Legends hold that once upon a time, some mathematicians were rather pleased about a 30-ish page result in functional analysis. Paul Erdos, upon learning of the problem, spent ten or so minutes thinking about the original problem, and came up with a two-line proof.

I believe I read about this first in the biography

The Man Who Loved Only Numbers, and it seems as though the internet maintains this legend (q.v. here, here, here).This seems extraordinary, which leads me to some skepticism. I cannot seem to find any other reference to the actual proof or the problem. Is this simply an urban legend? Did it actually happen? What was the problem, and what was the original 30-page result?

**Answer**

I sent Professor Purdy an email. I asked him what he recalled about the incident. With his permission I’ve copied his correspondence below.

Dear Jacob,

Yes, I was there, and I’m the one who told the story to Paul Hoffman,

who then included it in his book “The man who loved only numbers.”The 30 page proof was written by Jack Bryan just before Erdos came to

visit, at Texas A & M University. The problem was written on the

blackboard in the mathematics lounge and Erdos saw it and asked “Is

that a problem?” I told him yes, and he went over and wrote a two line

proof on the blackboard. It’s the most incredible thing I ever

witnessed, and that’s why I told Paul Hoffman the story. Ron Graham

told Hoffman to talk to me because I knew Erdos well.Much later it became obvious that Erdos loved this story, and I asked

him how he did it without knowing the subject. He said, smiling, “Oh,

I was a good student at school!”I have come to realize also that Erdos was one of those mathematicians

who could tackle an unknown area as if he knew it. He also prized this

ability in others. He once demonstrated to me that Fred Galvin had

this ability. Fred was at the board and Paul asked him a question, and

he answered it, and he asked Fred “Had you seen these things before”,

and Fred answered that he hadn’t, and Erdos turned to me and said

“See!”George

**Attribution***Source : Link , Question Author : Emily , Answer Author : JSchlather*