Tuesday 17 June 2008

Math-fiction

I came up with a mental exercise today. I will try to predict how mathematics will look in the far future or in no time, it is a math fiction, everything is possible.

Mathematics in the XXII century

A classical mathematical notation will be replaced with a strict machine-friendly format. The concepts like sets and relations will not change, but we will construct sets and relations differently. There is a set-builder notation and it already makes a lot of troubles. A computer-friendly notation would allow automatic syntax checking, inclusion/exclusion test, or even advanced hypothesis verification. The next-generation computer-aided math package will be implemented in TeX 2.0, a new scientific publication language format that will push the cooperation between so called human inteligence to higher levels! Using new math tools we will solve most of the millenium problems with ease. We will clarify complexity theory classes, also write no more than two page long proofs for Riemann and Hodge hypothesis. In the mean time, pentagonal tiles of type 15 will be covering all of our residence floors. The new mathematical tools will be very powerful because we will proof that P is equal to NP or even we will figure out that every algorithm require not more than logarithmic to input data size steps on the so called Big-Bang machine. We will be Big-Banging parallel universes whenever sorting a column in a spreadsheet. Last but not least mathematics will hit the trenches. All those uneducated people (mostly engineers and nature "scientist") will use standarized terminology.

There was a time when "real" mathematics was done with a pencil, paper and fresh mind only, and many mathamaticians actually still believes it is the only way to do it and other tools are only unnecessary complications.
And what do you think about it ?

1 comment:

Robert said...

It would be interesting to imagine such a time. Mathematics has already advanced to such a point where it makes more sense to do with machines than manual calculation with a pen and paper. I believe that it is not entirely impossible for your hypothetical world to exist one day, when looking back on how it has already changed.

Perhaps computers will be directly wired to our brains, and we can use them to perform exact trajectory calculations for our next step to ensure we never trip.