Why Calculus is Called "The Calculus"

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In summary: In summary, Calculus is sometimes referred to as "The Calculus" because there are various types of calculi, each a specific method for calculating something. The most famous are differential and integral calculus, which are typically referred to as "The Calculus" or simply "Calculus". This may stem from the historical use of "the" in front of the word "calculus" to give it a sense of importance, similar to saying "the computer". The idea of "the calculus" being a fancy-pants branch of mathematics is likely a misconception and may have originated from the use of "the" in other languages, such as Arabic and French.
  • #1
Math Is Hard
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Why is Calculus sometimes referred to as "The Calculus"? I mean, I never studied The Algebra or The Trigonometry?
What makes it such a fancy-pants branch of mathematics that it deserves it's own article?
 
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  • #2
Ha Ha! Good question.

I think the answer is that there are several "calculi". A calculus is, as the name implies, a method for calculating something, and calculi for different "somethings" are not related to each other. A partial list...

1. Differential calculus (for calculating slopes of curves)
2. Integral calculus (for calculating areas under curves)
3. Propositional calculus (for 'calculating' conclusions from premises in symbolic logic)
4. Wick calculus (for calculating normal ordered products in quantum field theory)

There are others, but I think you get the idea. By far, the most famous of these is the material contained in #1 and #2. Given the preeminence of those particular calculi, they are typically called "The Calculus" (big "C"), or simply "Calculus".
 
  • #3
What a great answer - thanks so much for the clarification! I am going to share this with the other students in my Calc class. I am sure they've been curious about this, too!
 
  • #4
No - it's nothing to do with there being several forms of calculus. A 'calculus' was an ancient Roman calculating device (like an abacus) which used small stones ('calculus' is Latin for 'pebble'). So to say 'THE calculus is useful...' rather than 'Calculus is useful...' is much the same thing as saying 'THE computer is useful...' rather than 'Computer is useful...'. However, it's now an archaic form that almost no-one uses unless they are being pretentious.

Interestingly, the 'al' part of al-gebra is Arabic for 'the' so 'the algebra' would be doubling up on the 'the'.
 
  • #5
Hmmm... that's interesting, too.
From the way you have described it, it seems almost as if Calculus has an imaginary "method" after it.
For instance, if you said I am studying "the Calculus method" or "the
Calculus methods", it works better than saying I am studying "Calculus method".
But I still think the "The" lends it just a tiny bit of loftiness. I wonder if David Berlinski's book would have sold just as well if it were called A Tour Of Calculus?

Anyway, thanks for taking the time to respond to my question. I appreciate your thoughtful answer.
 
  • #6
this interesting discussion reminds me of the work by the great grandfather of calculus archimedes, called "the method".
 
  • #7
I believe Tom Mattson is right, and not rdt2. See here. Here you can see a little on the history of Algebra. It could be wrong, but it says nothing to the effect of "al" meaning "the" in this context. They say "al-jabr" means, "reunion" (not the reunion), etc.
 
  • #8
W(hy)tf is mathwonk dragging up these old threads...?

But anyway... http://www.m-w.com/cgi-bin/dictionary?book=Dictionary&va=algebra&x=0&y=0 [Broken]

Main Entry: al·ge·bra
...
Etymology: Medieval Latin, from Arabic al-jabr, literally, the reduction

I'm more inclined to trust Merriam-Webster than Wikipedia :P
 
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  • #9
Muzza, I'll agree to that. Of course, I can't be certain since I don't know any Arabic.
 
  • #10
"Al" most certainly means "the" in arabic. Many star names begin with "al," like Aldebaran, the eye of the bull.

- Warren
 
  • #11
And of course, the most famous one of recent times, Al Qaeda: "The Base".

My answer was just a reasoned guess, but it sounded good to me. :P
 
  • #12
I've never heard of "The Calculus" before. That sounds a bit pretentious.
 
  • #13
Dear Muzza,

I just found out about this cool site and went through everything the first day on the job.

This is a rather fun site and presumably topics here will attract new interest from time to time.

best,

mathwonk (roy).
 
  • #14
Hey, Mathwonk - welcome to PF, by the way! :smile:
 
  • #15
Jin314159 said:
I've never heard of "The Calculus" before. That sounds a bit pretentious.

We could call it Al Calculus. Makes it sound more sinister. :devil: And its members definitely have Weapons of Math Instruction. :biggrin:
 
  • #16
It was called "the infinitesimal calculus" for quite a while. When the nineteenth century proceeded the "infinitesimal" part began to be dropped, because no one believed anymore that infinitesimal quantities actually existed logically. So you might say the phrase meant "the calculus formerly called infinitesimal".
 
  • #17
quartodeciman said:
So you might say the phrase meant "the calculus formerly called infinitesimal".

Reminds me of "The Artist formally known as Prince". :biggrin:
 
  • #18
There is also "The Former Yugoslav Republic of Macedonia". That's the legal name of this country. That is an attempt to assuage the neighboring Greeks who consider the name "Macedonia" to be an historically-Greek entity, even though slavs have been living there for many centuries.
 
  • #19
heehee! wonderful.

cosa nostra lives again.
 
  • #20
this whole thread seems to reveal some innocence of the features of other languages by many, not all, of us. it seems clear that al does mean the in arabic, and in french also nouns such as algebra are usually preceded by an article like le or l' or la. i believe Newton also wrote in latin?
 
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  • #21
There is, famously, a village in England whose name, when translated, means Hill Hill Hill: each group who settled (angles, romans, celts, saxons, whoever) added hill in their own language to the name not realizing it was already so named.

http://en.wikipedia.org/wiki/List_of_tautological_place_names
 

1. Why is calculus called "the calculus"?

Calculus is called "the calculus" because it is a branch of mathematics that deals with the calculation of continuously varying quantities. The word "calculus" comes from the Latin word "calculus," meaning small stone or pebble. This is because early mathematicians used pebbles on a counting board to perform calculations.

2. What is the history behind the name "calculus"?

The term "calculus" was first used by the mathematician Gottfried Wilhelm Leibniz in the late 17th century. He borrowed the term from the Latin word "calculus," which was used in ancient Rome for a counting board. Leibniz used this term to refer to his new mathematical method for calculating continuously varying quantities.

3. How does calculus differ from other branches of mathematics?

Calculus is unique in that it deals with the concept of change and the calculation of continuously varying quantities. Other branches of mathematics, such as algebra and geometry, focus on the manipulation of numbers and shapes, respectively. Calculus is essential in many fields, including physics, engineering, and economics, where the understanding of change is crucial.

4. Is calculus difficult to learn?

Like any other subject, calculus can be challenging to learn at first. It requires a solid foundation in algebra and trigonometry and involves abstract concepts and complex calculations. However, with practice and determination, anyone can learn and understand calculus.

5. How is calculus applied in real life?

Calculus has numerous practical applications in fields such as physics, engineering, economics, and statistics. It is used to model and analyze continuous processes, such as motion, growth, and change. For example, calculus is used to calculate the trajectory of a projectile, determine the optimal shape of a bridge, and predict the growth of a population.

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