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Use this forum to discuss the philosophy of science. Philosophy of science deals with the assumptions, foundations, and implications of science.
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It's well known that math has many uses as an aid to science. Some examples are calculus, differential equations, statistics and even math itself if you count math as a science.
What do you think of recreational math? Is it worthwhile? A noted mathematician named Leonhard Euler explored the Konisberg bridges puzzle. The solution led to graph theory and topology, an important branch of math. Euler and Fermat also explored magic squares (which are the basis of Sudoku puzzles which populate supermarket shelves).
Another noted mathematician, GH Hardy, said he hoped that math will never be useful (although parts of it are quite useful so I wonder if he was misquoted).
What are your thoughts on this?
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Mathematics is a lot like philosophy. Whenever I talk about it with a group of uninitiated friends, I get blank stares and someone quickly changes the subject. But on a serious level, mathematics is commonly known for its use in everyday life such as addition in paying bills, much like how philosophy is known for applied ethical theories, such as altruism. But both have deep theoretical sides that are hard to realize in everyday situations but are (or rather, I consider) very good personal development tools. When I debate the limits of reason, and the philosophy of linguistic history, it is hard to justify in everyday practical terms, but it is beneficial to my well-being in many other important (to me) ways. Whether or not something is worthwhile is very much a subjective value call, although there is evidence that mathematics can improve your cognitive abilities (although I'm inclined to think any activity other than passive entertainment can improve your mind). Engaging in even simple arithmetic for personal pleasure is a good confidence builder on its own. You have a problem, then you solve it. When you are facing problems in life that seem insurmountable, having a problem you can solve and knowing you can solve it can perhaps give you the confidence for harder ones in other situations.
The Mind of MH
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If by useful you mean having some measurable impact on the betterment of society, I would argue that no, math does not have to be useful to be worthwhile. If math is considered a type of language to express a unique type of meme, then even the math that is useless can still have meaning, as it serves to transfer ideas from one person to another or describe an individuals observations to themselves.
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I think usefulness is an good indicator of truth. If any mathematical or scientific theory is false, it ain't gunna be no use coz it don't work.
"There are some ideas so absurd that only an intellectual could believe in them." - George Orwell
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Mathematics is just a puzzle game its usefulness is just by pure chance read.
gamahucherpress.yellowgum.com/wp-conten ... MATICS.pdf
MATHEMATICS ENDS IN MEANINGLESSNESS
(Mathematics will become to be seen as just an artificial man made game an elaborate puzzle game used to exercise the left hemisphere of the brain-with some lucky/fluky applications to the real world. A puzzle game that is made to be consistent with certain rules that are made to make mathematics consistent – and when an inconsistency is found new ad hoc rules-like the axiom of separation- are made to ban the problem and make mathematics consistent again Mathematics will become to be seen as just an artificial man made game an elaborate puzzle game)
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What is the difference between useful and worthwhile?
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Not much difference. But if there is one, I'd say that "worthwhile" is slightly more of a value judgement than "useful". Saying that a tool or activity is useful simply states, as a matter of fact, that it facilitates the achievement of a pre-existing goal. Saying that an activity is worthwhile often seems to be a judgement of its innate merits.
The Dark Wanderer
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If something does not have any practical or leisurely application, then I see no point in pursuing it.
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Math can be recreationsl for sure. Euler managed to show that 26 is the only number squeezed between a square and a cube. Five squared is 25 and three cubed is 27. Finding the proof is recreational. There’s even an entry in wikipedia https://en.m.wikipedia.org/wiki/Recreat ... athematics
Many people find sudoku recreational.
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Addition, subtraction, and other similar operations do not represent the crux of mathematical inquiry or knowledge. They are arithmetic processes, and arithmetic processes are not the essence of mathematics, but just one small part. So, while we say that we use addition, subtraction, etc. on a daily basis, we only mean that we use arithmetic consistently, not mathematics.
Therefore, it is essential to differentiate between mathematics and arithmetic. Mathematics is more like a language; it also involves much intuition and a very strong ability to analyze, synthesize, and extrapolate. Serious mathematics is much like great literature. Their usefulness cannot be defined. They enrich the human experience in myriad ways, and different people draw different things from mathematics and literature. In this sense, mathematics is certainly useful (it enriches the lives of those who practice it seriously). Arithmetic, on the other hand, is ubiquitous and provides more tangible outcomes.
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No. Math does not have to be useful to be worthwhile.
Unknown means unknown.