Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Tomorrow is a very special day for both my students and I: we will be starting a calculus course. I'm looking for some nice quotes to read to them to convey just what a complete game changer calculus was. I've done a quick Google search, but nothing acceptable comes up.

I don't want anything too old fashioned, or too stuffy. Can anyone recommend anything to help me inspire a new generation of blossoming mathematicians?

Edit: I'm specifically interested in quotes that mention calculus by name, and that mention its impact upon mathematics.

share|cite|improve this question
Are you sure a quote is the best way to do this? Depending on which angle you're coming from, either showing some examples of how fundamental calculus is, or recounting key events in the history of mathematics, might be a better approach. Quotes can be great but I doubt their appeal to the average (presumably) 18-year-old (speaking as a 21-year-old who greatly appreciates the value of calculus). – Clive Newstead Oct 8 '12 at 22:17
I can't give you a quote from a famous person, but I'll gladly tell you about my own experience. Calculus is what makes me love math. Before I knew calculus, math was memorization of meaningless concrete formulae with tedious connections to abstract shapes. Now it is the math that is abstract, and it describes real things. – kojiro Oct 9 '12 at 2:07
up vote 4 down vote accepted

This is from Wikipedia:

"Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of equations."

I don't remember the source but I liked this one:

"The importance of calculus is that most of the laws of science do not provide direct information about the values of variables which can be directly measured. This is why it's important to have a mathematical way of talking about change. That's why you see the concept of the derivative used throughout science"


The source is

He has written a paragraph about importance of calculus,you might get some idea from there,I hope. I enjoyed reading it.

share|cite|improve this answer
Yeah, I found that page. Thanks. I was hoping for a nice sound bite. It looks like I'll have to settle for von Neumann's quote: "The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics, and… still constitutes the greatest technical advance in exact thinking.” – Fly by Night Oct 8 '12 at 20:53
It is awesome quote. And I'ld like to tell you that you're an excellent teacher. Not many make this much effort. – TheJoker Oct 8 '12 at 20:57
Thanks for your kind words. I love mathematics, and I want to pass that on to my students. Especially as a differential geometer. I feel like I'm introducing them to my baby. – Fly by Night Oct 8 '12 at 21:20
@FlybyNight Your students may also enjoy reading von Neumann's interesting article The Mathematician (the source of the above quote). – Bill Dubuque Oct 9 '12 at 0:12

This is a nice collection as well:

Personally, I liked this one attributed to Laplace:

It is interesting thus to follow the intellectual truths of analysis in the phenomena of nature. This correspondence, of which the system of the world will offer us numerous examples, makes one of the greatest charms attached to mathematical speculations.

share|cite|improve this answer
This is a nice list of general mathematical quotes, but calculus is only mentioned once. I'm giving a calculus course and want to emphasise the importance of calculus. They won't realise that analysis is related to calculus; they don't know what calculus is. – Fly by Night Oct 8 '12 at 20:40

I can you recommend the collection of quotes from Doron Zeilberger

share|cite|improve this answer
I am unable to view this link. My web-browser tells me it is unsafe and directs me back. – Fly by Night Oct 8 '12 at 20:40
In my browser it works perfectly. – Adi Dani Oct 8 '12 at 20:44
I didn't say that the link didn't work. My web-browser tells me that it is an "untrusted connection". – Fly by Night Oct 8 '12 at 20:46
It is safe site just go ahead! – Adi Dani Oct 8 '12 at 20:54
The link seems safe, and is pretty useful (as a collection of quotes that is!) – TCSGrad Oct 9 '12 at 4:46

(From The Unreasonable Effectiveness of Mathematics in the Natural Sciences)

"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning."

share|cite|improve this answer
This is a nice mathematical quote, but it doesn't mention calculus. I'm giving a calculus course and want to emphasise the importance of calculus. – Fly by Night Oct 8 '12 at 20:38
@FlybyNight While it does not mention calculus by name, the fact that it mentions "the laws of physics" suggests that the author had calculus-type mathematics in mind (almost surely he was thinking of differential equations especially). You could preface the quote with this information. – Austin Mohr Oct 8 '12 at 21:00

An advice from Jean d'Alembert to those who questioned the calculus could be appropriate :-) :

$$``\text{Allez en avant, et la foi vous viendra.''}$$

$$\text{(Push on and faith will catch up with you)}$$

(from these quotations or the answer from Piero D'Ancona at MO in 'Describe a topic in one sentence')

Silvanus Thompson's 1914 book "Calculus Made Easy" (available here) starts with :
$$``\text{What one fool can do, another can.''}$$ $$\text{(Ancient bimian Proberb)}$$ (this was often cited by Richard Feynman)

Thompson added (page 13) :
"Considering how many fools can calculate, it is
surprising that it should be thought either a difficult
or a tedious task for any other fool to learn how to
master the same tricks."

share|cite|improve this answer
Thanks for the corrections @AustinMohr ! – Raymond Manzoni Jul 22 '14 at 23:00

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.