I am gone yet shape what comes to be, a shadow behind both you and me. I hold the lessons, joys, and pain, touch me not, yet I still remain. What am I?

I remain when all is lost, I'm what was left in the box. Alongside courage, I form power, but alone, I can't save the hour.

Those that have me despise me, those that want me don’t deserve me, Alone among countless friends, fifteen minutes until it ends, What am I?

It's not real but does exist, it helps to determine where a plane will drift, you'll see it in math but never on a ruler, and it was first annotated by a man named Euler

You always find me in the past. I am made in the present, but in the future I am nothing. What am I?