Professor Francisco Santos of the University of Santander in Spain announced that he had disproved what is known in mathematics circles as the Hirsch Conjecture. Professor Santos will be presenting his proof in July at the 100 Years in Seattle Conference, dedicated to the mathematics of Klee and Grunbaum.
We talk a lot in ReadWriteWeb about the products of mathematics, the programs and devices that amplify and extend the reach of our human dreams. But we rarely talk about the structure that underlies these things and makes them possible. There’s a reason for that. Math is hard. So, I wrote a sonnet.
I have emailed Professor Santos and asked him for an educated lay-person’s explanation of the conjecture, his process of disproving it and the implications of mathematics for a wider world. I will share his contribution with you when I get it.
The Hirsch Conjecture, Disproved
Does math describe reality we know
Or is it just a self-referring system?
Do overlapping circles, either/or,
Obscure a vital truth, or truths sustain?
When someone like Santander’s Paco Santos
Reaches out and wrings conjecture’s neck,
Does he build, or simply banish phantoms?
Tell us what you’ve done was for our sakes.
Vertices in polytopes connect
By paths no more than d’s length less than n,
Unless this theorem of Klee and Walkup, d-step,
The tyranny of Hirsch and Dantzig ends.
And if it does, are human souls ennobled?
Is one more bolted door to stars thrown open?