Gold is physical, Fiat is political and Bitcoin is mathematical.
Gold gets much of it's value and appeal from the metal as it is physical. As a result of it's scare nature, it is extremely difficult to produce, as it is quite durable and it can almost cost a fortune to make a counterfeit of it. However it's monetary system can be hugely dependent on the activity of humans, as they determine how it is stored, transferred and even its pricing.
When we talk of Fiat, whee talking about a currency that is mostly institutional, here its supply and rules are hugely controlled and influenced by the key monetary institutions. It's a currency where the government has the authority to change and influence the rules that govern it, and also central banks have the authority to execute its rules as they deem fit.
Having said that, we can see that with Bitcoin, a while new direction is established. The fire rules of Bitcoin is not determined by a supposed politician, or an office. They are written into a protocol and enforced by a distributed network. And obviously its limit is capped at 21 million l. You can't wake up to call a vote as to why that states limit should or shouldn't exist. Networks would verify transactions in line with the rules that each participant can bank on checking.
A reason why Bitcoin is suggested to be mathematical. With Bitcoin, we're seeing a network that verified a transaction according to rules.
However, one can't say that Bitcoin is purely Math, Math is like the principles or foundation and with Bitcoin you still need as system; electricity miners and users.
With gold, trust is placed in the properties of an object, with Fiat trust is in institutions but with Bitcoin one can say trust is in the ability to verify rules.
I would suggest that Bitcoin is the superior or better option of the three. What I can strongly point out is that Bitcoin gives a pathfinding perspective of how we see money.
Bitcoin is seen to be mathematical because there are other means it's been classified like the nodes, the sectors, the units, the electricity, the miners and others but to mention a few. The most shocking part of everything is that, these government have no general or universal control over Bitcoin thereby making it more challenging for them to easily manipulate the price of the free swings in the market.
Do you know the most revealing and most important aspect of Bitcoin? It'd shown us the true path and how we can come along with making sure Bitcoin is not seen as some sort of kind digital currency where we can simply transfer and receive Bitcoin at the comfort of our homes.