Instigator / Pro
1
1500
rating
8
debates
50.0%
won
Topic
#5055
Math is an art and is not a science
Status
Finished
The debate is finished. The distribution of the voting points and the winner are presented below.
Winner & statistics
After 1 vote and with the same amount of points on both sides...
It's a tie!
Parameters
- Publication date
- Last updated date
- Type
- Standard
- Number of rounds
- 5
- Time for argument
- Three days
- Max argument characters
- 10,000
- Voting period
- Two weeks
- Point system
- Winner selection
- Voting system
- Open
Contender / Con
1
1492
rating
15
debates
50.0%
won
Description
I am taking the position that math is an art, and that math is not a science. We will use the following definitions:
Math - The discipline studying numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations.
Art - The conscious use of skill and creative imagination especially in the production of aesthetic objects.
Science - The systematic study of the structure and behavior of the physical and natural world through observation, experimentation, and the testing of theories against the evidence obtained.
Round 1
I must first demonstrate that math is an art. That math requires the conscious use of skill should be obvious. If this were not true, no one would ever struggle in math class, nor would unsolved math problems exist. Next, that it requires creative imagination may seem obviously wrong to anyone who has never reached its higher levels, but in fact the math done by grad students and mathematicians requires a great deal of creativity. Consider math prior to later college years as similar to an art teacher guiding students through a drawing line by line. They do not need to apply their own creativity, nor do they need to understand why each step works. They may memorize procedures to draw certain objects like cats and human faces, similar to how a math student memorizes formulas. This knowledge will be helpful for them later on in their journey with art, but it will not remain prevalent. In a similar way, lower level math is simply a way of preparing for "real" math. One could still question this, pointing out that this lower level math is also the math the most people use on a regular basis, however, consider that someone who does not pursue art will likely only need their simple memorized drawings, if anything. Having addressed the fact that lower level math is undeniably uncreative, and having explained how it does not necessarily harm my point, I will now move on to the fact that higher level math, and the math that mathematicians do, is indeed highly creative. Math requires creative problem solving and innovative thinking. Often creativity may be required to have the necessary insight to complete a problem. Take, for example, the problems found on the AMC 12. (1) They require minimal background, but many have clever solutions which would be impossible to find by simply applying the formulas memorized in school. A more detailed investigation into mathematical creativity may also be found in my sources. (2)
Next, I will demonstrate the claim that math is not a science. Firstly, the definition requires that the discipline study the physical and natural world. Math is most certainly not physical. It can be applied to the physical world, but numbers, shapes, and other mathematical objects are not inherently physical, and are rather defined in the abstract. (3) (4) One could still reasonably argue that since math's "intended use" is for the natural, physical word, it does not violate this part of the definition. However, what is a lot clearer is that it does not satisfy the rest of the definition whatsoever. Math does not utilize experimentation or anything resembling the scientific method. Moreover, once a mathematical fact is established, it cannot be challenged by future evidence, since math is not based on evidence, but on deductive proofs. Famous conjectures such as the Collatz Conjecture have been demonstrated to be true up to very high values of n (5), but this does not mean they are accepted as true in general simply from this evidenced based style of reasoning.
Sources:
- https://artofproblemsolving.com/wiki/index.php/AMC_12_Problems_and_Solutions
- https://files.eric.ed.gov/fulltext/EJ750778.pdf
- https://www.math.brown.edu/reschwar/INF/handout3.pdf
- https://www.britannica.com/science/Euclidean-geometry
- https://www.quantamagazine.org/why-mathematicians-still-cant-solve-the-collatz-conjecture-20200922/
Oxford
1.
the systematic study of the structure and behavior of the physical and natural world through observation, experimentation, and the testing of theories against the evidence obtained.
"the world of science and technology"
Similar:
branch of knowledge
area of study
discipline
field
2.
ARCHAIC
knowledge of any kind.
"his rare science and his practical skill"
Numbers themselves are abstractions, yes. But in most cases, barring complex theoretical maths, the abstractions are standing for physical quantities. Regardless of the point of abstract versus physical in nature, math is a study, a knowledge.
The umbrella term of science holds math within a "branch of knowledge", "area of study." Math is indisputably a knowledge of sorts, and thus is within the term science.
Math has its own term "mathematics" to more accurately represent the manner in which it operates.
I will agree that math, especially at high levels is very artful, and deserves to be appreciated for the creativity necessary to perform innovations within the field.
Yet I see no reason that science and art must be mutually exclusive.
Math, in my view is both science and art. To argue that math is not scientific in nature would be very dismissive of the study and understanding of mathematics. To argue that math is not artistic in nature would be dismissive of the creativity and beauty of the subject.
Low level mathematics may be considered more scientific and rigid with no need for artistic thought, and some very high level maths could be considered much more artistic in nature, though they require the rigid science underneath to build upon creatively.
Round 2
Oxford1.the systematic study of the structure and behavior of the physical and natural world through observation, experimentation, and the testing of theories against the evidence obtained."the world of science and technology"Similar:branch of knowledgearea of studydisciplinefield2.ARCHAICknowledge of any kind."his rare science and his practical skill"
By accepting this challenge you agreed to the definitions stated in the description:
I am taking the position that math is an art, and that math is not a science. We will use the following definitions:Math - The discipline studying numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations.Art - The conscious use of skill and creative imagination especially in the production of aesthetic objects.Science - The systematic study of the structure and behavior of the physical and natural world through observation, experimentation, and the testing of theories against the evidence obtained.
