Up until relatively recently (the last century or so), most ordinary paper currency and coinage was directly redeemable for gold. This is because many of the wealthiest countries followed the gold standard, a monetary system where governments tied a fixed exchange rate for national currency to gold. As part of this system, countries kept sufficient reserves of gold in their vaults to 100% back their circulating currency supply, ensuring currency-for-gold exchanges were always possible.

However, this also constrained the economy in the middle of the Great Depression, since governments were unable to simply source more gold to expand their money supply and stimulate spending.

The system was abandoned by Australia and New Zealand in 1929-1930; Canada, Germany, and the United Kingdom in 1931; and the United States partially left the standard in 1933.

It wasn't until 1971 that the United States fully left the gold standard, after then-President Richard Nixon ended the interconvertability of the U.S. dollar into gold, thereby nullifying the Bretton Woods system and essentially ending the age of the gold standard.

Instead, countries switched to a fiat model, where the national currency isn't backed by a commodity like gold, allowing central banks to print new money whenever needed. Although it doesn't have intrinsic value, the value of fiat money is set by changes in supply and demand, as well as the strength of the government behind it. Since governments only accept payment of taxes in fiat currency, and tax evasion is illegal, their value is also partially maintained required tax payments.

So while fiat currencies are not formally backed by anything, we tend to buy into our fiat currencies with the confidence that they will be accepted elsewhere in exchange for goods and services. Essentially, our confidence in fiat currencies generates purchasing power, and therefore value, for fiat currencies.

But our confidence in fiat currencies suffers from a problem of induction. In other words, we presuppose that a sequence of events will occur as it always has, based on our previous experience. We can't really say for certain what lies ahead for the value of our traditional fiat currencies. Without a currency being formally tied to a commodity like gold, value becomes a contingency rather than a guarantee.

Is Bitcoin backed by mathematics?

Like the U.S. dollar, Bitcoin is not backed by a physical commodity, and instead derives its value in other ways.

Since Bitcoin doesn't have a centralized entity that enforces its value, and it isn't backed by any commodity, many people mistakenly believe this means Bitcoin doesn't have any value.

However, Bitcoin currently has an individual unit value of around $30,000, and a total market capitalization—defined as the unit value multiplied by the number of Bitcoin in circulation—of over $625 billion, clearly demonstrating that it is considered valuable by a large number of people.

But Bitcoin isn't actually backed by anything physical—only the complicated mathematics underlying its blockchain technology and controlled supply. This ensures Bitcoin remains limited in supply and is resistant to censorship—which imbues it with some of its value. As Anthony Pompliano said in a panel discussion on CNBC, "If you don't believe in Bitcoin, you're essentially saying you don't believe in cryptography." For Pompliano, blockchain technology endows Bitcoin with inherent value, almost like a gold standard for crypto.

The rest of Bitcoin's value can be attributed to the fact that it was the first successful monetary system to operate without a centralized entity pulling the strings—meaning its supply can't be forcefully inflated, it can't be easily confiscated like gold was during the 1930s, and it offers a level of financial freedom that few (if any) fiat currencies can match.

Bitcoin has also been shown to have utility value; thousands of merchants now accept it as payment for goods and services. In two countries, El Salvador and the Central African Republic, Bitcoin has been adopted as legal tender, meaning that merchants have to accept it (though in the former, at least, adoption has reportedly been patchy).

The level of confidence seen in a currency can be indicated, or even preserved, by its level of usage around the world. Whether it is performing well relative to other fiat currencies, the U.S. dollar is—and will be for the foreseeable future—a currency that can be spent almost anywhere. As a result, consumers are confident in the dollar. Purchasing power and practicality are valuable commodities themselves.

On the other hand, Bitcoin is still some way from the mainstream. The crypto community has come a long way since the first Bitcoin transaction was spent on a pizza, but until mass adoption takes place, confidence in Bitcoin will ultimately not be as high, or as widespread, as confidence in established fiat currencies.

Despite their obvious differences, Bitcoin turns out to be similar to a fiat currency insofar as it is backed largely by consumer confidence. As belief in the crypto space grows, so too will confidence in Bitcoin.