Arithmetic Quote by Abraham Robinson
“Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc... But the next quite logical step after the reals, namely the introduction of infinitesimals, has simply been omitted. I think, in coming centuries it will be considered a great oddity in the history of mathematics that the first exact theory of infinitesimals was developed 300 years after the invention of the differential calculus.”
About This Quote
Source Book: "Non‑standard Analysis" by Abraham Robinson, 1966
Mathematics omitted infinitesimals despite their logical fit, an historical oversight now seen as a missed opportunity.
In simple terms: Infinitesimals were ignored.
Key Takeaway
Recognize and integrate overlooked concepts.
Themes
mathematics
history
innovation
Mood
analytical
curious
Type
academic
historical
When to use this quote
- teaching calculus
- research methodology
- philosophy of science
Key Concepts
logic
foundations
calculus
Questions to Reflect On
- Why were infinitesimals excluded?
- What benefits could they bring today?
A Different Perspective
Adopting new foundations can face resistance from established curricula.
![“Foreshadowings of the principles and even of the language of [the infinitesimal] calculus can be found in the writings of Napier , Kepler , Cavalieri , Fermat , Wallis , and Barrow . It was Newton 's good luck to come at a time when everything was ripe for the discovery, and his ability enabled…” quote by Anonymous](https://sms4smile.com/quotes/img-quotes/e09/anonymous-1_ability_foreshadowings-of-the-principles-and-eve_273197.jpg)