Numbers themselves are abstractions, yes. But in most cases, barring complex theoretical maths, the abstractions are standing for physical quantities. Regardless of the point of abstract versus physical in nature, math is a study, a knowledge.
Once again, by accepting this challenge you agreed to the definitions stated in the description. As math was defined in the description, it studies numbers (along with various other abstract entities). Nowhere does it reference physical quantities. You also bring up that math usually uses numbers to represent physical quantities. This is not the case. When learning math in school, word problems may be used to help to ground us in reality, but most math (it does not need to be "complex") is done in the abstract, with no units.
The umbrella term of science holds math within a "branch of knowledge", "area of study." Math is indisputably a knowledge of sorts, and thus is within the term science.
Once again, we are using the definitions provided in the description.
I will agree that math, especially at high levels is very artful, and deserves to be appreciated for the creativity necessary to perform innovations within the field.Yet I see no reason that science and art must be mutually exclusive.
I agree with you here. Science and art are not mutually exclusive. That is why I am making two distinct claims: Math is an art. Math is not a science.
Math, in my view is both science and art. To argue that math is not scientific in nature would be very dismissive of the study and understanding of mathematics. To argue that math is not artistic in nature would be dismissive of the creativity and beauty of the subject.Low level mathematics may be considered more scientific and rigid with no need for artistic thought, and some very high level maths could be considered much more artistic in nature, though they require the rigid science underneath to build upon creatively.
I am glad to hear that we agree that math is an art. We can therefore restrict our attention to the claim "math is not a science."
To summarize, we agree that math is an art. As to my claim that math is not a science, you attempted to debunk my argument that numbers and other mathematical objects are abstract, and not physical as the definition of science would require. I have put forward a counterargument, but regardless of whether or not your refutation of this claim is considered successful, you did not even attempt to refute my claim that math does not satisfy the definition of science because it does not use experimentation and cannot be changed by future evidence, which was the main point of my argument. If there is so much as one condition that the definition of science requires that math does not satisfy, then it does not satisfy the definition of science. Since math does not satisfy this part of the definition, a claim that went unchallenged, it does not satisfy the definition of science.
Forfeited
Round 3
Extend.
Apologies for forfeiture, been having some personal issues.
Science does not require for a knowledge to be physical in nature.
The second definition, the archaic definition defined science as a study or knowledge
"knowledge of any kind".
The first definition refers to naturalistic science, which most people think of when referring to science.
Science is any knowledge.
Math has structure and necessitates knowledge.
Naturalistic science uses math, and math uses science, they are not mutually exclusive and typically have extensive overlap.
Science is an umbrella term that encapsulates any study or knowledge, from biology to theoretical physics, including mathematics. They are all studies of different processes and their interactions.
If you choose to omit the fact that science is an umbrella term that refers to any form of knowledge, then mathematics does not fall within, but I see no reason to omit the origins of science as "knowledge of any kind."
I believe you'd be hard-pressed to find anything that does not fall within science.
Visual arts, baking, gardening, all can be done without the scientific knowledge, but there is scientific knowledge behind them.
The only exceptions to science are personal arbitrary or supernatural claims, including morals, ethics, aesthetics, religion, and mythology, but there is science in the evaluation and the study of these subjects on the large scale.
Perhaps you could make the argument that science ought not to include mathematics, and I could see the potential for that argument, but as it currently is, mathematics is a knowledge of any kind.
In the description for your debate, you omitted the archaic definition for science, which I believe is fallacious.
I see the point of your argument, and I don't necessarily disagree with the basis of your reasoning. You would be correct if your assertion was that mathematics does not fall within physical science, but that is not your assertion. If you truly believe that mathematics does not fall into the umbrella term of science as a knowledge of any kind, then you must also contend that theoretical sciences are not science.
Round 4
Your main point seems to be that you disagree with the definition of science that I am using. Your points are entirely valid, and I would have considered editing the description if you had brought them up before hand, but now that you have already accepted you have agreed to the definitions layed out in the description. The description clearly says "We will use the following definitions." and it is understood that when you accept a debate you agree to all rules and conditions in the description of the debate. (1)
Source:
Sure, then you must contend that all theoretical sciences are equally unscientific due to their nature being non-experimental.
By your definition, math is not a purely physical science, it is a science of abstracts and representations. Though, I feel the need to contend that though math may not be physical in nature, it is absolutely natural.
I see no need to separate science from math or art.
Science is mathematical and artful. Math is artistic and scientific. Art is scientific and mathematical. They may not always be, but often there is overlap between the three.
If science is the understanding of the Universe, math is the language of the Universe, and art is the nature of the Universe.
Round 5
Forfeited
Forfeited
I would like to happily offer to win this debate against you, if you would happily accept my offer, I have very solid evidence and arguments of which are very simplistic and basic to understand.
Only one of my classmates are applying for a B.A in maths. Most others who intend a mathematic route are applying for B.S degrees.
Lot of geometry/math in Islamic art I've heard.
I 'think I recall Clausewitz mentions something about science and art, in his On War book.
Ooh, after Googling that a bit in variation, and reading the description in this debate, I'm interested in how this debate might go.
I don't think I've 'thought much about the concept of art.