Editing 2529: Unsolved Math Problems
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Math has many problems that remain "unsolved." This is not simply a matter of finding the correct numbers on both sides of an equal sign, but usually require proving or finding a counterexample to some conjecture, or explaining some property of some mathematical object. Sometimes this might involve extending an existing proof to a wider range of numbers like reals, complex numbers, or matrices. | Math has many problems that remain "unsolved." This is not simply a matter of finding the correct numbers on both sides of an equal sign, but usually require proving or finding a counterexample to some conjecture, or explaining some property of some mathematical object. Sometimes this might involve extending an existing proof to a wider range of numbers like reals, complex numbers, or matrices. | ||
− | A concrete problem is one that is very obviously connected to a real world process, while an abstract problem is one which seems unconnected to actual problems. In modern math, many problems tend to be very abstract, requiring complicated notation to adequately state the problem in the first place, like many of the {{w|millennium problems}}. On the other hand, many unsolved problems are very concrete | + | A concrete problem is one that is very obviously connected to a real world process, while an abstract problem is one which seems unconnected to actual problems. In modern math, many problems tend to be very abstract, requiring complicated notation to adequately state the problem in the first place, like many of the {{w|millennium problems}}. On the other hand, many unsolved problems are very concrete; for example, there are very many problems related to packing objects into spaces that are very difficult to solve although quite easy to state, such as the {{w|Collatz conjecture}}. Finally, Randall describes a third category of "cursed problems," that have strange, seemingly random behavior, such as the behavior of turbulence or the distribution of prime numbers. |
In the first panel, Ponytail describes a weird abstract problem. Her description seems to be a meaningless jumble of terms that are either mathematical or just ''sound'' mathematical. And the mathematical terms are from disparate branches of mathematics: group theory, topology, and calculus. | In the first panel, Ponytail describes a weird abstract problem. Her description seems to be a meaningless jumble of terms that are either mathematical or just ''sound'' mathematical. And the mathematical terms are from disparate branches of mathematics: group theory, topology, and calculus. |