Would creating Mathematics with computers be considered pure?

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Discussion Overview

The discussion revolves around the classification of computational mathematics and its relationship to pure mathematics. Participants explore whether using computers to visualize and create mathematical concepts can be considered pure, especially in the context of personal disabilities in traditional mathematical thinking.

Discussion Character

  • Exploratory, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant questions whether using a computer for visualization in mathematics can still be considered pure mathematics, given the traditional definitions of pure and applied mathematics.
  • Another participant asserts that pure mathematics is defined by its subject matter, implying that computational approaches could fit within this definition.
  • A later reply suggests that the classification of mathematics may depend on the field, indicating a nuanced view of purity in mathematics.
  • Concerns are raised about potential opposition to the idea of computational mathematics being pure, referencing historical debates such as the four-color theorem controversy.

Areas of Agreement / Disagreement

Participants express differing views on the classification of computational mathematics, with some suggesting it can be pure while others acknowledge potential opposition to this perspective. The discussion remains unresolved regarding the broader implications of using computers in mathematical practice.

Contextual Notes

Participants express uncertainty about definitions of purity in mathematics and the implications of personal experiences with mathematical disabilities. There is a lack of consensus on how computational methods fit within traditional categories of mathematics.

Who May Find This Useful

Individuals interested in the philosophy of mathematics, computational geometry, and the intersection of technology and mathematical practice may find this discussion relevant.

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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