
Calculus Made Easy (1914) [pdf] - Pamar
http://djm.cc/library/Calculus_Made_Easy_Thompson.pdf
======
theCricketer
MIT recorded a set of Calculus video courses back in 1970s that they have
since made publicly available. It is taught by a lecturer named Herbert Gross.
His style of lecturing is clear, he states why things are defined the way they
are and derives everything from first principles. There is an unusual mix of
rigor and focus on building understanding - where everything comes from. It
also taught me that math is about reasoning logically and rigorously and we
shouldn't always rely on intuition (at least while doing math). Deriving
almost all the basic calculus results that were drilled into me from the basic
concept of a limit, deltas and epsilons was really refreshing.

Compared to more recent OCW calculus videos, I found this to be better in
terms of respecting the learner's intellect, presenting the whole proof
rigorously and teaching the student to think a certain way.

Calculus Revisited: Single Variable Calculus | MIT OpenCourseWare -
[https://ocw.mit.edu/resources/res-18-006-calculus-
revisited-...](https://ocw.mit.edu/resources/res-18-006-calculus-revisited-
single-variable-calculus-fall-2010/index.htm)

Complex Variables, Differential Equations, and Linear Algebra -
[https://ocw.mit.edu/resources/res-18-008-calculus-
revisited-...](https://ocw.mit.edu/resources/res-18-008-calculus-revisited-
complex-variables-differential-equations-and-linear-algebra-
fall-2011/index.htm)

Calculus Revisited: Multivariable Calculus | MIT OpenCourseWare -
[https://ocw.mit.edu/resources/res-18-007-calculus-
revisited-...](https://ocw.mit.edu/resources/res-18-007-calculus-revisited-
multivariable-calculus-fall-2011/index.htm)

~~~
lunchladydoris
I just had a look at the first video in the first course on YouTube [0] and
was delighted to see Herb Gross responding in the comments. Clearly this is a
man who loves his subject and loves introducing it to others.

[0]
[https://www.youtube.com/watch?v=MFRWDuduuSw](https://www.youtube.com/watch?v=MFRWDuduuSw)

~~~
smnplk
Yes, what a gem of a man.He also posted his email address in the comments for
a young high school student for any further help. He is 88 years old now, I
hope he is in good health.

------
tzs
That PDF is just a bunch of scanned images of the book. It's large and
cumbersome in many readers.

There is a _much_ better PDF at Project Gutenberg [1].

The Gutenberg PDF is only 1.9 MB, compared to 12 MB for the scanned image PDF.

The Gutenberg page for this book [2] also has a link to the LaTeX source for
the PDF.

[1]
[http://www.gutenberg.org/files/33283/33283-pdf.pdf](http://www.gutenberg.org/files/33283/33283-pdf.pdf)

[2]
[http://www.gutenberg.org/ebooks/33283](http://www.gutenberg.org/ebooks/33283)

~~~
userbinator
You say 1.9MB, the Gutenberg page says 1.8MB, and the download itself is only
1.18MB thanks to gzip. The main difference is that the Gutenberg PDF is a
transcribed, cleaned-up version.

As much as this probably makes me sound like an audiophile, I actually prefer
the raw scans over what may essentially be a reprint. They show all the
blemishes, unofficial additions, and other marks that make the book look more
"real" and give it character.

In this instance, the raw scan has a picture of the cover, as well as an
interesting note handwritten near the beginning: "Property of Edward M Sumner"
with an address. IMHO these sorts of historical artifacts are worth preserving
too. I've come across scans with random notes, bookmark fragments, and
newspaper clippings included, and it's always fun to ponder how they got
there. (Who is this person and how did he get the book? Is he the one who
scanned it? Etc.)

~~~
noam87
This is why I love used books. My copy of Schopenhauer's collected essays has
gone through 4 owners since 1914, all 4 of whom have signed and dated the
front cover, all of 4 of whom have marked and underlined at different spots
(including, now, myself). My copy of Riverside Chaucer went through two
students before me. And they all pick up their own unique scents along the way
(my girlfriend jokes that I only buy books to smell them).

~~~
appleiigs
I'm with you guys! This book has some serious character. The cover,
handwriting, imperfections, and on top of it all, the writing style.

The problem with used books tho is that sometimes I find hair. Ugh.

