Hi @mathow.
Certainly when the drill pipe gets stuck in the well it is a very serious problem, as money is lost due to non-productive time and as the days go by the risk of having to leave the pipe at the bottom of the well and pump a cement plug and perform a side track increases.
It is very important the mathematical calculations, because for example when the drill pipe is being tensioned to release it from its jam it must be done under a force limit, because if this limit is exceeded the pipe can break, to know the tension limit it is necessary to perform some mathematical calculations that are involved in this operation.
Greetings and thank you very much for your valuable comment which encourages me to continue generating content like this.