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Functor97
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I have been thinking much on the nature of pure mathematics. I believe this forum would make the best place to post over say the philosophy section, as i am more interested in the opinions of working mathematicians and physicists than philosophers.
In my opinion pure mathematics is the core of every academic discipline we humans have so far explored. I would extend that to state, that mathematics is in essence the art of thought it is the science of anything, and that all other disciplines may be reduced to applied mathematical problems. I understand this is quite a contentious statement, and i would gladly welcome your point of view.
The more i ponder this, the more i think that mathematics is all we have. We interact with the outside world via our senses, but these senses give us a warped view of our surroundings. This screen has no color, but our retina perceives color, due to the wavelength of electromagnetic radiation reflected, and our understanding of electromagnetic radiation is based upon physical formula which are simply applied forms of mathematical theorems. Quantum mechanics does not make sense to our intuition built up on the large scale, so we rely upon mathematics to understand the phenomenon. Many physics students object to quantum mechanics and claim that it is fundamentally wrong or not complete, because they cannot envision exactly where a particle is at a given instant, yet the mathematics still guides us. When people ask "why do like poles repel?", the answer can get quite complex leading to quantum field theory, and if an individual keeps asking "why?" each subsequent step is correct, it quickly devolves into mathematical reasoning not physical. This has led me to agree with max tegmark and a few others who conjecture that our universe is actually a mathematical structure, yet i do have a problem with this as to why conscious minds view only a certain form of mathematics. Does our pursuit of knowledge being grounded in mathematics, mean that external reality (if there is any?) is grounded in mathematics, or is that just our best guess, so to speak.
More generally, do you believe that mathematical inquiry, such as say number theory, complex analysis or functional analysis explains more about reality then quantum field theory for when we solve number theory problems, are we working with the very code of the cosmos? So our theories of physics are just the subset of our Matthematical theorems. Do many mathematicians hold this view? I guess this is some form of Neo Platonism, and as an atheist, i find the issue of an external mathematics problematic. Do you believe that pure mathematics should be given credence over particle physics, for if this conjecture is true, isn't the dependence of the Axiom of choice within a large cardinal system just as suitable a grand unified theory as M theory?
Finally if mathematics is just axioms, and we cannot prove an axiom to be true, and yet mathematics is the basis of all science, does this mean absolute truth is beyond us? (Not advocating the ends justifies the means)
In my opinion pure mathematics is the core of every academic discipline we humans have so far explored. I would extend that to state, that mathematics is in essence the art of thought it is the science of anything, and that all other disciplines may be reduced to applied mathematical problems. I understand this is quite a contentious statement, and i would gladly welcome your point of view.
The more i ponder this, the more i think that mathematics is all we have. We interact with the outside world via our senses, but these senses give us a warped view of our surroundings. This screen has no color, but our retina perceives color, due to the wavelength of electromagnetic radiation reflected, and our understanding of electromagnetic radiation is based upon physical formula which are simply applied forms of mathematical theorems. Quantum mechanics does not make sense to our intuition built up on the large scale, so we rely upon mathematics to understand the phenomenon. Many physics students object to quantum mechanics and claim that it is fundamentally wrong or not complete, because they cannot envision exactly where a particle is at a given instant, yet the mathematics still guides us. When people ask "why do like poles repel?", the answer can get quite complex leading to quantum field theory, and if an individual keeps asking "why?" each subsequent step is correct, it quickly devolves into mathematical reasoning not physical. This has led me to agree with max tegmark and a few others who conjecture that our universe is actually a mathematical structure, yet i do have a problem with this as to why conscious minds view only a certain form of mathematics. Does our pursuit of knowledge being grounded in mathematics, mean that external reality (if there is any?) is grounded in mathematics, or is that just our best guess, so to speak.
More generally, do you believe that mathematical inquiry, such as say number theory, complex analysis or functional analysis explains more about reality then quantum field theory for when we solve number theory problems, are we working with the very code of the cosmos? So our theories of physics are just the subset of our Matthematical theorems. Do many mathematicians hold this view? I guess this is some form of Neo Platonism, and as an atheist, i find the issue of an external mathematics problematic. Do you believe that pure mathematics should be given credence over particle physics, for if this conjecture is true, isn't the dependence of the Axiom of choice within a large cardinal system just as suitable a grand unified theory as M theory?
Finally if mathematics is just axioms, and we cannot prove an axiom to be true, and yet mathematics is the basis of all science, does this mean absolute truth is beyond us? (Not advocating the ends justifies the means)
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