Is the Role of Mathematicians Becoming Obsolete with Advanced Computer Programs?

[WarPhalange]

I think mathematical research should be guided by physical applications, and I think that most people would be surprised by the large number of mathematicians who admit that they don't care if their work ever has any applications. Of course it is fun to prove theorems, and the body of pure mathematics is an amazing accomplishment for humankind. I am aware of all the standard examples e.g. Gauss' work on geometry that was not applied by Einstein until 50 years later etc. But I would ask everyone who defends the existence of pure mathematicians on these grounds to justify studying something like super edge magic graph labelings. How could that ever be useful?

We're using maggots to clean human wounds of rotten flesh. Never say that something will never be useful. Just because you can't think of a use for it, doesn't mean that nobody ever will. That's really arrogant of you.

Also, there's two ways of solving a problem:

1) Trying to make a tool for solving the problem.
2) Looking at tools that already exist to see if one of them will solve your problem.

It often happens that people use tools for purposes that they weren't built for, and still get what they want done. People might never stumble upon an answer to a question because of the mindset the question inherently invokes. Someone trying to solve something else might stumble upon it, though, because they are trying to do something with a different approach.

 

[The|M|onster]

Are you saying that super edge magic graph labelings have an application in computer science? Then please give me a citation, since I would be interested in this beyond the sake of argument.

Try the book Magic Graphs by W.D. Wallis. On page 13 it talks about an application of edge-magic total labelings in efficient addressing systems of communications networks. I read an article not to long ago about an application towards secret sharing schemes in cryptography. Also, if you search the literature out there, you will probably find that most of the journals that publish research on magic graph labellings are computer science journals.

I agree With WarPhalange. Just because you can't see an application doesn't mean there isn't one, and it doesn't mean one won't be found. Insisting that all pure mathematics research should be done with an application in mind would stifle creativity. It would be like telling a physicist or a chemist that their research has to have an immediate commercial use. It's thinking like that that hinders progress.

 

[atyy]

W. W. Sawyer, "Prelude to Mathematics", Chapter 1: ... To defend mathematics purely on the ground of its beauty is the height of heartlessness. Mathematics has cultural value; but culture does not consist in stimulating oneself with novel patterns in indifference to one's surroundings. ... Both the pure artist and the pure bureaucrat are wrong, or at least incomplete...

 

[The|M|onster]

I agree with that statement. It is important to have an appreciation for the applications of mathematics and I do. However, I am also someone who finds magic graphs to be interesting. In Crosson's first statement, he made it seem that if the maths doesn't have an obvious application, then it can't produce deep results. I also think that there seems to be a misconception that mathematicians are around primarily to build tools for scientists and engineers. The fact that people find uses for this stuff is excellent, but I don't see why anyone would be surprised when a pure mathematician says they don't really care how it all gets used. I personally just like to play with mathematical objects and let my thoughts follow them to their logical conclusions. In the end one just has to study what they love and not worry about what other people think.