answered on 3 Jul 2020:
last edited 3 Jul 2020 12:29 pm
To do great maths you have to be highly creative and also determined. Above all never give up when you get stuck. It is by persevering that you end up learning loads more. But did I mention that you should be really really creative : )
I agree with Chris Budd. The late John Conway once told me to pursue a problem to the point where any reasonable person would give up — then keep going! Another characteristic you need to develop is honest self-criticism.
For a student of maths, which is anyone doing maths really … we’re all still learning, one of the most important things is not to be discouraged by getting a question wrong. We all get things wrong, but if we don’t give up, we can learn something from that mistake.
I think you need some determination, and the ability to think logically, with the option to occasionally think ‘outside the box’. I am a Chartered Loss Adjuster, so not a pure mathematician, but maths, technology and science come into use every day in the job of determining liability for an insurance claim.
There are already many terrific answers here, so I can only further confirm what has already been said. Here are some characteristics that I think are important, in no particular order:
1. Technical expertise: Maths is very much an acquired skill, and you do have to develop this skill in order to use it. This is similar to how a professional musician or a professional footballer would have to hone their craft before they can do what they do.
2. Determination/effort: Many problems in maths are very challenging, and there is no substitute for the time and effort needed to tackle these problems. Similarly, you need a fair amount of grit to get past the “bad days”, when things are not going your way or you are stuck on a problem.
3. Creativity: People often think of maths as this purely technical or analytic discipline, opposite to “creative” fields in the humanities, but this could not be further from the truth. Solving complex mathematical problems often requires quite a bit of creativity and ingenuity – it’s just that you need technical knowledge on top of that as well!