~~~
sebastianconcpt
Might be proof of DNA of a previous owner. Depending on the historical value
that could be golden

------
djhworld
I'm embarassed somewhat to say this, but over the past few weeks I've been
taking the courses on Khan Academy on mathematics. I'm nearly 30.

and I'm not talking about brushing up on my linear algebra, that comes later,
I'm talking high school level mathematics, stuff that I've largely forgotten
or didn't "get" first time round.

I've seen these "machine learning for hackers!" articles who try to dish out a
bit of maths saying that's all you need, but I don't think you can escape the
fact that sometimes you just need to start from the beginning and work your
way up

~~~
Accacin
I don't think anyone can ever fault you for taking the initiative and learning
it in your own time.

I feel the same way though, I've been looking back through some basic algebra
on Khan Academy too because I feel maths is very much my weak point.

~~~
andai
My mom always told me I'd need better Math grades to become a programmer.

Since the 2nd program I ever wrote was a script to do my math homework for me,
I laughed at her.

Then I failed to pass the first year of CS bachelor. Twice.

I am very glad to see this most excellent book here, and will add it to my
collection.

~~~
jimmaswell
How did that happen? The required math courses got in the way?

~~~
J-J
Also attempting to finish CS BS but I have hit a wall in my late 30s unable to
pass pre-calc. I shudder at the daunting levels of Calc that come after to the
point that I'm debating switching majors just to "get a degree".

~~~
Jtsummers
This may not work for you, but I honestly didn't understand calculus until I
worked through Knuth's _Concrete Mathematics_. There's a portion of it
detailing rules on summations, which were (I realized at the time) the
discrete equivalent of integration (summation of functions over integers
versus integration which is summation of continuous functions). With my
(stronger) CS than math background, it just "clicked" for me. You could check
out the book from your university's library and see if this material helps
you. I can't put my finger on which specifically now (too many years later)
but various calculus concepts just fell into place as I worked through those
portions of the book.

------
kjhughes
Summer of 1980, going into my senior year in high school, I mentioned I'd be
taking Calculus next year to a co-worker a couple years older than I. He said
he had the best book in the world on Calculus, and he loaned me his copy of
Silvanus P Thompson's _Calculus made easy_. I thoroughly enjoyed that book,
benefited from its intuitive explanations, and forever appreciated his
recommendation.

If I may similarly influence anyone here, for themselves or someone they know,
to read _Calculus made easy_ to supplement their calculus coursework, I will
be happy to have paid the favor forward in some small way.

By the way, Kalid Azad may be our modern day Silvanus P Thompson. And he has
better tools[1], which he wields masterfully, than just pen and paper.
Recommended too.

[1] [https://betterexplained.com/](https://betterexplained.com/)

~~~
zdean
Would you happen to know of any websites, video series, books, etc that would
be in the same vein as these 2 sources but geared towards very young students
(elementary/middle school math)? ...so that they can understand it
conceptually from a young start.

EDIT: I'm working through Khan Academy with one of my kids...would like to
find other resources as well.

~~~
kjhughes
Hmm, how about a technique rather than a resource...

Look for opportunities to expand what they're doing in school. For example,
after my kids had covered place values in school, I taught them binary. Their
knowledge of base 10 is so much more robust when they learn base 2 as well.

Point is, I bet you already know plenty to be that ideal resource you seek for
them. Good for you for wanting to start early.

~~~
zdean
Thanks for that affirmation. I actually taught them binary counting too over a
weekend a few months back...I was amazed how quickly they were able to pick up
on it (3rd and 5th graders). With limited time/energy, I was hoping to find
some great resources to add to what I can provide them individually.

------
noam87
In a similar vein: "Probability Through Problems":
[https://archive.org/details/springer_10.1007-978-0-387-21659...](https://archive.org/details/springer_10.1007-978-0-387-21659-1)

I love this book. What's the best way to learn a mathematical field? To
discover it yourself, piece by piece!

