Math does not end. The reason being that Math is applied in various subjects. These subjects include business, sociology, medicine, computer science, quantum physics, etc. Currently we are witnessing how quantum physics and relatively growing, additionally as technology improves Math also grows. Otherwise we would not have any research done in the Math department at the universities globally, if Math were not growing.
To be honest the last subject will be very hard to say because there are so many ongoing research taking place at various universities across the globe, the main areas of research are Real and Complex analysis, Abstract Algebra and Topology(Geometry).
The extent we know Mathematics is the applications we use them for. The problems that can solve in Engineering, in development of new technology and the applications in business and in the economy. For real world problems that we cannot solve, that is the extent we know till and will continue till we know all problems are solved, which probably is never!
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