What do you think Mathematics is?

Is it just some numbers we have invented?
Is it really in existence?
Is it just in our mind? It is but an "imperfect approximation" ?

Many discussions are going on in other topics, so I started a new thread.

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Limericks, written by me: http://limericker.blogspot.com

I pick the first one, Mathematics is just a name with some number that invented by humans

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We come without a thing and gone without a thing. We need simple life. A cup of teas and a couple of meals per day, that is good enough. And this is my standard of living.

Why? Can't it really exist and may have been discovered?

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Limericks, written by me: http://limericker.blogspot.com

mathematics is derived from consistencies in reality.

Though if I would give you an apple, and another one, I would not be surprised you would have no more then one or no apples at all.

But this is something more for conditional variables which most of the times are a constant and zero.
(ex. you eat zero apples within the timeframe of giving the apples and counting the number of apples you have afterwards.)

Trying to include all the relevant facts and variables will then always give the best "approximation".

To do this approximation, you might sometimes have to invent a non-realistic reality with the aid of your imagination
With a few people, this inventing and imagining might even prove an yet unknown reality, which could be only be measured a century later with more advanced measuring devices.
Of coarse, this requires that you are aware of the facts (reality).

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Have you found the loop or the loophole?

Mathematics is a language that provides the discipline that allows us to quantify aspects of functions and relationships. It constrains fantasy and allows us to express the laws of physics sufficiently accurately to be falsifiable. Perhaps its the language of the creator (or the process of creation) of the universe. Also, it gives numbers a reason for being of such immense interest to us.

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For those inclined to oppose human meddling with the structure of the universe or the composition and configuration of objects and groups of objects within the universe, consider:
Whether there is a limit to the magnitude of a modulation of chaos below which order remains invariant? Or, is order but a fiction invented by perspectives applied over finite, however large, time intervals?

Absolutely.
One day, as has been suggested elsewhere on this forum, base 2 may one day replace base 10. Humans may one day discover that numbers play anincredibly huge part in the universe.
Remember: Everything has numerical value.

Mathematics has more to with functions and relationships than with numbers or numerals--regardless of the numeral base.

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For those inclined to oppose human meddling with the structure of the universe or the composition and configuration of objects and groups of objects within the universe, consider:
Whether there is a limit to the magnitude of a modulation of chaos below which order remains invariant? Or, is order but a fiction invented by perspectives applied over finite, however large, time intervals?

Right! And in that sense it can be applied to everyday life, and we humans will somehow, someday find a way to apply it to the workings of the universe!

My formal schooling (a long time ago in a galaxy far, far away) was in Math. Most pure Mathematicians would be horrified by the statement that Math is derived from consistencies in reality.

Math is derived from assumptions and logic, in total isolation from the universe around us. Math is a mental game - an artificial human construct. Any application to physical reality is an unintended (and to the real Pure Mathematician, unfortunate and undesireable) side effect.

The fact that it does, so consistently, turn out to be useful in describing the "real world" is really amazing. It irks Pure Mathematicians and delights physicists, but there is no reason why reality should be like that. I think Einstein once said something to the effect that the most amazing thing about the universe is that it is understandable at all. That it happens to be understandable through that artificial mental construct we call Math is one aspect of the amazing story.

I've heard of a theory that humans and other animals share a basic neural system called an "accumulator" that can clearly distinguish numbers of objects less than three or four but that cannot reliably discriminate between bigger numbers. Does anyone know about this?

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If God existed, science would be meaningless.

Does it have anything to do with pi, 3.14...?

Mathematics... a verb or a noun LOL?

I know one thing. Mathematics seems to work!

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I know so much, and yet so little

I disagree wholeheartedly. There are mathematical patterns that exist in nature, that humans discovered (rather than invented). Prime numbers are an example. Certain quantities of apples are able to be divided up evenly whereas others are not. This would still be the case if we weren't here to divide them up.

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Climate Change Australia

Sometimes I don't explain myself very well.

Of course there are mathematical patterns in nature. But we don't "discover" Mathematics the way we discover, say, a new sub-atomic particle. We create Mathematics, the way we created, say, a skyscraper.

Your example: Prime numbers are defined in precise Mathematical terms. Whether they existed in nature in some way since the Big Bang (or before? <G>) or not is of no importance to the Mathematician who developed the concept. Whether the universe exists or not, the Mathematical construct we call prime numbers, would exist. They are independent of physical reality. The fact that we can find them expressed in physical reality is almost a mystical mystery.

There are lots of examples of Math that was developed from assumptions (axioms) and logic, completely out of contact with physical reality. Some of it eventually finds physical application.

Non-euclidean Geometries are a great example. They were developed a couple of hundred years ago - they're weird and go against all our "common sense" (which is Euclidean <G>). They seem to have no application in the physical world. Yet, in the last 50 years or so, it turns out that the universe, on a large scale, is most likely non-euclidean.

When I was in High School, we took a Math section on "Groups, Rings, and Fields". I remember it vividly, because it was the first time I ran across "useless" Math. My teacher couldn't give an example of how group theory could be used. A visiting Math Professor from a very good University dropped into our class one day (a friend of our teacher) and I got a chance to ask him what use there was for this stuff, and he said there wasn't any - that Math didn't have to have a use. It really made an impression on me. But, by the time I finished University, they had discovered that certain sub atomic particles, and the way they interacted with each other, formed groups (Mathematically speaking), and all the Math that they needed to handle them had already been developed and was just sitting there waiting to be applied.

Sure, those sub atomic particles behave as a group whether we notice it or not. But it is equally true that group theory as a discipline would exist if those sub atomic particles behaved randomly. The fact that there is a connection between the two really is amazing, and could take this conversation into the forbidden, religious realm

I think that the elementary math that we use in daily life was discovered.
Calculus was invented to understand mechanics.
But then Mathematicians just began 'playing' with ideas and what could happen, etc. But the thing is the universe seems to be bizzare enough for our invented theories to be apllicable.
But Non-Euclidean geometry could have been invented in order to explain curved surfaces, like mountains,etc.
The essence of our discoveries is curiosity, and that seems to have led us into a whole new world.

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Limericks, written by me: http://limericker.blogspot.com