a small advice
This is for mathematics students who want to delve into a more applied field such as physics, biology or economics:
There is no doubt that you will encounter new sorts of mathematics. Learning these will not be a great challenge for you. The real challenge will be adjusting to the way the practitioners think in their respective fields, the way they reason while they are not scribbling down mathematical equations. Ideas are put into mathematically precise forms only after they are formulated in some intuitive sense. Published papers are very polished versions of a lot of messy thinking.
Being able to generate interesting hypotheses in these fields requires a lot of non-mathematical experience. That is why the transition will be tremendously enriching for you.
There is no doubt that you will encounter new sorts of mathematics. Learning these will not be a great challenge for you. The real challenge will be adjusting to the way the practitioners think in their respective fields, the way they reason while they are not scribbling down mathematical equations. Ideas are put into mathematically precise forms only after they are formulated in some intuitive sense. Published papers are very polished versions of a lot of messy thinking.
Being able to generate interesting hypotheses in these fields requires a lot of non-mathematical experience. That is why the transition will be tremendously enriching for you.
