How Valuable is Tool-Finding Experience for Student Researchers?

[Simfish]

Searching for the tool often takes a lot of time, so the professor is often better off outsourcing the work to the student (and the student can often take advantage of his Web 2.0 connections).

I'm just curious. I actually think that this is the type of research that I would do best at, since I tend to be resourceful

 

[Choppy]

I'm not sure I understand the question, because there appear to be some incorrect implications in it.

First off, you can't expect an increase in efficiency by 'outsourcing' research work to a student. As with any job a veteran is generally more efficient than a rookie.

Finding a 'tool' - particularly once you know what you're looking for - is often the easy part of the research. Identifying the correct tool and then mastering it's use are the hard parts. And most of the time, in my experience anyway, the tool doesn't exist and so you have to develop it.

Also, professors can surf Facebook just as easily their students can.

 

[mathwonk]

as already said there are several aspects to research: finding the interesting question, determining whether an existing tool suffices to attack it, using the tool to do the computation, or creating or modifying a tool that is adequate to the job. In pure mathematics these tools are abstract ones. One seldom finds an appropriate tool ready to hand, since in that case the problem would already have been solved by someone unless the problem had not been thought of. The method of analogy however can suggest to one that a tool already used on an other problem is appropriate if one can see the resemblance between the two problems, the old one and the new one. So it is possible to be the first person to realize that an available tool suits a given problem. E.g. Gerhard Frey noticed that a solution to Fermat's problem would lead to an anomaly in the area of modular forms. But ti still remained to create a lot of tools to pursue this.

In a recent paper a colleague and I gave a second proof of a conjecture about theta functions that had been proved earlier using the standard tool of the heat equation. We used instead the tool of deformation of singularities. This theory existed but we had to adapt it to the problem.

 

[Simfish]

First off, you can't expect an increase in efficiency by 'outsourcing' research work to a student. As with any job a veteran is generally more efficient than a rookie.

Finding a 'tool' - particularly once you know what you're looking for - is often the easy part of the research. Identifying the correct tool and then mastering it's use are the hard parts. And most of the time, in my experience anyway, the tool doesn't exist and so you have to develop it.

That's true. The thing with finding a tool, though, is that you don't always know how long it will take you. And due to this uncertainty, you might consider outsourcing the work to a student so that you won't have to waste your super-limited time trying to find it yourself. Yes, that's true - the tool often doesn't exist, in which case the student often has to develop it himself (which is what I had to do a couple of times).

It's true that professors can browse Facebook just as easily. But it also takes time to browse through all sorts of online media just to find the right tool.

as already said there are several aspects to research: finding the interesting question, determining whether an existing tool suffices to attack it, using the tool to do the computation, or creating or modifying a tool that is adequate to the job. In pure mathematics these tools are abstract ones. One seldom finds an appropriate tool ready to hand, since in that case the problem would already have been solved by someone unless the problem had not been thought of. The method of analogy however can suggest to one that a tool already used on an other problem is appropriate if one can see the resemblance between the two problems, the old one and the new one. So it is possible to be the first person to realize that an available tool suits a given problem. E.g. Gerhard Frey noticed that a solution to Fermat's problem would lead to an anomaly in the area of modular forms. But ti still remained to create a lot of tools to pursue this.

In a recent paper a colleague and I gave a second proof of a conjecture about theta functions that had been proved earlier using the standard tool of the heat equation. We used instead the tool of deformation of singularities. This theory existed but we had to adapt it to the problem.

Ah, thanks for the example. :) That's quite nicely written. Yeah, oftentimes people will create the tools (which are then often known as lemmas)