The Road Not Taken (Robert Frost; 1874 – 1963)
Two roads diverged in a yellow wood, And sorry I could not travel both And be one traveller, long I stood And looked down one as far I could To where it bent in the undergrowth; Then took the other as just as fair, And having perhaps the better claim, For it was grassy, and wanted wear; Though as for that, the passing there Had worn them really about the same, And both that morning equally lay In leaves no step had trodden black. Oh, I kept the first for another day! Yet knowing how way leads on to way, I doubted if I should ever come back. I shall be telling this with a sigh Somewhere ages and ages hence: Two roads diverged in a wood, and I— I took the one less travelled by, And that has made all the difference.
The most important 20th century mathematicians, in my opinion:
- Garret Birkhoff
- Øystein Ore
- Saunders MacLane
- Samuel Eilenberg
- William Lawvere
- Hundreds others
The best mathematics produced in any given century neither completely ignores the dominant paradigm(s) of that century, nor allows itself to be trapped by them. It works at the edges of established mathematics, moving freely between civilization and unfettered jungle. We should create more mathematics that is moderately subversive, that makes use of existing ideas when they're appropriate but ventures deep into the jungle when they're not.
A list of my favorite answers (more coming soon):