Is mathematics out there or in here? Mathematicians who are Platonists would bel

Question

Is mathematics out there or in here? Mathematicians who are Platonists would believe the basic core of mathematical objects (like the Pythagorean theorem, or the number Pi), has a real, objective and factual existence, as much as our universe itself. These mathematical objects are discovered, not invented, in a way similar to the idea that North America existed before Columbus discovered it. Constructivists or intuitionists believe that believe that mathematics (including what could be called its basic core) is a construction of the human intellect, in a way like language or music is.

Read the Mario Livio "On human mind and mathematics and the universe, hopefully to set the discussion. Then Front and Back, by Reuben Hersh, an intuitionist, and finally Math Out There , where Martin Gardner takes a Platonist position opposing Hersh. Then take a position yourself and post, hopefully giving reasons to support your position and making reference to the readings. Reply to at least three other postings.

Note that Reuben Hersh makes two different points in "Front and Back". Mathematics has a front room and a back room. The current discussion is definitely part of the "back room" of mathematics. However, the part of Hersh's paper relevant to this discussion are the "myths" in the latter half of Hersh's paper. This is the part that Gardner attacks in his article.

Explanation / Answer

There are some parts in mathematics like geometry sometimes it feels that way to us a new study suggests that even without mathematical training, the human brain may have certain intuitions about geometry, concepts that we don't learn but may be born primed to understand.

Some times we uses mathematics should always express in ordinary language the meaning of the assumptions we admits, as well as the significance of the results obtaine.

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