We give a brief overview of the evolution of mathematics, starting from antiquity, through
Renaissance, to the 19th century, and the culmination of the train of thought of history’s greatest
thinkers that lead to the grand unification of geometry and algebra. The goal of this paper is not a
complete formal description of any particular theoretical framework, but to show how extremisation
of mathematical rigor in requiring everything be drivable directly from first principles without any
arbitrar…
Read moreWe give a brief overview of the evolution of mathematics, starting from antiquity, through
Renaissance, to the 19th century, and the culmination of the train of thought of history’s greatest
thinkers that lead to the grand unification of geometry and algebra. The goal of this paper is not a
complete formal description of any particular theoretical framework, but to show how extremisation
of mathematical rigor in requiring everything be drivable directly from first principles without any
arbitrary assumptions actually leads to relaxing the computational difficulty along with maximal
conceptual clarity. With this, we consider a revision of the foundations of elementary geometry
and algebra based on the work of Grassmann and Clifford and apply it to conceptual and practical
problems of past and present modern mathematics and mathematical physics.
