A Tale of Alice and Bob

By now more than 90% of all e-mail in the USA is spam. When Bill Gates came up with the idea of making e-mail as expensive for companies as ordinary letters, he was 1. misunderstood and 2. misquoted. Nobody wants to stick stamps on an e-mail. An economic solution with an institution that sells virtual stamps is - everyone knows this - absurd. Laws to deter spam mail only work locally, not globally. So that option is out of the question as well.
The idea Bill Gates was championing was to make spam unprofitable. Only a technical solution can still get the better of this “plague”. One option, and this one is my favourite, is to demand a kind of deposit from the sender for delivering mail. For that we need to take a closer look at the SMTP protocol, which handles e-mail traffic. When server A, let's just call her Alice for simplicity's sake, wants to send a mail to another server - Bob - this is what currently happens. As if by a miracle (DNS), Alice finds her way to Bob.
Alice says: “Hello, I have a mail here for Bob”.
Bob replies “Yes, that's me, thanks!” and that's it. Brilliantly simple, simply brilliant. Except that a spammer goes from one front door to the next and drops a flyer through every letterbox. That doesn't cost him much effort. And there's the rub. It is currently far too easy to send mail to everyone from Bob to Zukovski. So the point is to make Alice's job harder.
Alice: “Hello, I have a mail here for Bob”.
Whereupon Bob says “Yes, that's me, but would you please solve the following arithmetic problem for me: sin(2 root 4)^2 ,1+3/4-((2+z) (1-y))+7.7”
Now Alice has to do a little arithmetic. If she says “6.45087080365692”, Bob checks the result himself, and if it is right, Bob accepts the mail. If, on the other hand, Alice says “Dunno, is the answer 42 or something?”, Bob says nothing more and keeps his door shut to Alice for at least a day.
Why would Alice give a wrong number, and what's with all the arithmetic? If Alice is honest and only wants to send Bob a mail, she only has to invest a fraction of a second in the arithmetic problem. If, however, Alice is a tramp and rings 10,000 doorbells at the same time to get rid of her flyers, then Alice has quite a problem. The deposit is the computing time Alice has to invest for us to prove that we are something special and that she isn't pushing advertising on us.
Running a server farm large enough to send as many mails as spammers do today would make the whole thing so unprofitable that the flood of spam could be pushed below 5% (optimistic estimate).