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Question: Does work in maths follow a method like the scientific method?
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Chris Budd answered on 16 Jun 2020:
Often it does, but with a twist. Creative maths often follows the following approach
1. Do lots of experiments (say on a pice of paper or on a computer)
2. Try to spot a pattern (maths is all about patterns)
3. Make a hypotheses
4. Test your hypotheses to make sure that it works on the cases you have looked at and any other new cases that you can find
… and now here is the twist which makes maths different
5. PROVE your hypothesis always works every time.
It is step 5 which makes maths different from the scientific method.

Liam Brown answered on 16 Jun 2020: last edited 16 Jun 2020 8:03 am
For me, it’s exactly the same, because I use maths and science together (we call this “applied maths”). I’m interested in cancer, so I can do the following:
1. Make a hypothesis, like that blood flow to cancer is important for treating it.
2. Write down mathematical equations that describe the blood, cancer and our treatment.
3. Test the equations, on paper or with a computer.
4. Observe the results and see if they make sense with what we see in the world.
5. If needed, modify the equations and go back to 3.
6. Make a conclusion. 
Katy Tant answered on 16 Jun 2020:
Although the steps we take can be similar (see Liam and Chris’s answers) the main difference between maths and other sciences is that mathematical theorems are absolute! They cannot be disproven. Which is pretty amazing…. there aren’t many things in life which are certainties!

Tina Zhou answered on 16 Jun 2020:
Maths is the foundation of science, so you do have different types of methods, especially in applied maths for industry modeling. I believe that in modeling, you need to follow many different methods which will need to depend on the problem you want to solve.

Arick Shao answered on 18 Jun 2020:
Yes, it does! Just as there is a “scientific method” for determining what are scientific facts, there is also a “mathematical method” for determining what are mathematical facts – namely, proofs! While a scientific claim is not credible until it has been confirmed through experiments, a mathematical claim is not credible until it has been proven.
In short, a proof is a formal logical argument, in which one begins with some assumptions (the hypotheses) and deduces some from them some conclusions. As a simple example, you might assume that x and y are even numbers, and then argue that x + y is also an even number. Of course, many interesting proofs are far more complicated and require a lot of skill and creativity to carry out.
To be more concrete, proofs are, in a way, like classic murder mysteries. You are given some evidence (the assumptions), and you have to use logical reasoning to figure out who the killer is (the conclusion).
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