Do we need mathematicians?

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  • #1
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Do we even need mathematicians? I ponded this question because I came accross this site:

http://functions.wolfram.com" [Broken] 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.
 
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  • #2
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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.
 
  • #3
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Certinaly not for lectures.
 
  • #4
mathwonk
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can computers take over our work of answering of stupid questions?
 
  • #5
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Who's going to write the computer programs?

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

Mathematicians of course.
 
  • #6
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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.
 
  • #7
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.
 
  • #8
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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.
 
  • #9
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you must not know much (anything?) about true mathematics.
 
  • #10
CompuChip
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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.
 
  • #11
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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.
 
  • #12
CompuChip
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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. :wink:
 
  • #13
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Do we even need mathematicians? I ponded this question because I came accross this site:

http://functions.wolfram.com" [Broken] 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.
 
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  • #14
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But (among other things), a mathematician. It seems logical to deduce that if you need Mathematica, you (in the end) also needed a mathematician. :wink:

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. :approve:
 
  • #15
CompuChip
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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. :approve:

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".
 
  • #16
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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.
 
  • #17
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Do we even need mathematicians? I ponded this question because I came accross this site:

http://functions.wolfram.com" [Broken] 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.
 
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  • #18
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.
 
  • #19
CompuChip
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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 :smile:
 
  • #20
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 :smile:

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.
 
  • #21
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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".
 
  • #22
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
 
  • #23
CompuChip
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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 :smile:
 
  • #24
symbolipoint
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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.
 
  • #25
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.
 

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