很大程度上(不是絕對)，幾何是思維對物理(物質)世界的條理化 ..

That is, geometry is the mind's organizer for sorting out physical phenomena. Notions such as points and lines are in essence organizers and thetefore can not be truly defined rigorously. Algebra provides the language to precisely and accurately manipulate with these organizers. The ongoing discussion here lacks that algebraic language.