The year 1776 is momentous for three events:

1. Issuance and signing of The Declaration of Independence.
2. Approximate date for beginning of "The Industrial Revolution". (Should be called "The Thermodynamic Industrial Revolution", since there was a "Mechanical Industrial Revolution" in the 12th and 13th centuries in Europe, resulting in thousands of efficient windmills and watermills.)
3. The publication of The Wealth of the Nations, by Adam Smith -- a book later called "The Bible of Capitalism" -- especially "laissez-faire capitalism", with NO GOVERNMENT CONTROLS.

(Adam Smith (1723-1790) said of himself, "I am a beau in nothing but my books.")

Essentially, Adam Smith thought he was doing in Economics what Isaac Newton had done is Astronomy. Newton explained the revolution of the planets around the sun as "controlled by the invisible hand of gravity". Adam Smith seems to have thought that a better society would result if "controlled by the invisible hand of self-interest".

Another word for unlimited self-interest is SELFISHNESS. This inspired Kenneth Lux to entitle his book, Adam Smith's Mistake -- How a Moral Philosopher Invented Economics and Ended Morality. (I respectfully suggest that you read it. It's an antidote for the Ayn Rand philosophy of total selfishness -- written by a woman who seemed to have no knowledge of who the real creators were!).

Putting this aside, a primary consideration in laissez-faire capitalism is MAKING DEMAND BALANCE WITH SUPPLY -- otherwise a serious OVERSUPPLY could be costly for Society as well as for marketers.

The rubric of laissez-faire capitalism is "The Law of Supply and Demand", allegedly formulated by the French economist, Jean-Baptiste Say (1767-1832). (Say's name rhymes with "sigh".) Say never actually wrote "supply creates its own demand", but his best seller, the "Treatise on Political Economy," published in 1803 (seven years after Smith's great work) contains the idea.

Say wrote, "I do not see how the products of a nation in general can ever be too abundant, for each such product (through payment of wages, profits, etc.) provides the means for purchasing another." Say also wrote, "The mass of products composes the mass of a nation's wealth, and wealth is no more inconvenient to nations than it is to private persons."

A century after the Frenchman's death, British economist, John Maynard Keynes, attributed Say's law to Say, and made him famous. This was in the Great 1930's Depression, when there was supply, but no buyers. Say's Law is supposed to be "A Law of Nature", and its proponents enveigh against those who INTERFERE WITH IT. BUT YOU CAN'T INTERFERE WITH A LAW OF NATURE -- such as THE LAW OF GRAVITY! You can only "hitchhike where it is going".

A really serious treatment of this "LAW" was given by Léon Walras (1834-1910), the French mathematical economist, and the leader of "the marginal revolution" in economics. Marginalists replaced the labor theory of value (of David Ricardo) with the marginal utility of value [AXIONIC!] to explain why goods exchange at particular prices, arguing that the marginal or last unit of became more significant than the introduction of utility. Assuming a "regime of perfectly free competition", in the Walrasian model,

• for each PRODUCT there corresponded A DEMAND FUNCTION and A SUPPLY FUNCTION;
• and, for each MARKET and to each PRODUCT there corresponded (analogous to EQUILIBRIUM OF FORCES in CLASSICAL MECHANICS) A POINT OF EQUILIBRIUM at DEMAND EQUALED SUPPLY;
• but EQUILIBIRUM in one MARKET depends on the conditions in MILLIONS of OTHER MARKETS;
• this invokes SIMULTANEOUS DETERMINATION OF PARTIAL EQUILIBRIA IN ALL MARKETS!

Math students will recognize this as a humongous MATRIX, requiring teeedjus MULTIPLICATION OF SUBMATRICES to DETERMINE POSSIBLE EQUILIBRIUM. And advanced math grads will shiver at the thought of "ill-determined matrices", with calculations "going to infinity".

Waving his hands, Walras claimed success. But 100 years of the best mathematicians have never been able to deal with "ill-determined matrices" of this sort. The PROBLEM is that WE DON'T KNOW WHAT THE DEMAND WILL BE, and THERE'S NO EVIDENCE THAT DEMAND WILL WORK OUT TO FIT OUR SUPPLY!

We can recover from this a HOMOLOGY, relevant to our theme of ARITHMETIC-ALGEBRA.

Of course! you know what a homology is. You've seen one of them in "multiple choices" on STANDARDIZED TESTS. Say, "A leg is to a human as ____ is to a vehicle", where one of the choices is "wheel". This fits the homological format as follows:
leg: human:: wheel: vehicle.
And you've seen homology in FRACTIONS:
2/4 = 3/6, that is, 2: 4:: 3: 6.

HOMOLOGY -- sadly neglected and misused -- is our MOST IMPORTANT TOOL OF DISCOVERY AND LEARNING! So, we have HOMOLOGY.
SUPPLY: DEMAND:: ARITHMETIC: ALGEBRA.

If we could work backward in "cycles of our economy" to see how (recorded) DEMAND LINKED UP WITH SUPPLY, then we might succeed here as much as we do in ASTRONOMICAL prediction; as we do in solving elementary algebraic equations; as we do in finding our way to destinations, or back home; etc.

However, THE ALGEBRA IS JUST TOO DIFFICULT AND MAY ALWAYS BE. But the point is -- IT'S STILL ALGEBRA!

Thus, not only THE FIDUCIARY component of our ECONOMY depends on ALGEBRA, but understanding of its BASIC FUNCTIONING depends on ALGEBRA!

But not The Worship of Adam Smith.