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Programme for 21 Century Math - Replacing Axiomatic Method

As I have discovered a new math method replacing 20nd century axiomatic method (I called it 21 Century Math Method^TM or 21MM. It is a definitional method like back to the time of Socrates.), I propose a new program for 21st century mathematics:

• Research logics related with 21MM method and relations of 21MM method with old (axiomatic and pre-axiomatic) mathematics.
• Rewrite and transform/generalize old axiomatic and pre-axiomatic math into 21MM formal system.
• Research Algebraic General Topology (see here) and related fields as probably the first nontrivial example of an application of 21MM method.
• Create software (autoprovers, algebra systems etc.) based on 21MM method.
• Extend and enhance 21MM method.
• Research how 21MM is interrelated with the Category Theory.

21MM is a real accomplishment of the programme of algebraization of mathematics today. (However particular theories such as general topology yet need to be formulated algebraically in 21MM.)

Note that this programme does not concern with particular problems and theorems like Hilbert problems. I hope that these will be solved by the way of research by this programme.

Will this be enough for 21st century? I don't know.

See Also

• The Concept of Post-Axiomatic Mathematics. Victor Porton - an introductory (largely philosophical) article which defines and declares what is post-axiomatic mathematics.
• alt.math.post-axiomatic newsgroup homepage (subscribe).

Copyright © 2004 Victor Porton. All rights reserved.

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