Timeline for Alternatives to Axiomatic Method

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Jun 15 '21 at 12:24 comment added ᄂ ᄀ Felix Klein is one of the superstars of 20th century mathematics and the validity of his work is beyond dispute. What? Like Jesus playing in a rock band?
Jul 5 '17 at 14:00 comment added Lawrence @user170039 There are such things as intuitionistic proofs. E.g. prove that a triangle is isosceles by making a copy, flipping it, and setting it down to exactly cover the original. However, if by rigour you mean that you have a series of logical statements that ends with the result you want to prove, you're likely to have already constrained yourself to axiomatic methods.
Jul 2 '17 at 12:10 history edited Mikhail Katz CC BY-SA 3.0
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Jul 1 '17 at 21:16 history edited Mikhail Katz CC BY-SA 3.0
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Jul 1 '17 at 21:16 comment added Mikhail Katz ...probably not be shared by many editors at the philosophy SE.
Jul 1 '17 at 21:15 comment added Mikhail Katz @user170039, Felix Klein is one of the superstars of 20th century mathematics and the validity of his work is beyond dispute. Notice that the term "rigor" did not occur in the formulation of your question. Its meaning is dubious and especially at the philosophy SE could come across as naive. Many mathematicians (though by no means all) tend to identify "rigorous mathematics" with "mathematics done in a ZFC axiomatic framework" and from that point of view certainly there couldn't be any rigorous work outside the axiomatic framework, yes. But that's a rather reductive view that would...
Jun 30 '17 at 15:50 history migrated from math.stackexchange.com (revisions)
Jun 30 '17 at 14:27 comment added user13627 My question is not whether axiomatic method is relevant to some part of mathematics (be its theory or application). My question is whether rigorous mathematics is possible without following the axiomatic framework. In that case "[h]as there been any research regarding the method itself "by which these facts are verified" as has been mentioned in the previous paragraph that is not the axiomatic method? If so, can some relevant literature regarding this issue be mentioned?"
Jun 29 '17 at 8:28 history answered Mikhail Katz CC BY-SA 3.0