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The value of science vs. that of maths
Essentially, I think that the difference between these two mentalities is that mathematics is built upon the premiss that it is a complete system beginning with a set of absolute principles. Science attempts to test absolute principles and, although it aims to found a system, it will ultimately remain incomplete. Mathematics therefore is a system of deduction (where the tenets are at once totally valid and subsequent conclusions must also be seen as absolutely valid) and science is a system of induction (where certainty is scarcely assumed and hypotheses are vigorously tested).
However, if mathematics is to remain 'absolute', it can only operate within defined boundaries and where options and choices are previously stated (and effectively limited). In our modern complex societies, economics and business are the last footholds of the mathematical rationality and with the advent of computers, mathematics as a discipline to be studied has lost its pragmatic worth.
The focus now should reflect the problems facing society (i.e. social and political ones) and a scientific/philosophical approach should be maintained to tentatively explore the unknown. The value of science as an academic discipline remains (as is reflected in the importance of technology and the exploration of our physical/metaphysical situation- developed through sub-disciplines such as physics, psychology and computer science). However, the value of insular, (‘pure’) a priori mathematics has totally diminished and applied mathematics is heading towards the same fate.
Any comments?
However, if mathematics is to remain 'absolute', it can only operate within defined boundaries and where options and choices are previously stated (and effectively limited). In our modern complex societies, economics and business are the last footholds of the mathematical rationality and with the advent of computers, mathematics as a discipline to be studied has lost its pragmatic worth.
The focus now should reflect the problems facing society (i.e. social and political ones) and a scientific/philosophical approach should be maintained to tentatively explore the unknown. The value of science as an academic discipline remains (as is reflected in the importance of technology and the exploration of our physical/metaphysical situation- developed through sub-disciplines such as physics, psychology and computer science). However, the value of insular, (‘pure’) a priori mathematics has totally diminished and applied mathematics is heading towards the same fate.
Any comments?
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maths all the way!!!!!!!!
You need maths to deal with complex systems such as economics and the weather as well. Particularly in regard to economics, applied maths is still important. Pure maths does have some pragmatic value (theoretical physicists tend to need ever more complex mathematical techniques) but it's main draw has always been, and still is, intellectual interest.
Number theory maths (I think) is used in cryptography (encryption, security etc.) alot, so Computers have found a use for pure maths.
Lucid87
Essentially, I think that the difference between these two mentalities is that mathematics is built upon the premiss that it is a complete system beginning with a set of absolute principles. Science attempts to test absolute principles and, although it aims to found a system, it will ultimately remain incomplete. Mathematics therefore is a system of deduction (where the tenets are at once totally valid and subsequent conclusions must also be seen as absolutely valid) and science is a system of induction (where certainty is scarcely assumed and hypotheses are vigorously tested).
However, if mathematics is to remain 'absolute', it can only operate within defined boundaries and where options and choices are previously stated (and effectively limited). In our modern complex societies, economics and business are the last footholds of the mathematical rationality and with the advent of computers, mathematics as a discipline to be studied has lost its pragmatic worth.
The focus now should reflect the problems facing society (i.e. social and political ones) and a scientific/philosophical approach should be maintained to tentatively explore the unknown. The value of science as an academic discipline remains (as is reflected in the importance of technology and the exploration of our physical/metaphysical situation- developed through sub-disciplines such as physics, psychology and computer science). However, the value of insular, (‘pure’) a priori mathematics has totally diminished and applied mathematics is heading towards the same fate.
Any comments?
However, if mathematics is to remain 'absolute', it can only operate within defined boundaries and where options and choices are previously stated (and effectively limited). In our modern complex societies, economics and business are the last footholds of the mathematical rationality and with the advent of computers, mathematics as a discipline to be studied has lost its pragmatic worth.
The focus now should reflect the problems facing society (i.e. social and political ones) and a scientific/philosophical approach should be maintained to tentatively explore the unknown. The value of science as an academic discipline remains (as is reflected in the importance of technology and the exploration of our physical/metaphysical situation- developed through sub-disciplines such as physics, psychology and computer science). However, the value of insular, (‘pure’) a priori mathematics has totally diminished and applied mathematics is heading towards the same fate.
Any comments?
im not sure im at the same level of understanding of maths/science as a lot of people, but i still think maths is pretty important.. one example.. encryption of the higher end now involves primarily the prime numbers (but the very large ones).. the discovery of larger and larger prime numbers is still however confined to the realms of pure maths, and although you say the "advent of computers", maths is still an important discipline to master.. although i do agree there is a greater degree of freedom in this era to study more applied courses e.g. medicine, law, economics.. mainly so that most people can earn more money, maths does not have this attractiveness..
This may be nonsense, or crassly over simplistic, but this is my view...
Biology, at it's core it becomes chemistry. Without basic biochemistry, there would be no other "biology" to study.
