Is there a way of generating true random numbers only using pure maths?

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I know that true random numbers can be generated using measurements taken from the atmosphere, but is there any way of doing this mathematically, without any measurements taken from the external world?

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Mathematics only describes and analyzes. As such, it can describe pure randomness, but it makes little sense to say that using mathematics you can create random numbers, as if it were some physical phenomenon with causal powers to do so. That said, mathematics can help you think about how to create random numbers.