I am asked sometimes what a matroid is. I often revert to our sacred writings and recall the encounter of Alice with the grinning Cheshire cat. At one stage the cat vanishes away, beginning with the tip of its tail and ending with the grin, which persists long after the remainder of the cat.
“I expect you saw a lot of loose grins wandering around” said Humpty Dumpty. “Yes, indeed” said Alice. “But with some of them you could see they belonged to cats. I kept trying to imagine what the cats behind them were like.”
“What an Auslandish thing to do” said Humpty Dumpty.
“Oh it’s very interesting” said Alice. “I look at the grin and I see the eyes and whiskers and the ears and the warm furry body and the long sinuous tail.”
“You put it very graphically” said Humpty Dumpty.
“But I can’t do it with all the grins” said Alice. “Some of them have the most uncatly shapes. Whatever can be behind them?”
“That’s what makes it interesting” said Humpty Dumpty. “You have to classify the Uncats.
It now will be right to describe
Each particular batch
Distinguishing those that are Fanos and bite
From K. Kuratowskis that scratch.”
“I’ve heard something like that before” said Alice crossly. “The creatures here all recite far too much poetry.” And she stalked angrily away.
– W. T. Tutte