You're making the point here. It's the software that makes our lives significantly better, which is the most important one.
However, as software is everywhere, the original question is the same thing as "what physical invention" is the most important one?
From one standpoint this could be something like the wheel or electrical light, i.e. Bios, compiler or a network stack in the software world. Or, something way more personal, like health care related software for the loved ones or some more profane stuff.
To make the question even less tangible, software in general can be replaced more easily than physical things, most of the time.
Leaving highly classified and for whom kinda questions aside, I must say it's the software that the good guys SWIFT (http://swift.com) use to run the global financial network.
The SWIFT Network has no real alternatives and entire countries teeter towards bankruptcies when they're banned from using it.
The last time the US banned Iran, Iran reportedly lost $100M; everyday!
It sounds like software that important shouldn't be something that any particular country should be in control of (as much as I like to stop the leadership of Iran).
highly classified stuff, but in its day likely a FORTRAN implementation, the OPLAN is not simply a computer program but is a heuristic of human operations that is modified depending on current intelligence briefs, and asset deployment and distribution. The ARPANET [DARPANET] was a major part of this.
I’m not by any means an Android fan, but I have to admit that AOSP has done more to make computing accessible to almost everyone in the world than any other platform.
I had a teach who once was reviewing the history of computing. She explained how time sharing was invented in the 1960s. The ability for a computer to do more than one thing at a time, was a HUGE improvement.
