Pure mathematics or applied mathematics?

Which do you think? If someone were to encourage you to take a university class, which would you choose? Which category takes more shelf space in your bookcase? Tell us your favourite!

  • Pure mathematics
  • Applied mathematics

0 voters


I think applied is better as it allows you to create formulae which will be used or help people in the real world

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It depends on the subject matter in the modules, how engaging the tutoring is and how much additional reading you are prepared to do around the subject.

If you enjoy abstract ideas, convergent and divergent series and love the axioms of algebra, set theory (and then having to prove the theory for n+1) then Pure mathematics may be for you.

If you enjoy at calculus and integration, vector calculus, chaos theory and hydrodynamics then Applied may be for you. (Along with a copy of Erwin Kreyzig’s Advanced Engineering Mathematics)

Although if it’s university and you’re playing the system, then go for the one where you get higher grades (Statistics!).

The question immediately reminded me of Hardy’s 1952 “A Course of Pure Mathematics”, a wonderful and timeless work.

I learned to love so-called pure mathematics when I realised how useful and downright poetic it can be. Useful? Wouldn’t it then be applied mathematics?

A very simple example. In the study of natural sciences (i.e., everything that does not concern the humanities, for example, various engineering sciences), it is not uncommon for students to underline complex variables and complex functions or to somehow embellish vectors. Those who have understood complex numbers and their field quickly question why this is necessary. Also, an engineer’s answer to the question of what a vector is is often: something with a direction and length. What would a mathematician answer: A vector is an element of a vector space. :wink:

In one book, the author started writing in his dedication about the monument in honour of Hamilton: He had noticed that there was a crack between the words “a mathematician and engineer” and he would like to mend this crack with this book. I hope for that too. :slight_smile:

Pure mathematics relates to the world like ancient Greek and Latin to language comprehension: it can help to understand and contextualise things and provides a wonderful foundation. However, learning the foundation should, in my opinion, only take place once the applications on it have been understood. Isn’t it?


still trying to work out what is going on here. Please can you try and tell…

I just thought it might spark some fun interesting comments, some community engagement, to give a topic of discussion. I like pure mathematics, abstract stuff. Others prefer applied mathematics, solving problems related to the real world. The difference in perspective can make for fun conversation, insights, maybe a greater appreciation for mathematics as a whole.

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I have to admit I do like the theoretical side of things, as thinking like that using thought experiments can allow you to connect out of the box stuff to real world application.

I think applied is still the one for me, as I like to see things work for me and others

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stochastic processes… usually called probability/pre calc… all you need

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I personally love learning math as a tool for the things I do and create, so I’d have to pick applied mathematics.

However, I have a friend who’s absolutely enthralled with pure mathematics as he’s described it has kind of looking into the future of what will be applied mathematics. I love the idea that it’s finding solutions to problems we don’t even know we have yet.

It’s very fitting for my friend as he loves to be very prepared for everything he does!

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For me, pure mathematics. I could solve problems in applied mathematics, and get a result which was the answer predicted by this model… which ignored friction. And I could do a problem and get a result from a model… which ignored losses due to heat. And I could do a problem and get a result from a model, which ignored - oh, what, radioactive decay. And while I could appreciate that such errors as these models might have, relative to reality, are orders of magnitude smaller than what’s lost in the noise with regards any physical measurements, it always felt just the littlest bit… unclean. So, instead of working with models ‘close enough’ to a reality you really want to measure or predict, for as fuzzy as that phrase is, the perfectionist intellectual part of me likes that in pure math, the model isn’t pretending to be anything other than what the model is.