Chemistry, when it comes down to it, is physics. The statistical laws which govern chemical reactions and such forth are in essence physics. Also, the fundemental unit of chemistry, the electron, is just one of a nice big happy physical family of leptons.
Physics, when you come down to it is a mathematical representation of everything we perceive in the universe.
My arguement, therefore, is that there is therefore no real difference between science and maths and this question is, therefore, redundant!
Biology, at it's core it becomes chemistry. Without basic biochemistry, there would be no other "biology" to study.
Chemistry, when it comes down to it, is physics. The statistical laws which govern chemical reactions and such forth are in essence physics. Also, the fundemental unit of chemistry, the electron, is just one of a nice big happy physical family of leptons.
Physics, when you come down to it is a mathematical representation of everything we perceive in the universe.
My arguement, therefore, is that there is therefore no real difference between science and maths and this question is, therefore, redundant!
polthegael
This may be nonsense, or crassly over simplistic, but this is my view...
Biology, at it's core it becomes chemistry. Without basic biochemistry, there would be no other "biology" to study.
Chemistry, when it comes down to it, is physics. The statistical laws which govern chemical reactions and such forth are in essence physics. Also, the fundemental unit of chemistry, the electron, is just one of a nice big happy physical family of leptons.
Physics, when you come down to it is a mathematical representation of everything we perceive in the universe.
My arguement, therefore, is that there is therefore no real difference between science and maths and this question is, therefore, redundant!
Biology, at it's core it becomes chemistry. Without basic biochemistry, there would be no other "biology" to study.
Chemistry, when it comes down to it, is physics. The statistical laws which govern chemical reactions and such forth are in essence physics. Also, the fundemental unit of chemistry, the electron, is just one of a nice big happy physical family of leptons.
Physics, when you come down to it is a mathematical representation of everything we perceive in the universe.
My arguement, therefore, is that there is therefore no real difference between science and maths and this question is, therefore, redundant!
but i think the original poster is saying that in essence the 3 sciences are applications of maths, i.e. they are a subset of the whole of maths...
but as science is the only bit of maths that we use every day, can we just exclude all other areas of maths completely.. i.e. is the rest of (pure) maths pointless now that we have advanced our mathematical knowledge to the 3 sciences
Lucid87
Essentially, I think that the difference between these two mentalities is that mathematics is built upon the premiss that it is a complete system beginning with a set of absolute principles. Science attempts to test absolute principles and, although it aims to found a system, it will ultimately remain incomplete. Mathematics therefore is a system of deduction (where the tenets are at once totally valid and subsequent conclusions must also be seen as absolutely valid) and science is a system of induction (where certainty is scarcely assumed and hypotheses are vigorously tested).
Lucid87
However, if mathematics is to remain 'absolute', it can only operate within defined boundaries and where options and choices are previously stated (and effectively limited). In our modern complex societies, economics and business are the last footholds of the mathematical rationality and with the advent of computers, mathematics as a discipline to be studied has lost its pragmatic worth.
Lucid87
The focus now should reflect the problems facing society (i.e. social and political ones) and a scientific/philosophical approach should be maintained to tentatively explore the unknown. The value of science as an academic discipline remains (as is reflected in the importance of technology and the exploration of our physical/metaphysical situation- developed through sub-disciplines such as physics, psychology and computer science). However, the value of insular, (‘pure’) a priori mathematics has totally diminished and applied mathematics is heading towards the same fate.
Any comments?
Any comments?
Without maths, we don't have science.
Some of the main areas of research and interest in physics today rely, at least partially, or originated from, the research of mathematicians. Chaos theory and topology for example.
You could say, I suppose, that without science, maths has no practical function, but you could equally say that without maths, there is no science. I think it is therefore pointless to ask which one has more value as they are inextricably linked.
Some of the main areas of research and interest in physics today rely, at least partially, or originated from, the research of mathematicians. Chaos theory and topology for example.
You could say, I suppose, that without science, maths has no practical function, but you could equally say that without maths, there is no science. I think it is therefore pointless to ask which one has more value as they are inextricably linked.
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But maths is a science 
Pure mathematics is often useless when originally done, but much of today's "useful" maths lay unused for decades. If you are able to expand our knowledge of mathematics it doesn't matter whether you can immediately find a use for it, someone later on may find your work very useful indeed.
Pure mathematics is often useless when originally done, but much of today's "useful" maths lay unused for decades. If you are able to expand our knowledge of mathematics it doesn't matter whether you can immediately find a use for it, someone later on may find your work very useful indeed.
Maths hints at all sorts of things when doing science, I'm sure there are numerous examples of physicists having identified some behaviour, then a mathematician comes along and say "is the negative root significant?" or similar. As has already been excellently stated in the thread, they're inextricably linked.
