A math-based currency, also referred to as a cryptocurrency, is a digital asset with verifiable mathematical properties, similar to how we can reliably verify gold as an atom with 79 protons. Math-based currencies exist as digital assets in their own right and can be transferred directly between users (as fiat cash could be) without relying on any centralized protocol operator. VRP exists as a math-based currency on the Ripple protocol.
The supply of a math-based currency is governed by the laws of mathematics. There is no human intervention beyond the creation of the protocol rules. This is in contrast to the many “virtual currencies” that can be issued without restriction by companies and people (such as airline miles, reward points, etc.).
Bitcoin was the first example of a math-based currency. Bitcoin exists natively as a digital asset. It is not a balance that is redeemable somewhere, and it does not have risk to any counterparty like “digital fiat” currencies (such as your online balance with a bank). You could hand someone a thumb drive with bitcoin on it, and in doing so, you are transferring the asset itself, like handing over cash, as opposed to transferring an IOU or someone’s promise to pay. It does not require trust in any third party.
As this applies to Ripple, VRP exists natively within the Ripple protocol as a counterparty-free currency, just like bitcoin does on the Blockchain. Because VRP is an asset, as opposed to a redeemable balance, it does not require that users trust any specific financial institution to trade or exchange it. Users of the Ripple protocol are not required to use VRP as a medium of exchange or as a store of value. The Ripple protocol is currency agnostic. Users can use their preferred currency, whether that’s USD, BTC, VRP, or any other.