I wish this were a series.

~~~
JadeNB
It _is_ a series: [http://link.springer.com/search?facet-
series=%22714%22&facet...](http://link.springer.com/search?facet-
series=%22714%22&facet-content-type=%22Book%22) .

------
allsunny
I have an embarrassing amount of Calculus books. My dad taught the subject in
a high school and community college; I suppose I have a soft spot for it.
"Calculus Made Easy" is a good book though I do think there are better ones
these days. Some of the lexicon has changed and there are topics covered in a
modern Calculus textbook that aren't covered in the original book (that I
personally think are worthwhile spending time on). The updated version with
Martin Gardner does have blurbs where necessary to point it out. The Kline
book is a MUCH larger read, but is what I would recommend if you want a
reasonably priced Calculus book that's easy to grok. Otherwise, I think it's
hard to go wrong w/ the Stewart books. Work through the problems as they do in
the book, you will come away w/ what you need. Finally, if you want a
whirlwind tour, Calculus for Dummies by Mark Ryan is great.

Time spent learning Calculus is worthwhile; and if nothing else, understand
the fundamental theorem. Overwhelmingly impressive.

------
mixedmath
For what it's worth, this is available as a much leaner pdf [1] on Project
Gutenberg now, including the TeX source that some kind person used to update
it.

[1]:
[http://www.gutenberg.org/ebooks/33283](http://www.gutenberg.org/ebooks/33283)

------
baldfat
The prologue is 100% dead on and what I have always thought in terms of the
easy part of calculus needs to be taught early. I would have never been able
to vocalize what he said in the short half page of text.

We teach math backwards. We have a population that can barely do 4th grade
arithmetic and it is socially okay.

Children and people believe that decimal points are accurate and that
fractions are abstract when the exact opposite is true. 1/3 of a pizza is real
and 0.333333 is a fake number.

We also teach movement and change as a word problem i.e. a train leaves
Chicago at 25 MPH and another train leaves Flint, MI at 35 MPH when will the
trains meet? That answer is an estimation of an unattainable constancy but
people believe it is logical conclusion.

Pre-Calculus (needs to be repackaged with the idea of the one consistent in
our world is change) should be taught before Algebra and Geometry. Make math
into something where people can truly understand abstract and concrete. People
actually think calculus is a hyper abstract algebra when in fact it is putting
math into real world solutions.

The number one problem is calculus is 100% dependent on the teacher. A great
teacher will make this work and a lower skilled teacher can absolutely kill
almost all learning.

~~~
laughingman2
I think you this will interest you. Its a mathematician's lament on how the
current system of teaching math is wrong.

[https://www.maa.org/external_archive/devlin/LockhartsLament....](https://www.maa.org/external_archive/devlin/LockhartsLament.pdf)

------
impendia
I assigned this in an Honors Calc II class I taught at a state university.

The main text was Stewart (decided at the department level), but I was
teaching the Honors section which provided a good opportunity for me to ask
for something extra. I had my students read this book alongside Stewart, and
write weekly short essays comparing the two approaches. Many of the students
turned in some quite good writing.

This is an outstanding book.

------
OJFord
Heavens - I'd have never guessed titles like '~ Made Easy' were as old as
that.

I don't know why exactly, it just sounds modern.

~~~
emodendroket
1914 is pretty modern.

~~~
OJFord
It's all relative. Obviously I mean that it sounds vastly more recent than
1914 to my ear.

And anyway, I confess I don't know the industry at all, but I doubt anyone
would talk about 1914 as representing 'modern publishing'.

~~~
emodendroket
A lot of the elements of what we'd call "modernity" were either introduced or
became widespread in the course of the first World War so I'm not trying to
just be a jerk here; I think it really is a useful dividing line.

~~~
OJFord
I'm not sure I agree to it being anything stronger than a 'catalyst' period,
but regardless; as elsewhere, by 'modern' I meant 'more recent than it is'.

------
thechao
I learned calculus from this book, as did my dad, and my grandfather. My
daughters will learn from this book.