Pure maths at a high enough level becomes more of an art subject than a science (claimed by G Hardy in "A mathematician's Apology") but an art form which can only be appreciated by a comparitavely small group of specialists but regularly people can find practical uses for new aspects of mathematics retrospectively (as Revelation said, pure maths was used retrospectively in both cryptology and in different aspects in computing). If new concepts had not been found by trying to further the knowledge of pure maths, then we may not have understood or invented a great many more "practical" objects and concepts which rely on new principles. Who is to say when we have reached the practical end of pure maths? Should we have stopped when we could do simple arithmetic? Should we have stopped when we discovered irrational numbers? Should we have stopped with the advent of calculus? Should we have stopped when we discovered imaginary numbers? Should we stop with basic topology? The answer to all of those must be no. It's interesting that you describe maths as "defined in boundaries" when I'd argue that physics, chemistry and biology have far more defined boundaries. Maths is the only science in which everything that proceeds a new theory is still valid, whereas in the other sciences, new theories replace redundant ones. Many of the major developments in mathematics over the past two millenia have been when mathematicians have changed the very fundamentals of mathematics. Axioms may be agreed apon, but people may still work outside the boundaries of the status quo.
As for the argument that the other sciences should be further studied to "tentatively explore the unknown", why can we not do the same in maths? Who is to judge when mathematics has reached it's useful apocalypse? If we don't study the maths alongside the developments in the other sciences, you will quite probably reach a point where the maths we have cannot find solutions to problems or be very inefficient.
Good topic though.
As for the argument that the other sciences should be further studied to "tentatively explore the unknown", why can we not do the same in maths? Who is to judge when mathematics has reached it's useful apocalypse? If we don't study the maths alongside the developments in the other sciences, you will quite probably reach a point where the maths we have cannot find solutions to problems or be very inefficient.
Good topic though.
Not having done further maths at A-Level, I'm probably going to sound like a dopey pillock when I ask this, but how do mathematicians rationalise the existence of imaginary numbers like i? (isn't i the square root of -1 or something?)...in which case, only a +ve and a -ve multiplied can give an overall -ve number, so isn't it impossible for -ve numbers to have sq. roots? I'm very confused about this...
However, I do agree about pure maths transcending in to the realms of art the deeper you go into. That's what I've been told by many mathematicians, whereas the reason I have always liked maths is because it's so logicaL, and it "doesn't move" as it were, but this sq.root of -ve number thing seems to throw that reasonong completely out of the window!
However, I do agree about pure maths transcending in to the realms of art the deeper you go into. That's what I've been told by many mathematicians, whereas the reason I have always liked maths is because it's so logicaL, and it "doesn't move" as it were, but this sq.root of -ve number thing seems to throw that reasonong completely out of the window!
meepmeep
Maths is the only science in which everything that proceeds a new theory is still valid, whereas in the other sciences, new theories replace redundant ones. Many of the major developments in mathematics over the past two millenia have been when mathematicians have changed the very fundamentals of mathematics. Axioms may be agreed apon, but people may still work outside the boundaries of the status quo.
I would disagree with the only in that first sentance, sometimes theorys do not replace old one in science, and work in conjunction with exsisting theories, the best example being Newton's laws and Ensteins theory of Relativity. I see your point, but I think the same thing can happen in science (hence the objection to only) tho I think as you say it happens to a lesser extent.
There are several interesting views on this matter... but
a- if fundamental mathematical axioms are being redefined continuously, how can 'pure maths transcend into the realm of art' if it hasn't found its figurative brush
b- it seems as though maths attempts to bring absolutism and symmetry to everything it analyses and represents and it is thus continually wrong because to begin to make complete logical proofs without specific context, would mean that mathematicians are fully aware of every factor in existence- which they simply cannot be. Maths can only work with predefined boundaries e.g. with numerical data- the only real use for maths- and this can now be performed by computers.
c- on the other hand, aren't most scientific hypotheses rooted in experimental (empirical) evidence and are constantly qualified (i.e. crudely with ‘if’ or ‘but’- without declaring absolutism). They are also split into sub disciplines e.g. physics, biology- each with different principles instead of trying to tie ends that aren't there together.
Hence science's real search for the truth, hence science’s greater value??
a- if fundamental mathematical axioms are being redefined continuously, how can 'pure maths transcend into the realm of art' if it hasn't found its figurative brush
b- it seems as though maths attempts to bring absolutism and symmetry to everything it analyses and represents and it is thus continually wrong because to begin to make complete logical proofs without specific context, would mean that mathematicians are fully aware of every factor in existence- which they simply cannot be. Maths can only work with predefined boundaries e.g. with numerical data- the only real use for maths- and this can now be performed by computers.
c- on the other hand, aren't most scientific hypotheses rooted in experimental (empirical) evidence and are constantly qualified (i.e. crudely with ‘if’ or ‘but’- without declaring absolutism). They are also split into sub disciplines e.g. physics, biology- each with different principles instead of trying to tie ends that aren't there together.
Hence science's real search for the truth, hence science’s greater value??
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