How to discover Sigmoid function?

Hi everyone
I understand the definition and application of the Sigmoid function in Logistic Regression, but I’m curious about how it was discovered. Is there a mathematical proof of how it was found?
Thank you

The sigmoid function isn’t a theorem, so there is no proof or derivation.

I suspect it was developed by exploring the characteristics of exponential functions. Some sources say it was developed by mathematicians in the early 1800’s.

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