Does Classifying Mathematics as a Science Affect Its Usefulness?

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Discussion Overview

The discussion revolves around whether mathematics should be classified as a science. Participants explore the definitions of science, the methodologies of mathematics and science, and the philosophical implications of these classifications. The conversation includes theoretical perspectives and personal interpretations of the nature of mathematics and its relationship to reality.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Philosophical reasoning

Main Points Raised

  • Some participants argue that mathematics is not a science, citing its reliance on proofs rather than experimental validation.
  • Others propose that mathematics, while different from natural sciences, still qualifies as a science, possibly as a formal science.
  • A distinction is made between natural sciences, which are concerned with reality, and mathematics, which is seen as an abstraction not directly tied to reality.
  • Some participants emphasize that the methodologies of science and mathematics are fundamentally different, with science relying on experimentation and mathematics on axiomatic consistency.
  • There are claims that certain branches of mathematics, such as statistics and optimization, do engage with reality, though this is contested.
  • Several participants express the view that mathematics is more akin to an art or a language, rather than a science.
  • Discussions on the historical context of mathematical concepts, such as complex numbers, highlight their development for beauty or utility rather than realism.
  • Some participants identify as platonists, suggesting that mathematical concepts exist independently of human thought.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether mathematics should be classified as a science. Multiple competing views are presented, with ongoing debate about the definitions and implications of such classifications.

Contextual Notes

Definitions of "science" vary among participants, leading to differing conclusions about the classification of mathematics. The discussion reflects a range of philosophical perspectives, including realism and idealism, which influence participants' views on the relationship between mathematics and reality.

  • #31
Tom Gilroy said:
Certainly if computer science is a science, then mathematics must also qualify.

There's truth to the adage: "Anything that calls itself a science, isn't a science."
 
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  • #32
CRGreathouse said:
There's truth to the adage: "Anything that calls itself a science, isn't a science."
Indeed. I mean, who came up with "Political Science" anyways. That makes no sense. In my opinion, whoever thought that up needs a smack. Hard.
 
  • #33
Unroductive Arguments! More than one kind of science exist. Life/Biological Sciences, Behavioral Sciences, ... some method should exist for classifying computer fields and mathematics as whatever classification of sciences they are.

If Mathematics is a science, then is it more useful than if it were not?
If Mathematics is not a science, then is it less useful than if it were?
Is it any less or more important just because it may or may not be a science?
Many things we do relate to various Mathematics, and the relevant Mathematics helps to understand those "many things...". Same with many things which we may study.
 
  • #34
I retract my previous comments that mathematics is not a science.

Mathematics stands in the midpoint between philosophy and science. It could be defined as either.
 
  • #35
mathematicians argue from definitions. definitions vary but here are several.. mathematics certainly fits some of them;

a branch of knowledge or study dealing with a body of facts or truths systematically arranged and showing the operation of general laws: the mathematical sciences.
2.
systematic knowledge of the physical or material world gained through observation and experimentation.
3.
any of the branches of natural or physical science.
4.
systematized knowledge in general.
5.
knowledge, as of facts or principles; knowledge gained by systematic study.
6.
a particular branch of knowledge.
7.
skill, esp. reflecting a precise application of facts or principles; proficiency.
 
  • #36
symbolipoint said:
Unroductive Arguments! More than one kind of science exist. Life/Biological Sciences, Behavioral Sciences, ... some method should exist for classifying computer fields and mathematics as whatever classification of sciences they are.

If Mathematics is a science, then is it more useful than if it were not?
If Mathematics is not a science, then is it less useful than if it were?
Is it any less or more important just because it may or may not be a science?
Many things we do relate to various Mathematics, and the relevant Mathematics helps to understand those "many things...". Same with many things which we may study.

However we define Mathematics, it won't change anything about how useful it is to us. We can still choose to classify it in whichever way we find appropriate.
 

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