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 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,
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.