To Mathematics Fans and Lovers, If you please write a lesson you learnt from the Great Math. that affect on your experience and behavior of your life.
This is a very good question, with many possible answers.
Mathematics tends to derive its inspiration from the twists and turns of natural phenomena such as the changing illumination of morning sunlight on various objects such as tree leaves, the paths of comets in the nighttime sky and the path traced by a moving particle (i.e., a string or what is known as a world line). Euclid's Elements are really a handbook for the discovery of mathematical structures that resemble structures in nature. Here are some examples.
https://www.math.ust.hk/~mamyan/sc1110/Elements.pdf
Def. 2: And a line is a length without breadth.
Example from nature: The path traced by a moving particle (string or world line) has no breadth.
For the Historical background for Euclid's Elements, see
http://www.math.ubc.ca/~tbjw/308/HistoryI.pdf
For an introduction to string theory (world lines), see
https://www.jstor.org/stable/38267?seq=1#page_scan_tab_contents
My own experience with Mathematics is centered round proximity and the nearness or separation of various objects, especially the nearness of sets. See, for example,
https://arxiv.org/pdf/1602.03734.pdf
http://arxiv.org/pdf/1506.04249.pdf
http://research-publication.com/articles/AMSJ/2015/AMSJ-2015-N2-2.pdf
I learnt from mathematics:
There may be many ways lead to the same solution, and it's better to use the shortest way to save my time and effort.
That is, to reach my aims I must go through the shortest way that leads to it.
This is a very good question, with many possible answers.
Mathematics tends to derive its inspiration from the twists and turns of natural phenomena such as the changing illumination of morning sunlight on various objects such as tree leaves, the paths of comets in the nighttime sky and the path traced by a moving particle (i.e., a string or what is known as a world line). Euclid's Elements are really a handbook for the discovery of mathematical structures that resemble structures in nature. Here are some examples.
https://www.math.ust.hk/~mamyan/sc1110/Elements.pdf
Def. 2: And a line is a length without breadth.
Example from nature: The path traced by a moving particle (string or world line) has no breadth.
For the Historical background for Euclid's Elements, see
http://www.math.ubc.ca/~tbjw/308/HistoryI.pdf
For an introduction to string theory (world lines), see
https://www.jstor.org/stable/38267?seq=1#page_scan_tab_contents
My own experience with Mathematics is centered round proximity and the nearness or separation of various objects, especially the nearness of sets. See, for example,
https://arxiv.org/pdf/1602.03734.pdf
http://arxiv.org/pdf/1506.04249.pdf
http://research-publication.com/articles/AMSJ/2015/AMSJ-2015-N2-2.pdf
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