History of Mathematics:
Where Does Mathematics Come From?
We know that tallies, in some form, originated in sub-Saharan Africa some 35,000 years ago. You also learned about the number systems, equations and geometry practiced by the Egyptians and Mesopotamians about 4000 years ago. Then, you learned about the Greeks who married the practical mathematics of Egypt and Mesopotamia with philosophy, logic, and abstraction. You have seen everything from basic tallies to calculus in countries in various parts of the world.
Viewpoints
Video: Stanislas Dehaene, “Where do mathematical intuitions come from?” (7-8 min)
Plato – Mathematical Platonism
Hardy, Godfrey H., A Mathematician’s Apology, London, Cambridge University Press, 1941.”
I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove and which we describe grandiloquently as our “creations,” are simply the notes of our observations.”
Kronecker, Leopold, Jahresberichte der Deutschen Mathematiker Vereinigung. (1893)
“God made the integers, all else is the work of man.”
Lakoff, George, Núñez, Raphael E., Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being. Basic Books (2000)
“Mathematics as we know it is … a product of the human mind…. It comes from us! We create it, but it is not arbitrary [because] it uses the basic conceptual mechanisms of the embodied human mind as it has evolved in the real world. Mathematics is a product of the neural capacities of our brains, the nature of our bodies, our evolution, our environment, and our long social and cultural history.” (page 9)
Is Mathematics Invented or Discovered?
For many centuries, the history of mathematics has gone back and forth trying to decide this question. Do mathematicians just discover and “name” relationships that have an independent existence or do they create the relationships in their own minds and then apply them where they seem to fit in reality? Are they are mental constructs only?
Respond
Write a post responding to the questions: Where does mathematics come from? Are we born to do mathematics? Is it something that exists outside of us? Do we create it or discover it? Support your viewpoint with evidence from sources, correctly documented.
You should use the text and linked materials in the course as sources along with sources available from the college online library: http://www.esc.edu/library/ *Log in: andrey_kravchenko292 *Pass: aK1986
Place this order with us and get 18% discount now! to earn your discount enter this code: special18 If you need assistance chat with us now by clicking the live chat button.