Would creating Mathematics with computers be considered pure?

In summary, the high school student is wondering if using a computer to visualize mathematics would be considered a useful tool for someone with a disability in mathematics. They also question if computational mathematics, which combines pure and applied mathematics, is still considered pure. The student mentions a quote from Hardy's "A Mathematician's Apology" about the beauty of pure mathematics versus applied mathematics and wonders if they are overthinking it. They also mention their future career in computational geometry and the idea of purity in mathematics.
  • #1
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Here's something a Highschool student would ask:

If I have something considered a disability in mathematics i.e visual thinking LoL , using a computer to visualize mathematics would be considered a useful tool.

Pure mathematics is defined as generalizing abstraction , it is the how's and why's of mathematics.

If applied mathematics is supposed to be ugly and dull under a physical truth in a mathematical framework , would using a computer to study as well as create the beautiful and brilliant be considered pure?

Computational Mathematics , is often a hybrid of the two , so why is it filed under applied?
Is it because of the implementations and designing of algorithms to study mathematics , but I only want to use a computer to visualize things I can't and to represent my output - my creations? I guess I'll need to use them anyways.

Can we open our minds here? I just need reinforcement the main answer is blatantly yes.
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This started out because an opinion made by Hardy in a Mathematicians Apology is mostly being misunderstood by me , if physical truth is ugly and dull , why do other's consider it beautiful , he thinks one aspect of reality is more prettier than the other , he's just making biased comparisons. But it still haunts me to this day , is it really ugly and dull just applying? Am I ruminating too much?

I am also asking this question because I have a future career in computational geometry and I would want to know if this is considered pure , as the idea of purity being the purist of the water seems to intrigue me , but it's nothing important.
 
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  • #2
Pure in what sense? Pure mathematics? Yes. Pure mathematics is defined by what it studies.
 
  • #3
Thanks :D
 
  • #4
Thats a relief.

Well I guess , pure by field.
 
  • #5
That's not to say you wouldn't encounter opposition. Just think back to the whole four-color theorem flame war...
 

1. Would creating Mathematics with computers be considered pure?

The answer to this question is subjective and depends on the definition of "pure" mathematics. Some argue that mathematics created with computers is not considered pure because it relies on technology and programming, while others argue that the concepts and theories developed are still based on pure mathematical principles.

2. Can computers replace human mathematicians?

No, computers cannot replace human mathematicians. While computers can perform calculations and solve equations at a much faster rate than humans, they lack the creativity, intuition, and critical thinking skills that are essential for advancing mathematics.

3. Is mathematics created with computers less reliable?

It can be argued that mathematics created with computers is not less reliable, as the calculations and solutions are still based on logical and mathematical principles. However, it is important for researchers to thoroughly test and verify the results obtained from computer-generated mathematics to ensure accuracy.

4. How has the use of computers impacted the development of mathematics?

The use of computers has greatly impacted the development of mathematics by allowing for more complex and precise calculations, as well as the ability to visualize and explore mathematical concepts through simulations and models. It has also opened up new areas of research, such as computational mathematics and digital mathematics.

5. Are there any potential drawbacks to creating mathematics with computers?

One potential drawback of creating mathematics with computers is the reliance on technology, which can be susceptible to errors and malfunctions. Additionally, some argue that the human aspect of mathematics, such as creativity and intuition, may be lost if solely relying on computers. It is important for researchers to carefully consider and address these potential drawbacks when utilizing computers in mathematical research.

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