------
ashark
Good lord. I somehow took (and passed!) a year of high school calculus plus a
semester in college, and I never had a good sense for the word "Integral" in a
math context as anything but arbitrary jargon. _And_ I've spent a not-tiny
amount of time with BetterExplained's calculus. 30 seconds with this book and
it's obvious. Now I'm making connections with the French (of which I have
barely any, but any port in a storm) and it's solid in my mind.

Well. Now I have to read the whole thing I guess.

------
apo
After scanning for a few minutes, I was amazed at how readable the book is
given its age and my experience with books of similar age.

The book also does appear to go out of its way to keep language simple. For
example:

 _We call the ratio dx /dy "the differential coefficient of y with respect to
x." It is a solemn scientific name for this very simple thing. But we are not
going to be frightened by solemn names, when the things themselves are so
easy. Instead of being frieghtened we will simply pronounce a brief curse on
the stupidity of giving long crack-jaw names; and, having relieved our minds,
will go on to the simple thing itself, namely the ration dx/dy._

------
jstewartmobile
It's crazy the kids have to pay hundreds of dollars for the horrible books the
colleges require when brilliant things like this can be had for free...

~~~
jacquesm
It's not rare that supports the people teaching the class. Nothing like
pushing your own book to students that just _have_ to buy it. In some cases
the books don't even get used.

~~~
cat199
> Nothing like pushing your own book to students that just have to buy it.

This is a very small fraction of what goes on -

1) Many many professors have not written a/the book

2) You're not going to sell 1000000's of books through the 1 class you teach
every semester. A few, yes. But lots, no.

------
mdturnerphys
Just about missed the attribution in the epigraph:

 _What one fool can do, another can. -Ancient Simian Proverb_

Monkey see, monkey do?

~~~
KSS42
A fool that can plainly explain matters to another fool is not a fool.

------
transitorykris
This is an incredible book. I'm a visual thinker, and while this book lacks
all the glossy pages of illustration found in a modern Calculus textbook, the
writing style helps develop that visual intuition. In the same vein of concise
Calculus books, Serge Lang's Short Calculus is also great (if you need a
refresher, or if you're just starting out).

[https://www.amazon.com/Short-Calculus-Original-
Undergraduate...](https://www.amazon.com/Short-Calculus-Original-
Undergraduate-Mathematics/dp/0387953272)

------
emarthinsen
This is, actually, a really good book. Don't let the cheesy title throw you
off. I learned more in the first few chapters than I did after a semester of
calc classes. Highly recommended.

------
vixen99
Reading it as a kid I wasn't sure I trusted the author - Silvanus P. Thompson
FRS ('FRS' \- which I knew to be something rather prestigious) when he wrote
in the prologue "Being myself a remarkably stupid fellow, I've had to unteach
myself the difficulties . . . What one fool can do, another can."

------
sideproject
Why didn't any one tell me about this book when I was younger! This is so
good. :)

~~~
partisan
As someone who struggled through calculus, this book would have made a huge
difference for me. Just reading through the first few pages brought a smile to
my face that someone could so plainly explain these critical concepts in such
a familiar way. Why didn't my professors do that?

~~~
jacquesm
> Why didn't my professors do that?

Because to them it's obvious. Most maths teachers are so far ahead of the
students they forgot they once were students themselves.

I've had 3 different ones in high school and the difference was incredible.
All the way from 'only the best students learn anything' to 'everybody _earns_
at least a passing grade'.

Maths and physics were the classes where the quality difference between the
teachers stood out the most.

~~~
taejo
> Because to them it's obvious.

And to them it's wrong! Much is said in this book which is difficult (but not
impossible) to rigourously justify. It took centuries for calculus to be
placed on a rigourous mathematical foundation; this foundation (called "real
analysis", largely developed in the 19th century) is quite different from the
intuitive ideas presented in this book. The presentation here (in particular
the idea that dx² is negligible) _can_ be made rigourous through "non-standard
analysis", but this 20th century development is less-known (in fact, unknown
to many mathematicians) and perhaps even more difficult than real analysis.

