I was wondering, is mathematics an invention or a discovery by man ?
How is it possible that we can use mathematics to describe very complex situations and processes in various fields such as physics, astronomy, logic, economics, information technology etc, etc.
In short, what constitutes the relationship between reality and mathematics ?
Is mathematics the "metaphysics" of science or what ?
Just wondering ... any thoughts ?
IvanH.
Originally posted by ivanhoeJust a thought. if no one is around to do math, is it still in existence? It would seem to me that math is an invention of our minds to describe what's going on, not something that is independant of observation. 😀
I was wondering, is mathematics an invention or a discovery by man ?
How is it possible that we can use mathematics to describe very complex situations and processes in various fields such as physics, astronomy, logic, economics, ...[text shortened]... t ?
Just wondering ... any thoughts ?
IvanH.
Originally posted by Cheshire Cat
Just a though. if no one is around to do math, is it still in existence? It would seem to me that math is an invention of our minds to describe what's going on, not something that is independant of observation. 😀
Very interesting thought ...
I wonder what kind of consequenses arise assuming this ...
IvanH.
Mathematics deals with absolute truth. You can be sure Pythagoras' Theorem still holds on the other side of the universe. It is inconceivable that it or any other mathematical truth could be found to be false. (Incidentally I believe it has been etched onto the side of deep space probes, the reasoning being that any alien civilization the probe might encounter MUST have discovered P.T. in order to reach a certain level of development). That's what sets math(s) apart from other scientific and artistic diciplines - you're dealing with the fundamentals of reality, not human constructs. So we mustn't flatter ourselves that we've invented them! They were already there for the discovering.
Originally posted by jotWhether Pythagora's Theorem holds true on the other side of the universe does not matter. What matters is that it does not exist if some thinking being cannot observe it.
Mathematics deals with absolute truth. You can be sure Pythagoras' Theorem still holds on the other side of the universe. It is inconceivable that it or any other mathematical truth could be found to be false. (Incidentally I believe it has been etched onto the side of deep space probes, the reasoning being that any alien civilization the probe might encount ...[text shortened]... 't flatter ourselves that we've invented them! They were already there for the discovering.
Originally posted by royalchickenCould you explain this thought a bit more...(perhaps with simpler words😕)
Mathematics deals not with absl=olute truth, but with truth relative to arbitrary axioms. In this sense I feel the logical machinery behind it is absolute and independent of specific minds.
Mathematics is a body of ideas, a few of which are known to human minds. They are discovered and navigated through by logical inference (deduction) from a few assumptions (axioms) selected by the mathematician (navigator). The notations, conventions, and symbols are all invented by the navigator, but the ideas themselves exist as all other ideas do, without the aid of any mind. A mathematical statement is "true" if it follows logically from the axioms selected.
Originally posted by royalchickenThis certainly explains...
Mathematics is a body of ideas, a few of which are known to human minds. They are discovered and navigated through by logical inference (deduction) from a few assumptions (axioms) selected by the mathematician (navigator). The notations, conventions, and symbols are all invented by the navigator, but the ideas themselves exist as all other ideas do, w ...[text shortened]... ny mind. A mathematical statement is "true" if it follows logically from the axioms selected.
"My shipwrecked soul, cast upon empty, bitter bones.
Alone, i pondered how I came to such a state.
Alas, no curcease found I but knowing
I alone did navigate."
Originally posted by royalchickenI'm afraid I must disagree. No idea could exist if it was not thought of. Ideas are not indepent of thought they are created by thought. How could an idea exist if it was not thought up by the mind?
Mathematics is a body of ideas, a few of which are known to human minds. They are discovered and navigated through by logical inference (deduction) from a few assumptions (axioms) selected by the mathematician (navigator). The notations, conventions, and symbols are all invented by the navigator, but the ideas themselves exist as all other ideas do, w ...[text shortened]... ny mind. A mathematical statement is "true" if it follows logically from the axioms selected.
Originally posted by Cheshire CatOne problem with your argument. You say that it is an "Idea". Math is not an "Idea". If it were an idea, you would be correct. But math exists indepently of mind. It is not therefore an "Idea". It just is. Kind of like god... only repeatable, visible, reliable, truthful, demonstrable and useful.
I'm afraid I must disagree. No idea could exist if it was not thought of. Ideas are not indepent of thought they are created by thought. How could an idea exist if it was not thought up by the mind?
Originally posted by Cheshire CatCC, how does the physical world exist independently of your mind? If you take this position, then everything is a mental construct. If you wish to put anything outside of mind, abstractions must be included. But this is a longwinded and ever-present debate among mathematicians. "Do we invent or discover?" Paul Erdos, for example, would agree with me, as would GH Hardy. You would have people like Isaac Newton and Blaise Pascal on your side. I mention the names because they all wrote interesting things on this subject.
I'm afraid I must disagree. No idea could exist if it was not thought of. Ideas are not indepent of thought they are created by thought. How could an idea exist if it was not thought up by the mind?
One notable vacillator on this subject was Henri Poincare, whose popularizations of science are some of the best around.
I'm mostly just saying that if mathematicians "invent", then physical scientists really do too, becasue the nature of the existence of "objects" is just as questionable as that of ideas.
Originally posted by StarValleyWyA fine post sir 😀. Care to elaborate some more as you present a nice characterization?
One problem with your argument. You say that it is an "Idea". Math is not an "Idea". If it were an idea, you would be correct. But math exists indepently of mind. It is not therefore an "Idea". It just is. Kind of like god... only useable, visible, reliable, truthful, demonstrable and useful.