I think that comparing mining to "solving mathematical puzzles" gives too much credit to what mining really is. Mathematics is all about recognizing structure in the "puzzle" at hand, while bruteforcing SHA is actually the opposite of that.
edit: I'd think the best way to explain mining to an audience like that is by calling it number crunching.
I always thought that calling it "solving math puzzles" made it seem silly and probably put many people off, as it seems like a pointless way to earn rewards. I personally call it "securing the bitcoin ledger using crypto-math that prevents others from adding fraudulent payments". To me this sounds like something that miners ought to get paid for as they provide a function that everyone can agree is important. Once they have that overview understanding, which doesn't sound frivolous, then it's up to them if they want to dig into the math that achieves this. But it more favourably depicts what miners actually are paid for.
IMO the continued use of "solving math puzzles" is detrimental to people casually getting interested in Bitcoin.
This +21,000,000. The whole meme of "print free internet moniez your computer for solving puzzles" is a determent for further expansion. Anyone that meme would have appealed to should have joined 3 years ago. Today the margins on mining are small and shrinking. It is requiring real capital, real planning, and involves real risks. Today most people hearing "free moniez for solving puzzles" either will be pissed to find out this free moniez is going to require putting out thousands (possibly tens of thousands) of dollars into a complex, high risk venture or will just dismiss it as a scam. Face it the initial reaction to "free moniez" is SCAM. SCAM. SCAM. SCAM. SCAM.
Bitcoin is a currency and a payment system. Lets start there. What is the purpose of mining? Not HOW does Mining work but WHY do we have mining? PayPal doesn't have mining, VISA doesn't have mining. Why does Bitcoin have mining?
More importantly what is the only aspect of mining that "Joe Consumer" gives a flying crap about? It sure as hell isn't "free internet moniez". Mining keeps his transactions (and thus the value of the coins he holds) SECURE.
Mining = Transaction Validating = Security = Value. Far more people buy gold then try to excavate their own gold. The "mining" sales pitch immediately tunes out 99% of potential users. Personally I wish the word mining would go out of the vocabulary but please please for the love of Satoshi drop this "free moniez for solving puzzles" nonsense.
There is a very simple logical progression.
1)
START WITH COMMERCE. That is what your audience cares about. Bitcoin is commerce. Bitcoin enables the end user to send value anywhere in the world, nearly instantly, and at very low (sometimes zero) cost. Bitcoin enables the user to receive irreversible payments which can't be reversed due to fraud. If you aren't starting here at commerce and the benefits you are doing it wrong.
2) After you explain the benefits of Bitcoin it becomes immediately obvious
that the network must be secured. The network must ensure coins are only spent once. To do that requires the work of "transaction validators" = miners. Miners put transactions in a block and secure them by proving that a certain amount of work was spent to find a solution which solves the block. This ensures an attacker would need to "spend" just as much work to make a forgery. Blocks are combined into a blockchain which grows by consensus and .... FORMS A PERMANENT TRANSACTION RECORD which secures transactions against
misdirecting funds, forgery or duplication. The bold part is the only part consumers and merchants care about. If you don't discuss the
why then you are 100% wrong.
3) Now (and only after #1 & #2 are explained and if you have 10 minutes to talk then 9:30 should be spent on #1 & #2)
miners are compensated for this WORK they perform to SECURE the network. Miners receive small transaction fees (far lower than VISA or ACH, or Western Union). However when the network is young the amount of transactions may be insufficient to justify the expenses of miners to secure the network. So the network provides a SUBSIDY to miners. This subsidy is rewarded per block solved and decreases over time until the subsidy is gone.
My guess is most people who talk about Bitcoin are "mining nerds" and thus talk first about mining but honestly if gives a distorted view of Bitcoin and comes off as kinda ponzi/weird/scamish. It would be like explaining to someone what a personal computer is and starting with a very detailed explanation of how to play Counterstrike.