>>> Marylou Jenkins on "Existence Exists" 
 MJ> I am writing a paper on the philosophy of reality and existence. Do
 MJ> you think the relationship between mathematics and reality is actual,
 MJ> that is do we get out mathematics from studying nature, or does it
 MJ> somehow arise from consciousness? 
Speculations will never cease.  Mathematics is a cultural phenomenon.  Do 
note that it has a common cross cultural basis.  Math gets invented, or 
discovered if you like, by curiosity, by attempts to solve mathematical 
problems, by the need to describe precisely.  Physics is a major example that 
has inspired the calculus, vectors and much else.  So you see, mathematics is 
invented to study nature and mathematics does arise from our curiosity and 
inmate inventiveness.  So the answer to your question is yes, both.
In primitive times, there was little mathematics, mostly arithmetic 
noticeably counting.  Without arithmetic a sheep herder would know if a sheep 
was missing not by counting them but by identifying each one individually.  
Gosh he may have had more sheep than his ten figures. -)  Some even counted, 
1,2,many.  So you see, mathematics is a recent arrival, algebra arriving much 
later than Euclid's geometry.
So 5000 years ago what relationship was there between mathematics and 
reality?  Yes there has evolved an actual relationship between humans and 
mathematics.  As humans have differing opinions about reality, the 
relationship between mathematics and reality is like the relationship between 
humans and reality, vague, confused, indecisive. inconclusive.
... I think, therefore the universe thinks.
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