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WarwickZ
My name is Rick Zeamer, User name WarwickZ.
My main interest is in the philosophy of mathematics specifically in forming a foundation for mathematics not employing the presently accepted logic. As such I am concerned with a precise definition of what an object is, and what it is not. This question is relevant to the paradoxes of set theory and the nature of infinitesimals. The work I have done on this might be viewed as a continuation of Husserl's logical investigations and grows directly from the philosophy of science espoused by Edward Pols.
The foundation I am working on:
Apart from attempting to establish a philosophically non naïve foundation for mathematics my mathematical interests are in combinatorial group theory especially the theory of free groups and their associated near-rings. My PhD work was in this field and conjectured that characteristic subgroups of a free group of infinite rank can be factored uniquely as a product of primes. Proving this remains to the best of my knowledge an open problem. My attempts to prove it have led me to study graphs and their relation to subgroups of free groups.
I have certain political persuasions, such as that maps should be written on the right ((x)f rather than f(x)) and that quaternions are the right way to approach vector algebra and the mathematics of physics generally.
I have a strong interest in geometry and am always trying to find more transparent proofs of important results. My knowledge of physics is elementary but I am interested in learning more.
I would be happy to collaborate with anyone who can put up with my ignorance.
My main interest is in the philosophy of mathematics specifically in forming a foundation for mathematics not employing the presently accepted logic. As such I am concerned with a precise definition of what an object is, and what it is not. This question is relevant to the paradoxes of set theory and the nature of infinitesimals. The work I have done on this might be viewed as a continuation of Husserl's logical investigations and grows directly from the philosophy of science espoused by Edward Pols.
The foundation I am working on:
Apart from attempting to establish a philosophically non naïve foundation for mathematics my mathematical interests are in combinatorial group theory especially the theory of free groups and their associated near-rings. My PhD work was in this field and conjectured that characteristic subgroups of a free group of infinite rank can be factored uniquely as a product of primes. Proving this remains to the best of my knowledge an open problem. My attempts to prove it have led me to study graphs and their relation to subgroups of free groups.
I have certain political persuasions, such as that maps should be written on the right ((x)f rather than f(x)) and that quaternions are the right way to approach vector algebra and the mathematics of physics generally.
I have a strong interest in geometry and am always trying to find more transparent proofs of important results. My knowledge of physics is elementary but I am interested in learning more.
I would be happy to collaborate with anyone who can put up with my ignorance.
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