Is Pure Mathematics the Only True Form of Mathematical Study?

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Discussion Overview

The discussion centers around the value of pure mathematics versus applied mathematics, exploring whether pure mathematics is the only true form of mathematical study. Participants debate the merits of each approach, touching on theoretical understanding, practical application, and the historical contributions of mathematicians.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants argue that pure mathematics is the only worthwhile study, claiming it provides a deeper understanding of mathematical concepts through derivation and exploration.
  • Others challenge this view, suggesting that applied mathematics has significant value, citing historical figures like Archimedes and Newton as examples of mathematicians who contributed original work beyond mere application.
  • One participant asserts that practical mathematics is essential for understanding the world, contrasting it with what they describe as "mental wankery" associated with pure mathematics.
  • Another participant emphasizes the importance of understanding the derivation of equations rather than merely memorizing them, suggesting that this understanding enhances intellectual appreciation.
  • Some participants express frustration with the notion that applied mathematics is inferior, arguing that both theoretical and practical approaches have their place in the field.
  • Concerns are raised about the misconception that mastering basic computational skills equates to true mathematical ability.

Areas of Agreement / Disagreement

Participants generally disagree on the value of pure versus applied mathematics, with multiple competing views presented. There is no consensus on which approach is superior or more valid.

Contextual Notes

The discussion reflects a range of opinions and assumptions about the nature of mathematics, with some participants expressing strong emotional responses to differing viewpoints. The debate remains unresolved, with various perspectives on the role and importance of both pure and applied mathematics.

DavidSmith
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studying is pure mathematics which isn't intended to solve social, economic, or industrial problems.

Mathematics at its purest is the only mathematics I would recommend learning.

Learning practical mathematics deprives you of the true mathematics expeierience.

The only way to truly understand mathematics is to a. derive expressions yourself and b. derive new expressions using previous equations as building blocks.

Applied mathematics is essentially plug and chug. You put the values in the equation and get an an output but have a lack of understanding of how the equation was derived, not can you apply that knowledge to create new expressions.
 
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Wrong.
 
Yeah, and applied mathematicians like Archimedes, Newton, and Stokes never did anything of value. <sarcasm>. Did you crib this notion from G.H Hardy?
 
DavidSmith said:
studying is pure mathematics which isn't intended to solve social, economic, or industrial problems.

Mathematics at its purest is the only mathematics I would recommend learning.

Learning practical mathematics deprives you of the true mathematics expeierience.

The only way to truly understand mathematics is to a. derive expressions yourself and b. derive new expressions using previous equations as building blocks.

Applied mathematics is essentially plug and chug. You put the values in the equation and get an an output but have a lack of understanding of how the equation was derived, not can you apply that knowledge to create new expressions.

That outrageously misrepresents Mathematics as a tool.

Any scientific or technical analyst will at some time use numeric information and equations to derive algebraic formulas. Sometimes this may be part of arranging a system of not-necessarily linear systems of equations, and this person may need to solve the system, at least in practical values.
 
unit_circle said:
Yeah, and applied mathematicians like Archimedes, Newton, and Stokes never did anything of value. <sarcasm>. Did you crib this notion from G.H Hardy?

But they created original work and formulas.
 
DavidSmith said:
But they created original work and formulas.

So doesn't this contradict your original argument? Newton did more than just plug and chug. It looks to me like your're trolling. I could easily make the same argument in reverse.

The only math worth studying is math that has practical value, for we can then apply it to learn about the world around us. So called "pure math" is nothing but mental wankery, and anyone who does it is depriving themselves of the "true" experience of math, which is comparing numerical predictions to empirical data.

I COULD make this argument, but it seems pretty silly, in the same way that your original statement is silly.
 
It is a troll. Just ignore it.
 
Its interesting see how a proof was done. I agree that we lose a degree of appreciation when we simply memorize equations, identities, even calculus. The need for an equation, why it was sought after and discovered, in my opinion, more constructive to the intellect.
I agree
 
Mathematics is not a cult. There is no reason to look down on people who apply their knowledge to solve practical problems, as there is no reason to look down on those who apply their knowledge to solve theoretical problems.
 
  • #10
PLug and chug is not mathematics. A lot of people master plug and chug and thus assume falsely that they are good at mathematics.
 
  • #11
Seeing as this thread went nowhere months ago, I can only assume it will go nowhere once again. Locked.

- Warren
 

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