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I question whether mathematics is not an empirical science. True it has the power of absolute proof which is denied to Physics and Biology but except for that maybe it is the same.

Mathematicians look at "empirical data" which for them are mathematical objects - say such as Riemann surfaces - They examine the data through examples to understand their properties. They make hypotheses based upon these examinations and then test them on other examples. This may verify the hypothesis, or show that the hypothesis needs modification. At some point, if the investigation bears fruit, a theory may emerge that organizes the data and predicts the properties of yet unexamined data.

In short, it seems that mathematical research includes the same processes that are found in other sciences. Functionally, it is much the same.

Mathematicians look at "empirical data" which for them are mathematical objects - say such as Riemann surfaces - They examine the data through examples to understand their properties. They make hypotheses based upon these examinations and then test them on other examples. This may verify the hypothesis, or show that the hypothesis needs modification. At some point, if the investigation bears fruit, a theory may emerge that organizes the data and predicts the properties of yet unexamined data.

In short, it seems that mathematical research includes the same processes that are found in other sciences. Functionally, it is much the same.

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