Babbage, Newton, and Leibniz
Newton & Leibniz both discovered Calculus about the same
time. But they used a slightly different approach.
Newton was popular in England, of course. Leibniz was French.
At the heart of Calculus is something called "the derivative". Never
mind what that means. What is important here is that Newton wrote
the symbol for the derivative as one or two little dots over an x,
as shown below, whereas Leibniz wrote it like a fraction with
several letter "d"s. To wit:
Although Newton gets most of the credit for inventing Calculus, we
ended up using Leibniz' notation over Newton's to this day. But
Cambridge in the early 1800's, being English, refused to change.
Kinda like Americans of today who hold steadfastly to feet and
pounds and degrees Fahrenheit whereas the entire rest of the world
uses meters and kilograms and degrees Celsius.
It was Charles Babbage who created a popular movement at Cambridge
to switch to Leibniz' "d"s, and he did so with humor. He turned the
two notations into a metaphorical pun: "dot-age" for Newton's dots
("dotage" = no longer relevant, old age, senility), and "D-ism" for
Leibniz's "d"s, which are godly (deism).
Here is the story from http://ds-wordpress.haverford.edu/bitbybit/bit-by-bit-contents/chapter-two/2-3-babbages-early-life/
Charles Babbage entered Cambridge in 1810. Hardly a
bookworm, he was a charming, gregarious, and athletic young man,
with a fondness for whist and sailing. Even his serious pursuits
bore a lighthearted touch. During his years at Cambridge, for
example, the school was caught up in a controversy over the format
of the Bible. Should the book be printed with or without
explanatory notes? One side sought to make the word of God more
comprehensible to the masses, the other to preserve its literal
purity. Cambridge, which took its religion seriously, was littered
with posters and broadsides advocating one or the other side of
And the rest is history! Today, although we give Newton most of the
kudos for inventing Calculus, we use the Leibnizian system
exclusively. Few modern mathematicians would even recognize Newton's
"dots" today! And we have Charles Babbage and friends to thank for
At the same time, however, the university was less than zealous in
its cultivation of the intellect, and the school, Newton’s alma
mater and once the guiding light of European mathematics, had lost
its luster. English mathematicians were trained in an inferior
notation of calculus – the confusing dots of the Newtonian version
as opposed to the clearly defined d’s of the Leibnizian system –
and the rift between Britain and the Continent had widened to a
point where most English mathematicians couldn’t decipher the
publications of their Continental counterparts. English
mathematics was falling by the wayside, and Babbage, Herschel, and
most of the country’s bright young mathematicians and scientists
were unhappy with the quality of their education.
Nothing might seem more petty and inconsequential to us today than
the controversy between the dots and the d’s, but it was a
significant matter in the history of science, residue of the great
quarrel between Newton and Leibniz over the invention of calculus.
One spring day in 1812, Babbage picked up a broadside [leaflet]
that demanded, in absurdly exaggerated terms, the publication of
the unelaborated word of God. He couldn’t resist a parody. So he
wrote out a plan for the establishment of a society for the
propagation of “the principles of pure D-ism in opposition to the
Dotage of the university.”
The satire struck a sympathetic chord with his mathematically
minded schoolmates. Over the objections of the university
authorities, who frowned on independent student organizations,
Babbage and his friends established the Analytical Society. The
group was dedicated to the overthrow of the Newtonian way, and
Babbage, the intellectual rabble-rouser who founded it, was on his
way to making his mark in the world.
Like most undergraduate clubs, the Analytical Society was more
talk than action. It had about a dozen active members and issued
only one publication, Memoirs of the Analytical Society (1813),
consisting of mathematical papers written in the Leibnizian style
by Babbage and Herschel, before disbanding in 1814. (Herschel, the
society’s president and Cambridge’s best undergraduate
mathematician, graduated in 1813 and Babbage came down the
following year.) But the spirit of the group lived on. In 1816,
two years after Babbage had left college, he, Herschel, and George
Peacock, another ex-Analytical, launched a more mature sally
against the Newtonian dots with the publication of their
translation of a popular French textbook on calculus [Lacroix's
"Elementary Treatise on the Differential and Integral Calculus"].
Four years later, the three men wrote a two-volume calculus
workbook complete with solutions. The books accomplished
what the Analytical Society had not. They were adopted by
Cambridge teachers, and helped steer British mathematicians
back to the mainstream.