(Some) early mathematical loves: 

(In no particular order)

• At every moment there exists a pair of antipodal points on the Earth's surface with precisely the same temperature

• 0.999...... = 1

• Every prime number p induces a non-Archimedean metric on the rational numbers whose completion is not the real numbers

• A positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3

(Some) sources of mathematical inspiration:

• Michael Nielsen's Neural networks and deep learning book (NB: the "standard" activation function for most deep learning models these days is ReLU, not sigmoid)

• The Fold-and-Cut Theorem (HT: my colleague, Kathryn Lindsey)

• Brian Greene's The Elegant Universe, which inspired me to go back to school to get a PhD in math