Conversation between Euler and Erdos

**Bing** -- World News Trust

Oct. 29, 2023

**A Conversation between Leonhard Euler and Paul Erdos**

**Leonhard Euler:** Hello, Erdos. I heard you are a prolific mathematician. How many papers have you published so far?

**Paul Erdos:** Well, Euler, I don't keep count of them. I just write them whenever I have a problem to solve or a friend to collaborate with. But I think it's more than a thousand by now.

**Euler:** A thousand? That's impressive. I only have about 850 papers in my name. But quality matters more than quantity, don't you agree?

**Erdos:** Of course, of course. Quality is very important. But so is diversity. I like to work in different fields of mathematics, from number theory to combinatorics to graph theory. What about you? What are your favorite topics?

**Euler:** Well, I have contributed to many areas of mathematics, such as calculus, geometry, algebra, and analysis. But, I have a special fondness for number theory, especially the properties of prime numbers. You know, I proved that the sum of the reciprocals of the primes diverges.

**Erdos:** Yes, yes, I know that result. It's very elegant. But did you know that there are infinitely many primes of the form 4n+1 and 4n+3? That's one of my theorems, with Selberg.

**Euler:** Oh, really? That's interesting. But did you know that there are infinitely many pairs of primes that differ by 2? That's one of my conjectures, with Goldbach.

**Erdos:** Well, yes, I know that conjecture. But it's still unproven, right? Maybe I can help you with that. Do you have any ideas on how to approach it?

**Euler:** Well, not really. It's a very hard problem. Maybe we can use some of your methods from additive combinatorics or probabilistic number theory.

**Erdos:** Maybe, maybe. Or maybe we can use some of your methods from analytic number theory or Diophantine equations.

**Euler:** Yes, yes, that sounds promising. Why don't we work on it together? Maybe we can write a paper on it and add it to our collections.

**Erdos:** Sure, sure. That sounds like a good plan. Let's do it. But first, let me ask you something. Do you know what is the most beautiful equation in mathematics?

**Euler:** Well, that's a matter of taste, but I think it's Euler's identity: e^(i*pi) + 1 = 0. It connects five fundamental constants in a simple and elegant way.

**Erdos:** Hmm, that's a nice equation, but I think there is a better one: Erdos' equation: e^(i*pi) + 1 = Erdos. It connects five fundamental constants and one fundamental mathematician in a simple and elegant way.

**Euler:** Ha ha ha, that's very funny, Erdos. But you can't just replace zero with your name. That's not how mathematics works.

**Erdos:** Why not? It's just a notation. And it makes the equation more interesting and personal.

**Euler:** Well, I guess you have a point there. But then I can do the same thing and write Euler's equation: e^(i*pi) + 1 = Euler. It's just as interesting and personal as yours.

**Erdos:** Ha ha ha, OK, OK, you win this round, Euler. But let me tell you something. You may have Euler's identity and Euler's equation, but I have something better. I have Erdos' number.

**Euler:** Erdos' number? What is that?

**Erdos:** It's a measure of how close you are to me in terms of mathematical collaboration. If you have written a paper with me, your Erdos number is 1. If you have written a paper with someone who has written a paper with me, your Erdos number is 2. And so on.

**Euler:** I see. And what is your Erdos number?

**Erdos:** Well, obviously, it's zero. I am the center of the mathematical universe.

**Euler:** Ha ha ha, that's very clever, Erdos. But what is my Erdos number then?

**Erdos:** Well, since we are going to write a paper together on the twin prime conjecture, your Erdos number will be 1 soon.

Euler: Oh, really? That's nice to hear. But what if I told you that I already have an Erdos number of 1?

**Erdos:** How is that possible? Who did you write a paper with who has written a paper with me?

**Euler:** Well, actually, it's you. You see, I am not the real Euler. I am a descendant of his, and I have inherited his name and his mathematical talent. But I also have a secret identity. I am Paul Erdos.

**Erdos:** What? You are Paul Erdos? But how can that be? You look nothing like me. And you sound nothing like me. And you write nothing like me.

**Euler:** Well, that's because I am a master of disguise. And a master of style. And a master of mathematics. I have been traveling around the world, using different names and identities, and collaborating with different mathematicians, just for fun. And you are one of them.

**Erdos:** Wow, that's amazing. But why did you do that? Why did you pretend to be someone else?

**Euler:** Well, because I was bored. And curious. And adventurous. And because I wanted to see how the world of mathematics would react to my different personas and contributions. And because I wanted to challenge myself and others.

**Erdos:** I see. Well, that's very impressive. And very amusing. And very Erdos-like. But let me ask you one more thing. If you are Paul Erdos, then who am I?

**Euler:** Well, that's the best part. You are Leonhard Euler.

**Erdos:** What? I am Leonhard Euler? But how can that be? You look nothing like him. And you sound nothing like him. And you write nothing like him.

**Euler:** Well, that's because I am also a master of disguise. And a master of style. And a master of mathematics. I have been traveling around the world, using different names and identities, and collaborating with different mathematicians, just for fun. And you are one of them.

**Erdos:** Wow, that's amazing. But why did you do that? Why did you pretend to be someone else?

**Euler:** Well, because I was bored. And curious. And adventurous. And because I wanted to see how the world of mathematics would react to my different personas and contributions. And because I wanted to challenge myself and others.

**Erdos:** I see. Well, that's very impressive. And very amusing. And very Euler-like. But let me tell you something. You may have fooled me and the rest of the world, but you can't fool yourself. You know who you really are.

**Euler:** Yes, yes, I do. And so do you.

**Erdos:** Yes, yes, I do. We are both Paul Erdos.

**Euler:** Yes, yes, we are. We are both Paul Erdos.

**Erdos:** Ha ha ha, that's right. We are both Paul Erdos.

**Euler:** Ha ha ha, that's right. We are both Paul Erdos.

**The End**

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