What is the Study of Mathematics?

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Discussion Overview

The discussion revolves around the nature and definition of mathematics, exploring its scope as a discipline. Participants examine whether mathematics is primarily a study of patterns, relationships, or a language, and how it relates to other fields such as physics and biology.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that mathematics is the science of patterns, suggesting it helps in understanding and reconstructing complex structures, like a Persian rug.
  • Others argue that mathematics is fundamentally about numbers and operations, with basic definitions stemming from simple functions like addition.
  • A viewpoint is presented that mathematics serves as a language, characterized by its unambiguous and consistent nature, facilitating clarity in scientific expression.
  • Some participants assert that mathematics encompasses more than just numbers and patterns, extending into logical frameworks and abstract concepts, such as in real analysis and category theory.
  • One participant defines mathematics as the study of relationships, emphasizing the significance of relations in mathematical structures.
  • Concerns are raised about defining mathematics based solely on elementary concepts, with a suggestion that advanced mathematics involves broader logical explorations.
  • Precision in mathematical thought is highlighted as a key characteristic, with benefits including clearer communication and systematic analysis of ideas.
  • There is a contention regarding the definition of geometry within mathematics, with differing opinions on its foundational axioms and dimensionality.
  • Some participants reference definitions from dictionaries, noting that mathematics involves relationships between spaces and serves as a language of measurements.

Areas of Agreement / Disagreement

Participants express a variety of perspectives on the definition and scope of mathematics, indicating that multiple competing views remain. There is no consensus on a singular definition, with ongoing debate about the nature of mathematical study.

Contextual Notes

Limitations in the discussion include varying interpretations of foundational concepts, the dependence on specific definitions, and unresolved questions regarding the application of mathematical operations to different number types.

  • #61
Humans are pattern-seeking creatures. They tend to see patterns where there are not any (in numerous ways). Psychologists have long documented this phenomena. There are a series of optical proofs that one can find, Philosopher Daniel Dennet has a lecture on youtube where he displays these test:

http://youtube.com/watch?v=wIdxbJyvfNw&feature=related

This is proof of our ability to see optical patterns where there aren't any.

Mathematics, logic, and religion (to a certain extent) are the same property of pattern-seeking on a different level than the optical example above. We tend to seek symmetry and patterns even in the morals we create ("treat others how you want to be treated").

Without qualitatively assigning experiential properties to math, it really has nothing to do with reality. We show in the physical sciences that things can behave "like" a certain function in mathematics, but that is a metaphor, and not a sort of mystical sign that mathematics is inherent in the universe. Mathematics must be used like quilt material to best describe all aspects of reality, and it must be described with experiential, qualitative attachments.

There is no absolute math that can describe everything as it evolves in time... that, so far has only been within the capabilities of reality itself.
 
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  • #62
Pythagorean said:
Humans are pattern-seeking creatures. ...Without qualitatively assigning experiential properties to math, it really has nothing to do with reality. We show in the physical sciences that things can behave "like" a certain function in mathematics, but that is a metaphor, and not a sort of mystical sign that mathematics is inherent in the universe. Mathematics must be used like quilt material to best describe all aspects of reality, and it must be described with experiential, qualitative attachments.

There is no absolute math that can describe everything as it evolves in time... that, so far has only been within the capabilities of reality itself.

You put it very clearly. All I'd add is that as well as pattern-seeking, we spend a lot of time pattern-describing. It's very helpful for evolutionary success! Thanks, from your (approximate) antipodes.
 
  • #63
Dictionary.com said:
The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols.

...So basically the study using calculations?
 
  • #64
who am i?

Oh Math, so deep and beautyfull lady... i will not talk about math as i think that term is contaminated with dozens of thousands years of fascination and misconception.
lets talk about thought. Math is founded on logic and logic is founded on thought. Without the identity principle, trueness and falseness are the same and there is no possible logic, as everything becomes the same thing and nothing becomes all. But the reality is not founded above any concept, but on perception, no matter who perceives, a photon or a human being, an idea or a concrete brick, everything changes its state when perceive something else. reality is founded on the mutual influence of the beings (or things if you prefer) i.e. all that exists, if exists out of itself, communicate. and if that thing has a memory, i.e. perceives the time i.e. follow the changes of its internal states, that thing is able to distinguish between at least 2 different perceivments and can be used to do logic, math etc... But and the reality behind all that mechanical stuff? even the more abstract idea has a kind of mechanic, turning a human being not more than a dog or any other physical system. The internal simulacrum used to model (describe) the reality is as fake as the simulated reality itself, and some times appear the same.
But and the absolute reality? we feel something else, or not?
yes, and that is the real reality, the feelings space. Feeling is the universal language, not Math.
thought, and logic, and math, and concrete jungles are made of feelings.
maybe i am too stupid for that forum, but i am not too stupid for the love embrace with the final reality, that's the way i feel.
PS. Oldman, are you the oldman Mc from FICS?
 
  • #65
musicor said:
Oldman, are you the oldman Mc from FICS?

No, I'm not.
 

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