The USDA once wanted to make cows produce milk faster, to improve the dairy industry.
So, they decided to consult the foremost biologists and recombinant DNA technicians to build them a better cow. They assembled this team of great scientists, and gave them unlimited funding. They requested rare chemicals, weird bacteria, tons of quarantine equipment, there was a horrible typhus epidemic they started by accident, and, 2 years later, they came back with the ,,new, improved cow``. It had a milk production improvement of 2% over the original.
They then tried with the greatest Nobel Prize winning chemists around. They worked for six months, and, after requisitioning tons of chemical equipment, and poisoning half the small town in Colorado where they were working with a toxic cloud from one of their experiments, they got a 5% improvement in milk output.
The physicists tried for a year, and, after ten thousand cows were subjected to radiation therapy, they got a 1% improvement in output.
Finally, in desperation, they turned to the mathematicians. The foremost mathematician of his time offered to help them with the problem. Upon hearing the problem, he told the delegation that they could come back in the morning and he would have solved the problem. In the morning, they came back, and he handed them a piece of paper with the computations for the new, 300% improved milk cow.
The plans began: ,,A Proof of the Attainability of Increased Milk Output from Bovines: Consider a spherical cow...``
That is from here.
Interesting right? Well that gives a small idea on how to speculate problems in a mathematical way....!!