Dear All,

I would like to share with you a paper 'The Constituents of Sets, Numbers, and Other Mathematical Objects: Part One' of my good friend The Prophet of Köningsberg in which he constructed a category of constituent structures (sans cardinality).  As you may know, Cantor, in abstracting his Kardinalen of lauter Einsen, seems to have intended it as a first step towards getting at qualities (see Footnote 4 on p. 11 in Cantor's iauter Einsen).  Be that as it may, Bourbaki's deduction of structures (with structures as geometric objectifications of conceptualizations of qualities) can be considered as inaugurating the scientific study of qualities (Lawvere & Schanuel, Sets for Mathematics, p. 240).  Also, note that Professor F. William Lawvere in his seminal paper Axiomatic Cohesion explicitly states that he looks forward to the development of "categories of constitutive relations" for the express purpose of studying the constituent relations of cohesively varying bodies all around us directly in terms of their qualities as a refinement of the contemporary quantitative approximations of the objective qualities ( https://conceptualmathematics.wordpress.com/2012/06/04/perugia-notes-prof-f-w-lawvere/; https://zenodo.org/records/7164047. p. 2; https://conceptualmathematics.wordpress.com/wp-content/uploads/2013/02/spacesanddatatypes.pdf, p. 105).

In the light of all of the above, am I mistaken in thinking that mathematics is about qualities (along with their conceptualizations), while most mathematicians along with the rest of the humanity think mathematics is all about quantities (and calculations)?  If so, is there a need for a math outreach (a' la Galileo's physics outreach)?

Thanking you, yours truly, posina