I believe a lot of people graduate mathematics thinking that if what they are doing isn't at least as hard as third year undergraduate maths then it isn't 'real' maths and, by extension, while they did maths at university, they aren't now a mathematician. Even when what they are doing for a living is mathematical, it's just not cutting edge research.
The categories are listed below and full descriptions are given in the Science Council paper "10 types of scientist – science jobs are not all the same":
- Explorer
- Investigator
- Developer/Translational
- Service provider/operational
- Monitor/regulator
- Entrepreneur
- Communicator
- Teacher
- Business/Marketing
- Policy maker







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