Sunday, November 30, 2014

A neat problem from the 1989 Maths Olympiads

A few days ago, Universidad Complutense de Madrid hosted a celebration of the 50th anniversary of the Spanish Maths Olympiads. The programme involved three talks. The first was on "other number systems" (quaternions and octonions) and the second dealt with the roots of random polynomials. In the third talk,  Vicente Muñoz Velázquez presented his personal views on the nature of mathematics before discussing some of the highlights of his research area leading to Yang-Mills and Mass Gap.

According to Vicente, mathematics is a human product and its characteristics are:
  • (The rules of) Logic, 
  • (Modelling of) Reality, 
  • Beauty (transversality, relations between apparently distant fields, generalization and abstraction), 
  • Social activity,
  • Applicability. 
I could not help but think that those characteristics apply equally well to computer science, with the added twist that computer scientists are not only modelling reality, but also inventing and breathing life into "new realities".

During his talk, Vicente presented a problem from the 1989 International Maths Olympiad, in which he took part.

The problem was:

Prove that for each positive integer n there exist n consecutive positive integers none of which is a prime or a prime power.

This is a neat problem that perhaps some of you might like to try and solve.


Mohammad Alaggan said...

Would just like to note that Computer Science descended from Mathematical Logic and is actually considered a branch of Pure Math today. So the similarities are not coincidental. Moreover, math can (and often does) invent new realities. Think of modelling n-dimensional spaces. This is both modelling reality for n=3, and at the same time inventing new realities for which n is not equal to 3.

Luca Aceto said...

Points taken, Mohammad. However, even though some mathematicians do consider Theoretical Computer Science as a branch of mathematics, I don't think that this is the majority view yet.