Rigour is not necessary to understanding, and can even be fatal to
understanding, but it's how mathematicians work, and generally mathematics is
taught by mathematicians.

~~~
sundarurfriend
> this foundation (called "real analysis", largely developed in the 19th
> century) is quite different from the intuitive ideas presented in this book.
> ... (in particular the idea that dx² is negligible)

Thank you for posting this! Such things always bothered me in high school,
seemed like approximations that ought to bite you in the behind at least in
some corner cases. Another example from TLA:

> dy = 2cos(θ + 1/2 dθ) · sin 1/2 dθ

> But if we regard dθ as indefinitely small, then in the limit we may neglect
> 1/2 dθ by comparison with θ, and may also take sin 1/2 dθ as being the same
> as 1/2 dθ. The equation then becomes:

> dy = 2cosθ × 1/2 dθ

This again seems like very sloppy and careless kind of approximation that
ought to bite you in the back - but knowing there are just (supposed-to-be)
intuitive non-rigorous methods, and that these have actual rigorous backing,
somehow soothes me.

~~~
thanatropism
But this is true of every level of mathematics. See humorous proofs that 2=3
amounting to manipulations like 0 _a = 0_ b, cut the zeros, a=b. This is no
fault of "nonrigorous elementary algebra", it's a matter of remembering all
notations are abbreviations and you have to know how to manipulate them.

You can get away with dy and dx if you just think "I'm not writing integral
signs because they're annoying" and remember the rules of working with
integrals. This is how stochastic differential equations work -- they're not
even differential equations because Brownian motion is not differentiable,
they're just notation.

------
mcguire
Since no one else has mentioned it, there is an updated edition available in
print, with updates by Martin Gardener.

~~~
knight17
> ... a 1998 update by Martin Gardner is available from St. Martin's Press
> which provides an introduction; three preliminary chapters explaining
> functions, limits, and derivatives; an appendix of recreational calculus
> problems; and notes for modern readers. Gardner changes "fifth form boys" to
> the more American sounding (and gender neutral) "high school students,"
> updates many now obsolescent mathematical notations or terms, and uses
> American decimal dollars and cents in currency examples.

[https://en.wikipedia.org/wiki/Calculus_Made_Easy](https://en.wikipedia.org/wiki/Calculus_Made_Easy)

Seems like a good update to a classic, but there are some in the reviews
complaining about Gardner [https://www.amazon.com/Calculus-Made-Easy-Silvanus-
Thompson/...](https://www.amazon.com/Calculus-Made-Easy-Silvanus-
Thompson/dp/0333772431)

------
throwaway2016a
The prologue had me hooked... I have never read anything like this in a text
book. The self-deprecating humor immediately disarms you if you're the type
that would go into something like this intimidated. I am definitely reading
this.

------
payne92
Oh wow. Imagine typesetting that in hot metal, many many decades before TeX
and LaTeX!!

------
SilentM68
I've been looking for something similar to this but for Algebra, Trig, etc.
before relearning Calculus and came across this: Mathematics For The Pracicle
Man by Howe (1918?)
[http://www.aproged.pt/biblioteca/mathematicsforthehowe.pdf](http://www.aproged.pt/biblioteca/mathematicsforthehowe.pdf)
It's targeted to Engineering students and it's not lengthy, won't take me two
years to learn. Hopefully it'll be of same quality as Thompson's book?

------
InclinedPlane
I love calculus, it's such an amazing collection of fascinating, elegant (and
useful!) concepts that give you a transformative insight on mathematics in
general. It's very frustrating to see it taught so poorly so often though.

One problem that teaching calculus has is that it's very dependent on having a
solid foundation in other mathematics such as advanced algebra, trig, etc. In
today's school systems that encourage gaming the system as students and
teaching to the test as educators it's rare for most students to actually
understand or be competent with material they've allegedly studied. When they
hit something that starts off where they left off and builds upwards, if they
have any weaknesses in that foundation it will show immediately and slow them
down immensely.

Add on to that all the other problems of typical calculus instruction such as
a desire to make it hard as a matter of protecting calculus education as a
status symbol for "smart" people, the ability to ratchet up the difficulty
arbitrarily through requiring memorization of a potentially infinite set of
"trivia" (every trig. identity, every method of differentiation/integration,
and so on), while generally not concentrating on the abstract concepts or the
fundamentals.

------
officialchicken
There is a 1998 update to the book with "modernized" english (I think it is
clearer while preserving a dated style) and some additional chapters. ISBN-10:
0312185480

------
donquichotte
It's funny that a book from 1914 is formatted in a way that it is much easier
to read on my mobile phone than pretty much anything I can download from
google books.

------
c517402
IIRC this the book Richard Feynman said he checked out of the library and
learned calculus from. Also, Feynman made comments similar to those in the
Prologue.

