In both cases, mathematics is being used to solve a problem. The difference is the financial analysis is done to convince people to act in a way that makes it true. In physics, there is no convincing the atoms and particles to simply behave how you want them to.
To illustrate this, let’s say that a stock price has a pattern to it, that has been fit well with an equation. The equation with good confidence says Microsoft is going to be worth at 10% more in 2 months. A brokerage who owns millions of dollars of Microsoft stock takes this information, types it up, and tells it to as many of their customers who will listen. Then those customers who are convinced buy a bunch of Microsoft driving the price up and fulfilling the “prediction”. Was it the analysis? Was it the behavior induced by the analysis?
In physics, when we are calculating how electrons flow, or how steel bends, or any other physical phenomenon, the particles aren’t told about how they should behave based on the analysis.
Differentiating between these two ways of using analysis is where many people fall on their head. When we have a lack of trust in science, it’s possible it comes from someone who has been burned by trusting in something similar to the financial analysis, where the result doesn’t actually come from a fixed behavior of the universe. It then leads a person to believe that they can’t trust people who run numbers and analysis and perform “science”. However, it’s a false dichotomy, not all analyses is the same, and distinguishing which type you are engaging with is important.