Would creating Mathematics with computers be considered pure?

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SUMMARY

The discussion centers on the classification of computational mathematics and its relationship to pure mathematics. The participant questions whether using computers to visualize mathematical concepts, particularly for those with disabilities in traditional mathematical thinking, can be considered pure mathematics. They reference G.H. Hardy's views from "A Mathematician's Apology" and express a desire for clarity on whether computational geometry, a field they are pursuing, is deemed pure. The consensus leans towards recognizing computational mathematics as a legitimate form of pure mathematics, depending on its application and intent.

PREREQUISITES
  • Understanding of pure mathematics and its definitions
  • Familiarity with computational mathematics and its applications
  • Knowledge of G.H. Hardy's "A Mathematician's Apology"
  • Basic concepts in computational geometry
NEXT STEPS
  • Explore the principles of computational geometry
  • Study the implications of G.H. Hardy's philosophy on modern mathematics
  • Research the classification of mathematical fields: pure vs. applied
  • Learn about visualization tools in mathematics, such as GeoGebra or MATLAB
USEFUL FOR

Students and professionals in mathematics, particularly those interested in computational geometry, educators seeking to understand the intersection of technology and mathematics, and anyone exploring the philosophical aspects of mathematical purity.

Samardar
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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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Pure in what sense? Pure mathematics? Yes. Pure mathematics is defined by what it studies.
 
Thanks :D
 
Thats a relief.

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

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