Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient.
Historically, calculus was called "the calculus of infinitesimals", or "infinitesimal calculus". More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, variational calculus, lambda calculus, pi calculus, and join calculus. Wikipedia - Caculus
An English engineer wrote a calculus book in 1910 opening with the line what one fool can do, another can, and proved that almost everything making math feel impossible was put there on purpose by people who wanted it to stay exclusive.
His name was Silvanus P. Thompson.
He was a physicist, an engineer, a Fellow of the Royal Society, and a professor at the City and Guilds Technical College in London.
He had spent his entire career teaching calculus to working-class engineering students who needed the math to actually do their jobs, and he had watched generation after generation of bright kids walk out of math classrooms convinced they were stupid.
He knew they were not stupid. He knew exactly what was wrong, and he was about to say it in print in a way that would get him quietly hated by every academic mathematician in Britain.
In 1910 he published "Calculus Made Easy". He published it anonymously at first, listing the author only as F.R.S., which stood for Fellow of the Royal Society. He did not want his name attached to it until he saw how the establishment was going to respond. Because the prologue of the book was not a polite introduction. It was an accusation.
He wrote that calculus was not actually hard. He wrote that the people writing the standard textbooks were what he called "clever fools" who deliberately took the easiest parts of the subject and presented them in the most complicated way possible, because doing so made them look more impressive.
He wrote that they seldom take the trouble to show you how easy the easy calculations are" and instead seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way.
Then he opened the first chapter by telling readers something nobody had been willing to admit out loud. The reason calculus felt impossible was not because calculus was impossible. It was because the symbols had been chosen to feel impossible. The notation looked like ancient ritual on purpose. The Greek letters, the formal epsilon-delta definitions, the abstract limit proofs that opened every standard textbook, were not how Newton and Leibniz had originally thought about the subject. They were a 19th century renovation of the field done by professional mathematicians who wanted calculus to feel like a closed shop.
Thompson refused to use any of it.
He went back to the way Leibniz had thought about it 250 years earlier. The letter d in front of a variable, he told his readers, just meant "a little bit of. That was the whole secret. dx meant a little bit of x. dy meant "a little bit of y." dy/dx meant "a little bit of y divided by a little bit of x," which is just how steep the curve is going at that exact moment. Integration was the opposite. It just meant adding up all the little bits.
That is calculus. That is the entire subject. Everything else is technique, and the technique only works once you understand what you are doing.
A 12-year-old can follow that explanation. A 12-year-old cannot follow the opening chapter of a typical university calculus textbook. The gap between those two facts is the entire reason most adults walk around believing they are bad at math.
The book became one of the bestselling math books in history. Over a million copies. Still in print 115 years later. Still recommended by physicists, engineers, and self-taught learners as the only calculus book they actually finished. Martin Gardner revised it in 1998 and the foundation of the book did not need to change because Thompson had built it on Leibniz, not on the academic conventions that have come and gone since.
The deeper point Thompson was making is the part that should haunt anyone reading this in 2026.
Difficulty is often a marketing strategy. It is not always a property of the subject. When a discipline is taught in a way that feels impossible, the difficulty is doing a job for someone. It is keeping the field small. It is protecting the salaries and the status of the people already inside it. It is filtering out the kinds of people who would otherwise show up and crowd the room.
This happens in math. It happens in law. It happens in medicine. It happens in finance, in machine learning, in philosophy, in software. Every field has a layer of jargon and notation and ritual sitting on top of a core idea that is usually much simpler than the people inside the field want to admit. The jargon is not there to communicate. It is there to gatekeep.
The way you recognize a real teacher is that they keep stripping the ritual off. The way you recognize someone protecting their priesthood is that they keep piling it on.
Thompson finished his prologue with five words that are the entire spirit of his project. "What one fool can do, another can." He meant it as both a joke and a threat.
If a working-class engineering student in 1910 with no Greek and no Latin and no university privileges could learn calculus from a 200-page paperback, then so could anyone the establishment had been excluding for the previous 200 years.
Most subjects you have given up on were never as hard as the people teaching them needed you to believe. You were not stupid. The course was designed to make you feel that way.
What one fool can do, another can.
See Also
Arithmetic
Bhaskara II
Continuity
fundamental theorem of calculus
Laplacian
Limit of a Function
method of exhaustion
Stokes Theorem