Combination Quote by James Joseph Sylvester
“Number, place, and combination . . . the three intersecting but distinct spheres of thought to which all mathematical ideas admit of being referred.”
About This Quote
Mathematics can be categorized into three distinct yet intersecting domains: number, place, and combination.
In simple terms: Math ideas fall into three areas: numbers, positions, and groupings.
Key Takeaway
Understand these three mathematical perspectives.
Themes
mathematics
categorization
logic
structure
Mood
analytical
inquisitive
Type
educational
theoretical
When to use this quote
- classroom
- research
- problem solving
Key Concepts
philosophy of math
education
theory
Questions to Reflect On
- How do these categories apply to real problems?
- Can they be taught simply?
A Different Perspective
The definition may be overly abstract.
![“The world of ideas which it [mathematics] discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connexion of its parts, the infinite hierarchy and absolute evidence of the truths with which it is concerned, these, and such like, are the surest…” quote by James Joseph Sylvester](https://sms4smile.com/quotes/img-quotes/e72/james-joseph-sylvester-23602_absolutes_the-world-of-ideas-which-it-mathematics_338576.jpg)
![“[Mathematics is] purely intellectual, a pure theory of forms, which has for its objects not the combination of quantities or their images, the numbers, but things of thought to which there could correspond effective objects or relations, even though such a correspondence is not necessary.” quote by Hermann Hankel](https://sms4smile.com/quotes/img-quotes/9d5/hermann-hankel-65857_combination_mathematics-is-purely-intellectual-a-pur_2076406.jpg)
![“...There is no study in the world which brings into more harmonious action all the faculties of the mind than [mathematics], ... or, like this, seems to raise them, by successive steps of initiation, to higher and higher states of conscious intellectual being…” quote by James Joseph Sylvester](https://sms4smile.com/quotes/img-quotes/bc5/james-joseph-sylvester-23602_action_there-is-no-study-in-the-world-which-bri_23809.jpg)
![“[Mathematics] unceasingly calls forth the faculties of observation and comparison; one of its principal weapons is induction: it has frequent recourse to trial and verification; and it affords a boundless scope for the exercise of the highest efforts of imagination and invention.” quote by James Joseph Sylvester](https://sms4smile.com/quotes/img-quotes/301/james-joseph-sylvester-23602_boundless_mathematics-unceasingly-calls-forth-the_447035.jpg)
![“The object of pure Physic[s] is the unfolding of the laws of the intelligible world; the object of pure Mathematic[s] that of unfolding the laws of human intelligence.” quote by James Joseph Sylvester](https://sms4smile.com/quotes/img-quotes/36a/james-joseph-sylvester-23602_human-intelligence_the-object-of-pure-physic-s-is-the-unfol_679113.jpg)
![“Geometry, which should only obey Physics, when united with it sometimes commands it. If it happens that the question which we wish to examine is too complicated for all the elements to be able to enter into the analytical comparison we wish to make, we separate the more inconvenient [elements], we…” quote by Jean le Rond d'Alembert](https://sms4smile.com/quotes/img-quotes/0d9/jean-le-rond-d-alembert-26487_able_geometry-which-should-only-obey-physics_6945.jpg)
