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

[elfboy]

Do we even need mathematicians? I ponded this question because I came across this site:

http://functions.wolfram.com" and virtually every function created since the dawn of humanity is indexed somwhere in there. These identities were generated with mathematica. Yet a long time ago people spent years deriving most these formulas by hand. It seems like the role of mathematicians to derive stuff can simply be outsourced to sophisticated computer programs. Perhaps the type of work that computers can't do involves very abstract mathematics like game theory and topology.

 

[PowerIso]

Mathematics isn't simply about deriving stuff. I don't think a computer, on it's own, can solve all existences, uniqueness, and a myriad of other problems mathematicians solve. It's a useful tool, no doubt, but mathematicians do more than deriving functions.

The other day I derived a recursion with much help from mathematica, but that is only part of the problem, the real question I am after is now, "why is this relationship" true. So now I'm trying to prove it is true, something mathematica can't really do for me.

 

[Howers]

Certinaly not for lectures.

 

[mathwonk]

can computers take over our work of answering of stupid questions?

 

[JG89]

Who's going to write the computer programs?

Who's going to update the computer with new concepts that pop up?

Mathematicians of course.

 

[Count Iblis]

can computers take over our work of answering of stupid questions?

Actually, we are all computers. Darwinian evolution created ever complex neural networks, leading to our brains and those of other creatures.

So, you could imagine using a big supercomputer to train neural networks to become the brains of mathematicians.

 

[The|M|onster]

You have a very narrow view of mathematics if you think the only "abstract" subfields are game theory and topology. Do we really need mathematicians? Maybe not. But that's not going to stop some people, myself included, from pursuing it for the simple reason that it is a beautiful and challenging endeavor.

 

[thE3nigma]

I think we will need Mathematicians much more in the future than ever before. I am not a Mathematician myself but I know how helpful they have been in helping to develop our understanding of many of the chemical and physical principles we use today in society. Also if I am not mistaken, currently a lot of research is being made into Topology which is being used by string theorists.

Just my two cents on this topic.

 

[alligatorman]

you must not know much (anything?) about true mathematics.

 

[CompuChip]

Also, how do you think Mathematica has come to know about all these weird functions and smart techniques? Certainly not by evolution, or by just scanning in integral tables derived a long time ago by hand.

 

[Count Iblis]

Also, how do you think Mathematica has come to know about all these weird functions and smart techniques? Certainly not by evolution, or by just scanning in integral tables derived a long time ago by hand.

Steven Wolfram is a product of evolution.

 

[CompuChip]

Steven Wolfram is a product of evolution.

But (among other things), a mathematician. It seems logical to deduce that if you need Mathematica, you (in the end) also needed a mathematician.

 

[Hippo]

Do we even need mathematicians? I ponded this question because I came across this site:

http://functions.wolfram.com" and virtually every function created since the dawn of humanity is indexed somwhere in there. These identities were generated with mathematica. Yet a long time ago people spent years deriving most these formulas by hand. It seems like the role of mathematicians to derive stuff can simply be outsourced to sophisticated computer programs. Perhaps the type of work that computers can't do involves very abstract mathematics like game theory and topology.

Wow what an amazing Math site. Thanks for the share.

 

[Count Iblis]

But (among other things), a mathematician. It seems logical to deduce that if you need Mathematica, you (in the end) also needed a mathematician.

I agree. Now Dyson once said that it is amazing that the brain Homo Sapiens evolved while trying to survive on the African savannas can also be used to solve differential equations. So, perhaps it would be more effective to have a purpose build genetic algorithm that selects the best math skills directly.

Of course, you would need a huge computer to simulate neural networks as complicated as the human brain. In the future we may have that capability and then we'll be able to cook up a super duper Steven Wolfram from nothing who can then design a far better version of Mathematica.

 

[CompuChip]

can computers take over our work of answering of stupid questions?

I'm sure they could take over the work of making them up and posting them on PF...

I agree. Now Dyson once said that it is amazing that the brain Homo Sapiens evolved while trying to survive on the African savannas can also be used to solve differential equations. So, perhaps it would be more effective to have a purpose build genetic algorithm that selects the best math skills directly.

Of course, you would need a huge computer to simulate neural networks as complicated as the human brain. In the future we may have that capability and then we'll be able to cook up a super duper Steven Wolfram from nothing who can then design a far better version of Mathematica.

Yes, if it ever gets that far, I hope that will be the first task for such a supercomputer. At least it seems so much more useful than building the best computer ever and then have it print out "42".

 

[Alienjoey]

With the advancement of computers, we need mathematicians no more than we need doctors, since the majority of diseases, symptoms, and cures are indexed on the internet as well.

