Talk:Calculus

Expand Origins of Calculus

Why do we not include the Maya mathematicians? They developed calculus over 1500 years ago. Why are they left out of this discussion? 2601:184:0:4820:DF5:D1A4:6E29:76BD (talk) 12:43, 5 November 2023 (UTC)

Do you have a reliable source for this? D.Lazard (talk) 18:30, 5 November 2023 (UTC)

Semi-protected edit request on 7 December 2023

The 'Kerala School' identified the 'infinite series'- one of the basic components of calculus - in about 1350. The discovery is currently - and wrongly - attributed in books to Sir Isaac Newton and Gottfried Leibnitz at the end of the seventeenth centuries. That knowledge, they argue, may have eventually been passed on to Newton himself. But other names from the Kerala School, notably Madhava and Nilakantha, should stand shoulder. 14.102.51.22 (talk) 06:39, 7 December 2023 (UTC)

 Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format and provide a reliable source if appropriate. Cannolis (talk) 06:45, 7 December 2023 (UTC)

Rearranging sections - practical to history

Hello, I am thinking about rearranging the sections of this article to be more practical. The etymology and history sections should be after the Principles and applications sections like other science and mathematics articles. There is a main history of calculus page and in looking at the calculus article, it looks quite a bit like the history article in structure.

Most readers want to know about what calculus is in this article, not the history of it. Rearrange the sections or shorten the history of calculus section? Any opinions? Ramos1990 (talk) 05:30, 2 April 2024 (UTC)

About etymology: IMO, section § Etymology is totally inadequate for a mathematical article; the true mathematical etymology is the following is the following. "Calculus" is a Latin word that means "computation", and, at the time of Newton, Leibniz and (later) Euler most mathematics were written in Latin. Indeed, two of Euler's book are entitled Institutiones calculi differentialis (Foundations of computation with differentials) and Institutiones calculi integralis (Foundations of computation with integrals). So, the English word "calculus" is simply an abbreviation of these two titles. In my youth, the French equivalent of "calculus" was "calcul différentiel et intégral". So, a single sentence in the lead is sufficient for the etymology: "Calculus" is the abbreviation of the Latin phrase meaning "differential and integral computation".

About the history: There is a clear WP:REDUNDANTFORK between section § History and History of calculus. So § History must dramatically be reduced to the description of the revolution of mathematics that consisted of the introduction of real functions, differentiable calculus and integral calculus (from Newton and Leibniz to Euler). This is fundamental to well understand calculus. IMO, such a short history should play the role of the sections "Motivation" of many mathematical articles. IMO, the place of such a section cannot be decided before having a draft. D.Lazard (talk) 10:05, 2 April 2024 (UTC)

I concur that the history section is too long to come that early in the article, and it either needs to be shortened or rearranged. Mathwriter2718 (talk) 12:29, 6 July 2024 (UTC)

Semi-protected edit request on 6 May 2024

The following sentence in the applications section should use "its" in place of "it's" as the word is functioning as a possessive, not a contraction of "it is."

"Alternatively, Newton's second law can be expressed by saying that the net force equals the object's mass times it's acceleration, which is the time derivative of velocity and thus the second time derivative of spatial position." Harrison Clark (talk) 01:57, 6 May 2024 (UTC)

 Done Bestagon ⬡ 02:33, 6 May 2024 (UTC)

Biology implied not to be a science

Near the top of the article it states that "Today, calculus is widely used in science, engineering, biology, and even has applications in social science and other branches of math". This implies that biology is not considered a science. Is this a Wikipedia standard or just an oversight? RandomLuker789 (talk) 14:16, 10 May 2025 (UTC)

It was an awkward tweak to the lead from a few months ago. I've re-jiggered. Remsense ‥ 论 14:25, 10 May 2025 (UTC)

Blending lead 2 paragraphs and removing unnecessary information

Hello, I was thinking about blending the first 2 paragraphs in the lead section as follows:

Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.

Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns instantaneous rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus. They make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. It is the "mathematical backbone" for dealing with problems where variables change with time or another reference variable.

changing to:

Calculus is the mathematical study of continuous change. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns instantaneous rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus. They make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. It is the "mathematical backbone" for dealing with problems where variables change with time or another reference variable.

The reason for this change is to decrease the number of paragraphs in the lead section, as well as to remove some information about other mathematics branches (eg. geometry, algebra) that is not related to calculus. KraljLavova97 (talk) 22:59, 31 October 2025 (UTC)

I agree with this. In addition to being somewhat hard to follow (one must be a somewhat sophisticated reader to grasp what "the study of generalizations of arithmetic operations" means), the main text doesn't elaborate on that comparison, and the intro is supposed to summarize what the main text says. Stepwise Continuous Dysfunction (talk) 08:30, 28 March 2026 (UTC)

References

Reorder subfields

@Stepwise Continuous Dysfunction. Perhaps the article could have its own subfield. Differential calculus covers the limit and derivative as well as its application, which include minimal surface and the maximum-minimum, concave-convexity of a function. The integral calculus covers the integral, pre-definition by Riemann sum, and the method of calculating geometrical dimensions by area and volume. I thought stochastic calculus and differential equation could be included in those two, but they use both altogether.

To be clear, I'm halfway through, so I'll drop off my ideas here for now. Removing the formal definition and briefly explaining the definition without showing complex mathematical notations, whenever possible. If you have other ideas and disagree with mine, revert. Dedhert.Jr (talk) 01:03, 29 March 2026 (UTC)

I think the definition of the derivative in terms of a limit is more than important enough to include here. I also do not understand why the fundamental theorem is now classified as a "subfield". It's not a subfield of calculus; it's a theorem. It seems to me that you pruned too much (or perhaps I can't follow your intentions when you are only halfway through). Perhaps a radical revision of that magnitude should be done in a sandbox first, so that no one is confused at the intermediate stages. Stepwise Continuous Dysfunction (talk) 05:30, 29 March 2026 (UTC)

In my experience, it is common to teach limits, then derivatives, then integrals. This is the general order taken by most (though not all) books, and I think it is a good order to follow here. Stepwise Continuous Dysfunction (talk) 05:53, 29 March 2026 (UTC)

I think that removing too much notation makes the article less clear, because we end up talking in vagaries. Formulae can be intimidating, but they are also precise. I have tried to prune the instances that really didn't contribute value, and to move text that explains motivations and intuitions before the equations. Stepwise Continuous Dysfunction (talk) 06:25, 29 March 2026 (UTC)

History Section

The history section is too long, and this information is more appropriate for the article History of Calculus.I had removed couple of these but still the history section looks lemgthyMyuoh kaka roi (talk) 06:33, 29 March 2026 (UTC)

I agree that it was too long, particularly when we have History of calculus to hold all the details. Stepwise Continuous Dysfunction (talk) 06:41, 29 March 2026 (UTC)

I am highly doubtfull with this sentence which is present in the modern section which states that

Johannes Kepler's work Stereometria Doliorum (1615) formed the basis of integral calculus.

The given source is from NASA website and I can't find any other source mentioning this claim Myuoh kaka roi (talk) 08:10, 29 March 2026 (UTC)

Calling it the basis might be overstating it, but Kepler investigating wine barrels is a part of the history. Stepwise Continuous Dysfunction (talk) 02:05, 30 March 2026 (UTC)

References

Semi-protected edit request on 18 April 2026

In The second line is only an approximation to the behavior of the function at the point a because it does not account for what happens between a and a + h. Change

  second

to

  secant

 Done D.Lazard (talk) 14:03, 18 April 2026 (UTC)

Semi-protected edit request on 11 May 2026

In "Primary concepts and basic notation," line 4, word 3 ("a") must be removed for removing the grammatical error Carelesspirate (talk) 16:19, 11 May 2026 (UTC)

 Done. For future reference, line numbering various from display to display so isn't a good way to descirbe what word you are talking about. meamemg (talk) 17:17, 11 May 2026 (UTC)

@Meamemg Thaks for the tip. Carelesspirate (talk) 14:13, 29 May 2026 (UTC)