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Last night, I heard one engineer talking about work. He said that the mathematicians formulate the problems and then send these problems to be solved by engineers.

I thought that mathematicians solved problems in a sort of abstract world, and the problems they solved were initially solved in this abstract world and eventualy found as "useful" by others.

So how's the cooperation between them?

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There is not a great gap between mathematically minded engineers and many applied mathematicians. –  André Nicolas Sep 8 '12 at 6:41
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"Mathematician" and "engineer" are both words that describe a lot of people who do a lot of things involving a lot of other people and I don't see the point of trying to generalize in this way about what those things look like. What are you going to do with an answer to this question? What do you actually want to know? –  Qiaochu Yuan Sep 8 '12 at 6:44
    
Your view is plausible –  Ram Sep 8 '12 at 6:46
    
@QiaochuYuan I'm trying to probe a little on: 1 - The nature of work of each one; 2 - the nature of their cooperation. | Also, with the terms I used, I tried to specify people with degree on these areas. –  Igäria Mnagarka Sep 8 '12 at 6:46
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@Gustavo: if your question was "how do mathematicians and engineers cooperate?" why did you restrict your question to being about two hypothetical answers to this question? Why not just ask the question you wanted to ask? –  Qiaochu Yuan Sep 8 '12 at 6:55
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2 Answers

I only know about one problem formulated by mathematicians and solved by engineers; you can read about it here. Of course, there may be many others that just aren't coming to my mind.

There are certainly examples of problems originally solved as pure mathematics that were later found useful, but there is also a third category not included in your question, the problems formulated by engineers (and others) and sent to be solved by mathematicians.

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I'll be happy if you add something in this third class. –  Igäria Mnagarka Sep 8 '12 at 6:44
    
Perhaps Newton solved the astronomers' problem of why the planets obey Kepler's Laws by coming up with the inverse-square law of gravitational attraction. –  Gerry Myerson Sep 8 '12 at 6:50
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My experience in this area is limited to math/engineering revolving around problems with their roots in telecommunications. Typically what happens is something like following. Engineers come up with a way of doing something better than was previously known. They present the idea at a conference (or consult mathematicians at a nearby university). The mathematicians in the audience recognize the abstract (algebraic) structure, reformulate the question, suggest possible improvements/generalizations, and start working on it. Engineers then absorb that bit of theory (or not), come up with further questions and desirable properties, and the evolutionary cycle begins.

The words "engineer" and "mathematician" were used somewhat loosely above. Their respective educations may overlap significantly, but the labels fit reasonably well.

It doesn't always go optimally. There are several niches in coding theory, where mathematicians were so enchanted by a certain problem that they continued to work on generalizing the problems and their solutions long after the engineers lost all interest (cautiously raises hand).

Perhaps Goethe put it best (given that Knuth quoted him in a similar context):

"Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different."

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Original quote: Die Mathematiker sind eine Art Franzosen: Redet man zu ihnen, so übersetzen sie es in ihre Sprache, und dann ist es alsobald ganz etwas anders. Goethe, Maximen und Reflexionen, Nr. 1005. –  t.b. Sep 8 '12 at 22:19
    
@t.b. Vielen Dank! –  Jyrki Lahtonen Sep 9 '12 at 4:16
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