Comments on: Applied vs Theoretical Mathematics: False Dichotomy /rants/applied-vs-theoretical-mathematics-false-dichotomy/ sealed abstract class drew {} Sun, 27 Mar 2016 22:51:38 +0000 hourly 1 By: Thomas Munroe /rants/applied-vs-theoretical-mathematics-false-dichotomy/comment-page-1/#comment-7798 Wed, 09 Jan 2013 14:13:46 +0000 /?p=811#comment-7798 I am not a mathematician but I enjoyed your article immensely. I also agree with you. I believe “equal” is both a theoretical and applied term depending upon usage therefore it could be called just math. Equal also has other uses and definitions such as social status or physical match.

I dated a woman many years ago who had a masters degree in theoretical math. Now 25 years later I wondered what the hell was theoretical math? Thank you for helping me gain some understanding.

By: JP /rants/applied-vs-theoretical-mathematics-false-dichotomy/comment-page-1/#comment-7576 Mon, 21 May 2012 16:39:20 +0000 /?p=811#comment-7576 “If my motivation for doing mathematics…”

This is my understanding of the difference between pure and applied: one’s motivation.

As you say, language and therefore meaning comes prior to grammar, and when one speaks of “pure mathematicians” he/she means those who do mathematics for no reason other than to do so, whereas “applied mathematicians” are doing mathematics entirely for the sake of solving a problem *outside of “mathematics proper”*.

One difficulty is that we are attempting to create a two-party mathematical state, to use a political metaphor, whereas these categories do not actually partition the field.

I personally use the term “theoretical mathematics” to obscure the motivation; i.e., the theories (methods, axioms, &c.) underlying the final results. This is in some amount of opposition to especially computational mathematics, where one applies previously-discovered mathematical methods to uncover new results, often in distinct fields (which, as observed by the author, often have or appear to have a one-to-one mapping with the relevant mathematical structures).

It seems that such results sometimes lie outside of pure mathematics because they are particularities, whereas pure mathematics seeks general statements. Of course, a number of such results may then result in a general pattern and so feed back into pure mathematics.

Via science, engineering, “applications”, thought, or happenstance, the mathematical theoretician is motivated by all, but seeks the theoretical, mathematical foundation upon which the results may be “explained” or “proved”.

By: Evan /rants/applied-vs-theoretical-mathematics-false-dichotomy/comment-page-1/#comment-7517 Wed, 22 Feb 2012 02:11:00 +0000 /?p=811#comment-7517 I must respectfully disagree. Consider theoretical art versus applied art. Some people just want to sit in their studio and paint all day. That’s theoretical. Some people want to make art that people can see, touch, or even buy. That’s applied. Applied mathematicians want to use a tool to solve a problem. Theoretical mathematicians just want to use a tool for the experience of using a tool. That is not just a semantic distinction.

By: On music | Sealed Abstract /rants/applied-vs-theoretical-mathematics-false-dichotomy/comment-page-1/#comment-6908 Fri, 02 Sep 2011 09:16:54 +0000 /?p=811#comment-6908 […] blogged in the bast about how I don’t believe in a distinction between applied and theoretical math. But there is a distinction, a distinction […]