[按：下文是群邮件的内容，标题是新拟的。主旨是通过思想模型和简单图示，说明真正的应用数学注定是一场遭遇。]

This is coming to you from Yiwei LI (PhD, Applied math), Taiyuan University of Science and Technology  (TYUST) Taiyuan, China

Scratch time is a topic under the column of Theory of Mathematics (TOM), an attempted framework to understand invented and un-invented mathematics from the core.

It appears necessary to address some typical situations that one would meet in (genuine) applied math.

---- By "genuine", I refer to the situations occurring in a foreign field where mathematical problems arise.

---- You know what ? I feel difficult to continue.

---- Well, it's 4 o'clock and I'm watching a movie (Saving Mr. Banks), yet a dull one...

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So, I decide to share a thought model concerning genuine applied math.

---- In a way that everyone could understand, or that everyone might think they really understand.

---- Before one moves on, I declare no profession implication.

---- It's just a simple thought model on the abstract level.

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---- The problem can be illustrated like ——

---- This is from the objective perspective.

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---- To the problem holder, it looks like ——

Note: the green parts are assumed solved; the dark part is the assumed problem.

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---- So comes the assignment ——

Note: The gray parts are typically not visible to the one assumed to solve the problem.

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---- So comes the first step of the process of applied math (应用数学过程) ——

---- The assignment appears accomplished, from the perspective of the one assumed to solve the problem.

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However, to the problem holder, it looks like ——

---- The solution might be a foreign matter to the problem holder.

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---- So, after a long or not short while, comes the second stage of the process of applied math (应用数学过程) ——

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---- So all the modules are eventually identified, each of them is a a foreign matter to the one assumed to solve the problem.

---- As the other modules are so familiar to the problem holder that it may become a source of difficulties, contrary to the usual intuition.

---- And, all these efforts are very likely thought not necessary, in the view of the problem holder.

---- Actually, such efforts are either invisible to or not valued by the problem holder.

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---- So comes the dilemma ——

---- Should these other modules be implemented for the second time ?

---- Very likely one needs to solve them one by one.

---- The original architecture might not be compatible to the solution of the original assignment.

---- Actually, one has already sunk in by the cost.

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So comes the third stage of the process of applied math (应用数学过程) ——

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---- This appears the final station of the process to the one assumed to solve the problem.

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To the problem holder, it looks like ——

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(to be continued).