My name is Joshua Mullan. I am a mathematics student currently completing an undergraduate degree at the University of Melbourne. I plan to eventually complete graduate and post-graduate degrees, and pursue a career in academia.
My coarse-grained interests are primarily mathematics and mathematical physics, and to a lesser extent other areas of applied mathematics. My other main academic interest is law; perhaps I will pursue a law degree and legal career if I lose long-term interest in mathematics. Recently I have also found interest in art, primarily in classical figurative painting and portraiture, but also in photography, poetry, and music. I also spend a lot of time thinking about the philosophical nature of these interests, such as the foundational philosophies of mathematics and the natural sciences, as well as the philosophies of law and art. Such thinking is usually around foundational issues, as well as such matters as “good style.”
My fine-grained interests change as time goes by, but I generally find myself returning to the following. My main mathematical interest is geometry, particularly differential geometry and the geometrical study of differential equations. I also find algebraic geometry quite interesting but to a much lesser extent. I tend to prefer analysis over algebra, but of course it depends on the nature of the study. In general, I will find anything interesting if geometrical techniques are being used to study it. My interests in mathematical physics are generally within the geometric formulations of classical physics, in particular the formulation of classical field theory in terms of multisymplectic geometry. I also find mathematical quantization quite interesting; I hope one day to do some academic research into the quantization of multisymplectic manifolds and mathematically rigorous quantum field theory.*
My enjoyment of mathematical physics stands in stark contrast to my dislike of “theoretical” physics. It is my strong conviction that the level of hand-waving employed by physicists amounts to nothing less than conceptual vandalism. I believe that a strong grounding in rigorous mathematics is not just important, but necessary.
I intend to write occasional notes on this blog on topics that are of interest to me. The main purpose is to aid in the consolidation of my thoughts, and to serve as a future reference for myself. I decided to make them publicly available in blog form so that others who find themselves thinking about these topics can read along and hopefully gain a new perspective.
I WILL ONLY WRITE ABOUT THAT WHICH I AM QUALIFIED TO WRITE. I will not pretend to be an expert about things I am not, and it should be very clear in my posts when I have limited knowledge. An important example is the footnote on this page.
This page was last updated on 15/08/2021.
*I have no deep knowledge of these areas, I am merely interested in them. It is my hope that one day I will be able to speak authoritatively about them.
Of Interest Only to Me... 