As Paul Karl Feyerabend, science philosopher, in his brilliant book Against Method critisized the existence of scientific method in an anarchic way, I believe that there is nothing called scientific method and therefore one can claim that even if by chance the science has been useful up to now, there is no way to introduce some methods to produce new useful results.
However, classical economics texts shows that some economists believe so, when facing results in mathematical finance. "But I know I had a growing feeling in the later years of my work on the subject that a good mathematical theorem dealing with economic hypothesis is very unlikely to be good economics, and I went more and more on the rules:
1- use mathematics as a shorthand language rather than as an engine of enquiry,
2- keep to them till you are done,
3- translation into english,
4- then illustrate by the examples that are important for the real life,
5- burn the mathematics,
6- if you are not succeed in 4, burn 3.
This last I did often." said once Alfred Marshal.
In my home country, Iran, almost all of the economists tout the importance of mathematics while at the same time insists on the role of mathematics only as a language for economics.
However, if we analyze the creation of mathematical finance, neither of the following steps came true. Paul Samuelson, suggested Geometric Brownian motion as a model for price movements without any economical studies, just based on the fact that the price is not predictable and is positive. The model, now called Black-Scholes, which was inspired by the lost work of Bachelier (1900), is the consequence of pure mathematical thinking.
Unfortunately, many of my friends who study economics, believe that the model is a consequence of the Efficient Market Hypothesis, (EMH) introduced by Samuelson and developed by Fama. Although, EMH and Black-Scholes model are not fully independent, it was not EMH that created Black-Scholes model. The model is the result of collaboration of one mathematico-economist (Samuelson) and two famous pure mathematicians, L. J. Savage and H. P. McKean.
I remember a conference in Allameh Tabatabaie University in Tehran, where Prof. Jamshid Pazhouhian critisized my talk about dynamic portfolio optimization on Heston model where there where quit giant partial differential equations (PDEs) in my slides, mentioning that the work should start in economics not mathematics and the definition of economics is aligned with prediction. Isn't the Heston model by chance a econometrics model? Or the dynamic portfolio optimization much more economically reasonable than the paradoxical collection of Markowitz static portfolio optimization and Capital Asset Pricing Model (CAPM)?