Story 1: the problem of boiling water

A nosy person asked such a question: "If you have a gas stove, a faucet, a kettle and a match in front of you, what should you do if you want to boil some water?"

The questioner replied, "Put the water in the kettle, light the gas, and then put the kettle on the gas stove."

"If other conditions remain the same, but there is enough water in the kettle, then you should let the questioner confirm the answer and ask: How?"

At this time, the questioner confidently replied: "Light the gas, and then put the kettle on the gas stove.

But the questioner said, "Physicists usually do this, and mathematicians will empty the water in the pot and claim to turn the latter question into the former."

Feeling:

It seems that the mathematician's "pouring water into the basin" is superfluous. The creator of the story is not asking us to "empty the water in the pot", but to guide us to understand the unique way of thinking of mathematicians and transform them one by one.

Learning mathematics is not the memory accumulation of problem solutions, but learning to turn unknown problems into known problems, complex problems into simple problems and abstract problems into concrete problems. The transformation thought of mathematics simplifies our thinking state and improves our thinking quality. Transformation is not a matter-of-fact, one-thing, one-policy, but a matter of digging the core and prototype of the most essential problem, and then turning a new problem into a problem that can already be solved.