~~~
ramblerman
no that was Calculus for the practical man

[http://www.goodreads.com/book/show/7398477-calculus-for-
the-...](http://www.goodreads.com/book/show/7398477-calculus-for-the-
practical-man)

~~~
madrik
Feynman had read both books. He mentioned the prefatory quote from 'Calculus
Made Easy' in an interview given to Omni Magazine in 1979:

"... I had a calculus book once that said, 'What one fool can do, another
can'..."

I have this in Chapter 9: 'The Smartest Man in the World' in Feynman's book
'The Pleasure of Finding Things Out'.

~~~
ramblerman
Thanks for the correction, I didn't know that

------
mumrah
It's for sale on Amazon: [https://www.amazon.com/Calculus-Made-Easy-Silvanus-
Thompson/...](https://www.amazon.com/Calculus-Made-Easy-Silvanus-
Thompson/dp/0312185480/ref=sr_1_1?s=books&ie=UTF8&qid=1492741701&sr=1-1&keywords=calculus+made+easy)

------
jaclaz
In Italy there is a "similar" (in the sense that it manages to explain
calculus in a friendly and easy manner) book, that has been re-edited and re-
published since - I believe - 1929 or so:

[https://books.google.it/books?id=oHPmx_v1H6QC&pg=PP5&hl=it&s...](https://books.google.it/books?id=oHPmx_v1H6QC&pg=PP5&hl=it&source=gbs_selected_pages&cad=2#v=onepage&q&f=false)

the original is French, the Author Gustave Bessiere was an engineer,
mathematician and inventor:

[https://books.google.it/books/about/Le_calcul_intégral_facil...](https://books.google.it/books/about/Le_calcul_intégral_facile_et_attrayant.html?id=d7tKMQAACAAJ&redir_esc=y)

I don't think they are (yet) copyright free, though.

------
agumonkey
This popped on my twitter yesterday, that single page was more effective than
10 years of sweating. Speechless.

------
hilldex
I love how the first page (Ch. 1) tries to show that 'terrifying' calculus
symbols have very simple meanings, and so there's no reason to run away.

Less pleased, though not at _all_ surprised, that the book addresses 'fifth
form boys', with no mention of girls.

------
boyhowdy
As someone who dropped out of Cal II, the first few paragraphs of this book
gave me more understanding than I ever had in college... Either I was very
lazy, or my teachers couldn't express these simple ideas clearly, or both.

------
neuronexmachina
Fun fact: The author Silvanus Thompson was an early pioneer of what is now
known as transcranial magnetic stimulation. You can see him posing with his
head in a device for testing neurophysiological effects of alternating
magnetic fields in figure 4 of this paper:
[http://rsnr.royalsocietypublishing.org/content/61/1/5.figure...](http://rsnr.royalsocietypublishing.org/content/61/1/5.figures-
only)

------
Simorgh
This book is staggering. I'm on page 1. I've read a couple of dozen lines.
This has explained more about calculus then a decade and a half of seeing
related concepts.

------
georgewsinger
I believe this was Feynman's favorite book on calculus.

~~~
gigonaut
actually I believe that was "Calculus for the Practical Man" by J.E. Thompson
and it is also an excellent read.

------
iamiam
So many of these old textbooks are much clearer than ones of today. And
they're no-nonsense, "What one fool can learn, another can learn."

------
gejjaxxita
I read this book when I was 14, it belonged to my grandfather. I'd completely
forgotten about it but seeing it has really brought back memories.

------
martijn_himself
This looks like a brilliant resource.

My problem with advanced math is not so much the understanding of principles
but the application of these to solve new problems creatively.

I was able to master partial differential equations and pass exams but was
never able to apply what was learned to solve new problems which I found very
frustrating and was what ultimately led me to not pursue a career in the
field.

------
Safety1stClyde
It's like "Calculus for dummies" except with pounds, shillings and pence, and
Mrs. Ayrton's electrical arcs.

