| In a sense computer and electrical engineers/scientists did largely map out the base layers, over ~150 years from the 19th century through the mid 20th. I think equipment (broadly speaking) is foundational for mathematics. The "stack", as far as I interpret it, is something like 1. Being 2. Communication 3. Equipment -- a device you can put marks on and read off of 4. Discipline -- ability to reliably and skillfully manipulate the device 5. Submission The stage is set at this point for some "elementary mathematics" -- think back to elementary school. 6. Symbolism -- the equipment is not just equipment. Mathematical relevance springs here. 7. Geometry -- from vision we see area and edges, objects of perception, they are interpreted as mathematically relevant and hence symbolized. 8. Algebra -- manipulating our equipment with discipline, an equivalence is perceived between different sequences of operations. 9. Proposition -- conviction the relevant facts of geometry and algebra can be formulated clearly in declarations of the sort "if ... then ..., and ... (... and etc)". Higher level mathematics 10. Refinement
11. Proof 12. Application
13. Theory 14. Computer science, engineering, and design ... |