 

[wildman]

Do we even need mathematicians? I ponded this question because I came across this site:

http://functions.wolfram.com" and virtually every function created since the dawn of humanity is indexed somwhere in there. These identities were generated with mathematica. Yet a long time ago people spent years deriving most these formulas by hand. It seems like the role of mathematicians to derive stuff can simply be outsourced to sophisticated computer programs. Perhaps the type of work that computers can't do involves very abstract mathematics like game theory and topology.

Where do you think these functions come from? Fairies maybe? We need mathematicians to develop new functions and to interpret the ones we have.

 

[uncfelt1147]

A professor at my school solved an integral for some physics problem the other day that mathematica couldn't even solve... so Mathematica isn't that great after all.

 

[CompuChip]

A professor at my school solved an integral for some physics problem the other day that mathematica couldn't even solve... so Mathematica isn't that great after all.

Although the reason also might have been that Mathematica can only solve it when given certain assumptions (e.g. positivity of certain constants inside the integral), or that the integral actually did not converge but the professor got out a finite answer by some (borderline) illegal operation

 

[uncfelt1147]

Although the reason also might have been that Mathematica can only solve it when given certain assumptions (e.g. positivity of certain constants inside the integral), or that the integral actually did not converge but the professor got out a finite answer by some (borderline) illegal operation

I understand your argument, and in several cases you might be right, but number one the integral was just to complicated, he searched through books of integral tables to see if it had been solved and couldn't find anything, this professor is borderline genius. I know you don't want to believe that Mathematica could do any wrong, but unfortunately I believe differently.

 

[Topher925]

First, mathematica blows.

Second, we don't need mathematicians. Whenever I ask mathematicians for help solving a math problem, they either say "sorry, but I only do theoretical math" or "I can prove a solution exists, but I am unable to find it".

 

[uncfelt1147]

First, mathematica blows.

Second, we don't need mathematicians. Whenever I ask mathematicians for help solving a math problem, they either say "sorry, but I only do theoretical math" or "I can prove a solution exists, but I am unable to find it".

Haha no need to be so hasty and generalizing, but I understand

 

[CompuChip]

I understand your argument, and in several cases you might be right, but number one the integral was just to complicated, he searched through books of integral tables to see if it had been solved and couldn't find anything, this professor is borderline genius. I know you don't want to believe that Mathematica could do any wrong, but unfortunately I believe differently.

Trust me, I know it as well. On several occasions, working out expressions by hand was more accurate and less messy than Mathematica's attempts at integrating a function. Still I think most problems arise from user input errors, but if you say this was an exception I immediately believe you

 

[symbolipoint]

After 22 posts on this topic, it is finished. We certainly need mathematicians. They are the people who cultivate the Mathematics which technicians, engineers, and scientists use.

 

[WarPhalange]

Math is applicable to many things in life, not just physics or engineering, but business, economics, computers, etc. New uses are found every day, and the math doesn't just come out of thin air. You need to smash two mathematicians at really high speeds to produce an equation.

 

[CompuChip]

Math is applicable to many things in life, not just physics or engineering, but business, economics, computers, etc. New uses are found every day, and the math doesn't just come out of thin air. You need to smash two mathematicians at really high speeds to produce an equation.

Ahhh, so that's what they are trying to do at LHC! Then it's even more impressive than I thought, seeing that just the rest mass of a mathematician is of order 10^31 MeV.

 

[Crosson]

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?

 

[The|M|onster]

Well, what you just cited is something that falls in the realm of discrete mathematics and actually has application to computer scientists. Just because something doesn't have a specific physical application doesn't mean that it isn't applied in another field. In no way should all pure mathematics research be guided by physical applications. Some mathematicians will naturally drift in that direction, but otherwise just let the math guys do what they want to do.

 

[Crosson]

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.

If you are merely pointing out that the concept of a graph has applications in computer science, then I think you are dodging the question i.e. some areas of graph theory may be useful to humans, but still some heavily researched areas are most definitely not.

 

[atyy]

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.

http://www.labmath-itb.or.id/~icam05/InvitedLecture.htm
F.A. Muntaner-Batle (Uníversidad Internacional de Cataluña, Spain)
Embedding Graphs Into Super Edge Magic Graphs
The area of graph labelings has experimented a great development during the last three decades, and many applications of this area have been found and studied in other branches of science. For instance we can find graph labelings showing up in coding theory, X-ray crystallography, radar, astronomy, circuit design, communication network addressing and data base management. Also a close relationship exists between graph decompositions and graph labelings. Due to this close relationship, many problems involving labellings and trees have shown up and have proven to be very hard. In this talk, we will discuss some classical applications involving graphh labellings and we will study how close is a tree to be super edge magic by finding for any given tree T, a small super edge magic tree T’, that contains T as a subgraph.

Edit: On the other hand, almost all biologists routinely claim their work is clinically applicable in order to get funding.

 

[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.