Mathematical Problems: What are?
Channel: Amania Tv
Date: 2017-11-28

November 2017:

Welcome back Amaniacs, Mathematical problems are not arithmetic or algebra problems like you might see in school. This makes us wonder, What is a Mathematical Problem? Research problems in mathematics are conjectures about some abstract structure, usually but not always infinite in size, and to "solve" the problem is to logically prove whether the conjecture holds. For example, one classic result is the proof that there exist infinitely many prime numbers. This is not something you can check by testing all the cases. You need to reason logically about what it means for numbers to be prime. Hence, a Mathematical Problem is a problem that can be solved by logically proving whether the conjecture holds.

Attributions:

Doh De Oh by Kevin MacLeod is licensed under a Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/)
Source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1100255
Artist: http://incompetech.com/

Subtle Library by Fabian Measures (http://freemusicarchive.org/music/Fabian_Measures/) is licensed under a Creative Commons Attribution licence ( https://creativecommons.org/licenses/by/4.0/)
Source: http://freemusicarchive.org/music/Fabian_Measures/Emotion_Music/Subtle_Library