“Proof” is a tricky concept. “Proof of concept” is, if anything an even trickier concept.

Before we go on, a warning: If you buy into what follows and try to promote the ideas, you’ll gain a (or add to your existing) reputation as a persnickety pain in the keister. You might be better off just going with the flow, without worrying about all those nasty details that can be the difference between successful implementations and pouring money down a rabbit hole.

Still with me? Don’t say I didn’t warn you.

Mathematicians and geometricians more or less invented the notion of proof. They start with explicit assumptions, including a class of assumptions that are the rules of logic. They rigorously apply logic to their assumptions to create, one at a time, proved statements they can then rely on to take their proof to the next stage in the sequence (so long as their assumptions hold).

It’s like FORTH programming, where you combine defined verbs to create new defined verbs (and if you knew that you have, like me, joined the Geezing Geek Club).

Wouldn’t it be lovely if you could prove business concepts through pure logic? But you can’t.

Businesses are, among other things, collections of processes and practices. And business processes and practices have to handle, not only the mainstream set of inputs, but also a wide variety of exceptions. How employees handle many of those exceptions isn’t documented, because documenting them is impractical. There are too many of them and none happen often enough to be worth the time to document once an employee figures out what to do with it and moves on.

Which is just one reason proofs of concept are necessary in the first place. Add the rest (listing them is left as an exercise for the reader) and you get to the result: Logic can only get you so far. Then you need evidence.

Beyond mathematicians and geometricians is the next level of professional provers — researchers in the hard sciences. They develop hypotheses in much the same way mathematicians develop proofs, except that as scientists deal with the physical universe they have to accept that their assumptions might not always hold; also that there are almost always too many variables that might affect a phenomenon to include them all in a formal mathematical model.

Which is why they have to test their hypotheses through observation and experiments.

What scientists and philosophers of science figured out a long time ago, though, is that they can never prove anything through observation and experimentation, if for no other reason (and there are actually lots of other reasons) than that the next time they do the exact same thing, something different might happen.

So all good researchers understand that the best they can ever do is fail to disprove a proposition. Subject it to enough different tests and have it not fail any of them and, over time, they start to have confidence in it.

Which is why scientists have great confidence in Einstein’s theories of relativity and the Darwin/Mendel/Fisher theory of evolution by natural selection, and, for that matter, an increasing level of confidence in the theory of anthropogenic climate change: Each makes predictions about what scientists should find if the theory is true; so far, when scientists have looked, they’ve found what the theory predicts … or they’ve found something that doesn’t completely invalidate the theory but does call for modification or elaboration, after which the modified, elaborated theory is what’s subjected to future testing.

But they’re never certain, and good scientists never say they’ve ever proved anything. They say they’ve tested it thoroughly and it’s held up.

Think you’ll ever have the opportunity to test your business concepts this thoroughly?

Nope. At best you’ll be allowed to conduct one or two so-called proofs of concept, which are, by the above standards far far short of proof. Your average “proof” of concept is really nothing more than an attempt to disprove the simplest and easiest application of whatever the concept is to your business.

It’s a bit (but just a bit) like strapping a jet engine to the back of a cart and adding a big parachute. You might win a drag race with it, but you certainly haven’t proven the concept of jet-powered automobiles.

You’ve barely scratched the surface of testing it. If you have any more confidence than that, you’ll almost certainly find yourself in the middle of a fiery crash later on.