Uses of Topology: Learn What It Can Do

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Topology, the study of limits and continuity, has significant applications across various fields of mathematics, influencing areas such as calculus. While some new branches of mathematics are continuously being developed, many lack practical relevance. The discussion highlights the ongoing debate about the importance of concepts like fractals and catastrophe theory, which emerged in the mid-20th century. Overall, topology remains a foundational element in mathematical studies, with its uses extending beyond traditional boundaries. The exploration of new mathematical branches continues, suggesting that innovation in the field is far from over.
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I am not a math student but I have read some basic stuff about topology just because it sounded interesting, and I was wondering if people could name some uses of it, because it does not seem to have very many.

Also on a related question, how often are new branches of mathematics "invented"; do you see any happening in the future or do they all seem to be discovered already?
 
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Topology is essentially the study of limits and continuity which are of immense importance in calculus.

New branches of mathemtics are being "invented" all the time- of course, most of them are of no real interest. I think the jury is still out on "Fractals" or "Catastrophy theory" which were developed during the sixties and seventies.
 
Topology can be (and is) used in pretty much in any field of math.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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