are delightful weirdos in all fields :)