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One might say the Original Event in mathematics is Euclids axiomatisation of Plane Geometry.

Subsequent axiomatisation - such as Peanos Axioms for the natural numbers being an echo of that Event, and so not an Event as such, in itself. But merely an application of an already discovered idea - axiomatisation.

What are the nature of subsequent Events in mathematics?

One might pause here, and say why, given the natural numbers, did axiomatisation wait two millenia.

It surely isn't dependent on the difficulty of the task.

So, Peanos axioms is possibly then a sign of an Event.

Which one?

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    I imagine that the original mathematical event was the day some prehistoric hunter made marks in the sand, |||, to commemorate the three mastodons he killed. Surely Euclid is important, but his work is a relatively recent development. – user4894 Mar 17 '14 at 3:54
  • @user4894: Sure, Counting came first, and then Arithmetic and Mensuration. But thats why I said Mathematics as it is commonly understood in discourse - ie with deduction and axiomatics. Counting got resurrected with Cantor but thats a story already well-told. – Mozibur Ullah Mar 17 '14 at 4:04
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    A question of genius or a script run wild? Who can tell? :) – Drux Mar 17 '14 at 8:28
  • "But thats why I said Mathematics as it is commonly understood in discourse" -- Actually, you didn't say anything of the sort. Why are you posting garbage? – user4894 Mar 17 '14 at 14:01
  • @user4894: yes, you're right; I didn't; but I did say 'Mathematics', and it is commonly understood that this includes deduction and axiomatics, which is exemplified in usual discourse by way of 'Euclids axiomatisation of Geometry'. – Mozibur Ullah Mar 19 '14 at 4:23
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An important point to make is that, for a long time Mathematics was largely considered synonymous with Geometry--similar to how, today, there is a sense that Mathematics is essentially Algebra. Of course, professionals would deny this, but among the public there is certainly this sense; and among professionals, there is a feeling that, if a system doesn't have a corresponding abstract, algebraic expression in terms of symbols that are written in lines of text, then it's quite mathematical--or that it gains greater status as mathematical, once it has an algebraic expression. Since the ancients and medievals saw Mathematics as having Geometry as its core, they may not have thought there was so much that was interesting in axiomatizing numbers and other systems. When Descartes showed that all Geometry can be expressed algebraically and vice versa, interest in Algebra grew dramatically, and perhaps in light of that, it "only" took a few centuries thereafter to axiomatize other systems.

This is a mere informed guess, which I suppose is all you could get in response to this question, short of a historical research project.

  • I would suggest also looking into the history of formalizing logic, since it was really this project that ultimately led to the set theory foundations of modern Mathematics. – Addem Mar 17 '14 at 20:17
  • Sure, that's the historical trajectory that I'm referring to implicitly. I'd say Descartes analytic geometry, thinking of the plane as composed directly of points in terms of coordinates leads very easily to higher dimensions - its easy to generalise from 3 coordinates to n coordinates in a way that isn't possible synthetically. Though, having achieved that insight analytically, people are busy or have been busy to develop the same tools synthetically. – Mozibur Ullah Mar 19 '14 at 4:33
  • Sure, that's the historical trajectory that I'm referring to implicitly. I'd say Descartes analytic geometry, thinking of the plane as composed directly of points in terms of coordinates leads very easily to higher dimensions - its easy to generalise from 3 coordinates to n coordinates in a way that isn't possible synthetically. Though, having achieved that insight analytically, people are busy or have been busy to develop the same tools synthetically, taking to heart the slogan 'coordinates are an act of vandamism'. – Mozibur Ullah Mar 19 '14 at 5:07
  • I think your cooment, rather than your answer, is on the right track, that its probably the programme (or 'Event'!) of turning logic into mathematics via set theory (that predated Hilberts actual formal enunciation of it) that prompted the axiomatisation of Arithmetic - ie Peanos Axioms. – Mozibur Ullah Mar 19 '14 at 5:09

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