There are different tools for evaluating what has been done and what should be done. Confuse the two at your own risk.
The finance industry caused significant damage to the world economy because they confused the two. Given any set of data, patterns will inevitably emerge; but that doesn’t prove cause and effect. Applied mathematicians in the finance community were using their models of stock price changes to make huge bets in the market. Many were not interested in the details of the underlying company, only in the past movement of the company’s price in the stock market. Their game was even self reinforcing as long as the other big players used the same algorithms to price the stock. The competition evolved into who had the faster computer, and who had first access to the algorithm; not which company was the most sound and had the best cash flow.
Then, somewhere in the world, a butterfly beat its wings. And everything came tumbling down.
Small changes can make a huge difference. Multiple stable equilibrium points exist. Positive feedback loops exist. Scientist know this— chemists, physicists, mechanical engineers, electrical engineers, biologists, practicing physicians…and many mathematicians. These researchers and practitioners use mathematics every day, but they realize that any inference, any prediction of the future from the analysis, is dependent on including all the significant factors that influence the outcome. Their premises must be comprehensive and correct—leave out an important variable or make an erroneous assumption and huge mistakes are made. The conclusion of applied math, incorrectly applied without specific knowledge of the context of the application, is dangerous. In 1989 the arrogance of a couple of Nobel prize economists with their mathematical calculations caused a banking crisis and potential world crisis that required the concerted efforts of several countries to avert. They thought they knew all the variables involved. In 2008 history repeated itself.
Anyone in any field with intimate knowledge of their job knows there are a plethora of variables that one considers before taking action.
Artificial intelligence has just this past year been able to drive a car in the desert. The conditional statements in the computer algorithms to cover all the combinations of problems encountered are overwhelming. But a twelve year old can easily drive the same car through the desert (if he can see over the dashboard and tape blocks to the pedals for the accelerator and brakes). Computers and calculations can’t replace human decision making.
It’s impossible for the mathematical analyses you see in academic journals to take into account all the variables involved. To better simulate real life, the analyses would include conditional statements that cover all potential variables. They don’t. They might be entirely valid for that one place and time, and only with the restriction that you aren’t allowed to use your innate human abilities to adapt to any changes and alter the outcome.
The ability to adapt comes from experience and understanding. Experience comes from seeing similar situations multiple times. Understanding comes from knowing which factors are important, which aren’t, and what the outcome will be (understanding the theory). Experience without theory works most of the time; but experience with theory is what makes the difference between a technician and a professional.
Are you an applied mathematician with limited practical experience, are you a technician, or are you a healthcare professional? You may have a job description as one, but you may be any combination.