The clearest change of emphasis in mathematics at university is in the need to prove things. Much mathematics is too abstract or technical to simply rely on intuition, and so it is important that you can write clear and irrefutable arguments, which make plain to you, and others, the soundness of your claims. This ability to think logically and argue your thoughts clearly is incredibly valuable, both in mathematics and in the wider world.
Mathematicians usually work in either pure or applied maths (although recent advances mean that even traditionally pure areas of maths are seeing applications in medical imaging, art history, and e-commerce). An academic mathematician will be part of a research group (as your tutors will be when you're an undergraduate). These groups can be very specific (e.g. Analytic Topology) or inter-disciplinary (e.g. Mathematical Geosciences) and provide an opportunity to discuss your research with other researchers in your field. To become an academic students will typically study to undergraduate and Master's level, before doing a PhD in a mathematical area. Around 30% of our undergraduates go onto further study (including Master's and PhD programmes).
However, the majority of mathematics students don't go on to become academics. You can find out more in our careers section.
To find out more about the research going on in the Mathematical Institute why not take a look at the Oxford Mathematics Alphabet? Each letter is a short post written by one of our academicson a topic that they're researching and comes with links to further reading and a poster for you to print out.