Editing 1991: Research Areas by Size and Countedness
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 17: | Line 17: | ||
The 19 research areas are listed and explained in the [[#Tables of research areas|tables]] below. | The 19 research areas are listed and explained in the [[#Tables of research areas|tables]] below. | ||
− | In the title text, mathematicians may give a third answer that the concept of counting the things being studied is not reasonable, because the things are abstract or otherwise not discrete. There are many different types of math that blend into each other, and many have turned into separate sub-disciplines based on different interpretations of fundamental rules. As a specific example in geometry, different interpretations of how many lines you may draw parallel to another line through a given point has lead to | + | In the title text, mathematicians may give a third answer that the concept of counting the things being studied is not reasonable, because the things are abstract or otherwise not discrete. There are many different types of math that blend into each other, and many have turned into separate sub-disciplines based on different interpretations of fundamental rules. As a specific example in geometry, different interpretations of how many lines you may draw parallel to another line through a given point has lead to hyperbolic (infinite parallel lines) and spherical (0 parallel lines) geometric systems that are just as valid (and valuable, in some contexts) as the more commonly known Cartesian (1 parallel line) geometry. As a specific example of the blending, number theory and set theory and topology all interrelate and it is difficult to concretely say whether many theorems belong to one branch of math or another. |
==Tables of research areas== | ==Tables of research areas== |