~~~
allsunny
There is an actual "Calculus for Dummies", written by Mark Ryan, it's a great
book.

------
danm07
Wish my prof in college gave this as a course reading.

------
ankurdhama
In my experience, everything is easy if you DON'T try to learn it using
analogies and metaphors.

~~~
cool_shit
Terrible advice! I tell all of my students to find _as many_ analogies as they
can. You can never lose by increasing the number of ways in which you
understand something. Analogies, some may argue, are at the heart of
mathematics.

> Mathematics is the art of giving the same name to different things

Poincare.

> The art of doing mathematics consists in finding that special case which
> contains all the germs of generality

Hilbert.

> The vast majority of us imagine ourselves as like literature people or math
> people. But the truth is that the massive processor known as the human brain
> is neither a literature organ or a math organ. It is both and more.

John Green.

> Sometimes I think that creativity is a matter of seeing, or stumbling over,
> unobvious similarities between things - like composing a fresh metaphor, but
> on a more complex scale.

David Mitchell.

There is an ounce of truth in what you say -- metaphors can be abused to draw
false conclusions. This does not mean one should cower from using them.

~~~
ankurdhama
Everyone has their own philosophy of mathematics. To me, the core idea is the
idea of representations, such that those representations allow you to extract
patterns (aka similarity or commonality) from various cases.

~~~
nicklaf
I can't help but indulge a bit and now ask whether or not we can't​ extract a
common pattern from the two representations of mathematical cognition offered
by yourself and GP. :-)

~~~
ankurdhama
Not here but may be on "meta hacker news".

------
fad92
Does anyone have a recommendation in the similar vein for probability and
statistics?

------
emmelaich
That's a great prologue. A foreshadowing of the for Dummies/Idiots books.

------
nvarsj
Thanks for this - I had not heard of this book, and it looks remarkable!

------
sebastianconcpt
First chapter alone is a jewel. This is how great teachers sound like!

------
austenallred
I have nothing to say other than that I adore this book

------
mrcactu5
i know this is supposed to be a beginner textbook, but his discussion of
infinitesimal geometry uses an awful amount of Scheme Theory to justify.

------
xchip
Disappointing, I thought this was about making renal calculus...

(joke)

------
ensiferum
Great book! I have a hard copy, really recommended!

------
mrcactu5
these figures are so exquisite and the typography lazily guides me through

------
EGreg
This is a good book. But on page 5 you have an error: it should say
_trillionth_ instead of billionth. I find myself liking your approach, though.
You should change the font and insert some more diagrams.

Oh, what's that... you can't just republish instantly because electronic
computers haven't been invented yet? Well, just iterate and do things that
don't scale :)

~~~
nvoorhies
It's actually circa 1914 British usage rather than an error.

~~~
EGreg
Really? What'd they call a one followed by nine zeros then?

~~~
contravariant
A milliard.

The word is still used by countries that use the 'long scale', which has the
nice property that a billion = (1 million)^2 and a quadrillion = (1 million)^4
etc. If you can count in greek this also means that an n-illion times an
m-illion equals an (n+m)-illion.

~~~
cat199
This strikes me as a vastly superior way of doing things..

Any insight as to why things went 'the wrong way'?

~~~
sundarurfriend
Apparently [1], both ways of counting originate from France. This 'superior'
way came first and was adapted by the British, then our current way of naming
was created and adopted by the US. Wiki says this one then became the standard
because of USA's dominance in the financial world.

[1]
[https://en.wikipedia.org/wiki/Names_of_large_numbers#Extensi...](https://en.wikipedia.org/wiki/Names_of_large_numbers#Extensions_of_the_standard_dictionary_numbers)

