I've had discussion with earnest creationists who point at the fossil record and say "Look - there's no way you can get from A to Z. There's a huge gap." When something is then found that's an intermediate form, they then say: "See! I told you! Now you have two gaps, and it's even worse!!"

So my point is this. I've read what you say, and I can see that you earnestly believe that pure mathematics and the theorems it produces are of no use. I'm asking what it would take to change your mind. What evidence would you need to convince you?

Science is grounded on falsifiable conjectures, and makes progress by testing those conjectures. If you are unwilling or unable to tell us what would be sufficient evidence, then I am unwilling to start chasing ghosts. It seems to me that trying to convince you would be like trying to nail fog to a wall.

Engineering is a critical discipline, and without it, things wouldn't get made. However, engineers rely on techniques that are known to work, and often that knowledge is based on deep theoretical work. Error-correcting codes, via which we get images back from Mars, and which allow reliable communications over cost-effective links are based on theoretical work. Yes, people played about and found the principles, but then they leveraged work done a century earlier to get to the limits. Having done so, they explored the theorems to see what axioms they were based on, and worked to see if those axioms could be circumvented.

It's the interplay between pure theory and pure experimentation that gives us enormous benefits, but it appears that you are willing, even eager, to dismiss fields of which you have no knowledge, purely because you can't see how they can possibly be useful.

It's Blub[0][1], all over again, but here we're not on a linear continuum, we're in a richly interconnected web of dependencies.

Another example. Fourier Transforms were first explored as a purely theoretical construct, showing that functions (with appropriate properties) form a vector space, and that vector space therefore has a basis, and that we should therefore be able to decompose functions into a representation relative to some basis. For decades this was a novelty, and then people started to use it for real. The theorems show the limitations, and then the engineers explore what can be physically achieved within those limits. Wavelets are now often used in contexts where the usual Fourier basis of trigonometric waves prove to be less useful, but the underlying theory is identical, and is still applied. And we know it will work, because of the theorems that were proven decades ago. The vector spaces are, by the way, infinite dimensional, and the work to understand the infinities was done as a part of pure math with no obvious applications.

Another example. We know that some problems are equivalent to others, and we know that the current best algorithms for these problems are exponential. We therefore know, for sure, and not just because of experiments, that some instances of some search spaces will be infeasible without a major break-through. As a specific example of that, multiple times people have claimed efficient algorithms for problems known to be NP complete. In some cases I've been able to prove that their algorithms, while possible useful in general, are definitely not polynomial. I can do that because of the theorems I have to hand.

But you won't care, and I can't make you care. I'm not writing this for you, because you appear not to be willing to change your mind, or consider that a field of which you appear to know very little might just be useful.

No, I'm writing this for people who read your comments and wonder. I'm writing this for people who are willing to entertain the idea that things of which they know little or nothing might be useful in ways they can't yet imagine.

[0] http://www.paulgraham.com/avg.html

[1] http://en.wikipedia.org/wiki/Paul_Graham_%28computer_program...