Sunday, March 03, 2024

The letter to recommend John Nash was ``The Best Recomendation Letter Ever''- I do not think so.

There is an article about the letter Richard Duffin wrote for John Nash that helped John Nash get into Princeton: here. The title of the article is 

The Best Recommendation Letter Ever.

The article appeared in 2015. 

The letter is dated Feb 11, 1948. 

The letter itself is short enough that I will just write it:

Dear Professor Lefschetz:

This is to recommend Mr. John F Nash Jr, who has applied for entrance to graduate college at Princeton.

Mr. Nash is nineteen years old and is graduating from Carnegie Tech in June. He is a mathematical genius.

Yours sincerely, 

Richard Duffin

I am right now looking through 365  applicants for my REU program. (Am I bragging or complaining? When it was 200 I was bragging. At 365 I am complaining.) 

If I got a letter like that would I be impressed?


A good letter doesn't just say this person is  genius. It has to justify that. Examples: 

She did research with me on topological  algebraic topology. I was impressed with her insights. We are working on a paper that will be submitted to the journal of algebraic topological algebra. See the following arXiv link for the current draft. 

They  had my course on Ramsey theory as a Freshman and scored the highest A in the class. However, more impressive is that, on their own, they discovered that R(5)=49 by using their knowledge of both History and Mathematics. 

Writing a letter for Jack Lotsofmath  makes me sad we live in an era of overinflated letters. I worked with him on recursion theory when he was a high school student; however, he ended up teaching me 0''' priority arguments. 

So my question is

1) Why did just stating that John Nash was a genius good enough back in 1948? Was Richard Duffin a sufficiently impressive person so that his name carried some weight? His Wikipedia entry is here.

2) Maybe its just me, but if a letter comes from a very impressive person I still want it to say what why the applicant is so great. 

3) Was there more of an old-boys-network in 1949? Could the thinking have been if Duffin thinks he's good, then he's good. The old-boys-network was bad since it excluded blacks, women, Jews, Catholics, and perhaps people not of a certain social standing. But did it err on the other side-- did they take people who weren't qualified because they were part of the in crowd? And was Duffin's letter a way to say but this guy really is good and not just one of us.

4) I suspect there were both less people applying to grad school and less slots available. I do not know how that played out.

5) Having criticized the letter there is one aspect I do like.

Today letters sometimes drone on about the following:

The letter writers qualification to judge:

Example:  I have supervised over 1000 students and have been funded by the NSF on three large grants and the NIH on one small grant. Or maybe its the other way around.

The research project, which is fine, but the letter needs to say what the student DID on the project.

Example: The project was on finite versions of Miletti's Can Ramsey Theory proof. This had never been attempted in the history of mankind! This is important because the Can Ramsey Theory is fundamental to Campbell's soup. This connects up with my upcoming book on the Can Ramsey Theorem to be published by Publish or Perish Press, coming out in early 2025.

 Irrelevant things for my program or for grad school, though perhaps relevant for College: 

Example: He is in the fencing club and the Latin club and was able to trash talk his opponents in Latin. They didn't even know they were being insulted!

So I give credit to Duffin for keeping it short and to the point. Even so, I prefer a letter to prove its assertions.


  1. Perhaps Lefschetz already decided to accept Nash and told Duffin that he formally needed a letter, but he could keep it short.

  2. I suspect lots of this is just a result of concerns about recommendation inflation.

    I mean why do you care about anything but the recommender's judgement IF you know them to be an expert with substantial experience in the field? Do you think that you'll be able to figure out if the student tricked the recommender from a brief letter? Surely not.

    Rather, I think the reason one feels uncomfortable without detailed examples is the concern that a recommendor will feel pressure to exaggerate the student's abilities. But since people are far more comfortable exaggerating than lying details are what sell recs to us today.

    But if the culture of that time was one where such exaggeration was very uncommon this seems like it could be a great rec.

  3. Isn’t graduating from Carnegie Mellon at age 19 pretty good evidence that you’re a gifted student and perhaps a genius?

  4. Maybe Duffin was a good friend of Lefshetz's and knew Lefshetz trusted hi. In that case anything extra would be superfluous.

  5. Pre-sputnik the network was extremely narrow. Even post-sputnik, I applied to just two undergraduate programs and was accepted by both. It sometimes felt more like the programs were applying to the students, in the sciences. That's also when the Ivy League Jewish quota was discarded, for related reasons. Lots of changes, with federal funding as the motor.

  6. Letter writers qualification to judge is a hedge against brand recognition. People tend to weight a letter from an MIT professor more than from Middle of Nowhere U. But the latter professor might have had much more experience, mentored students who went on to go to MIT for grad school, etc.

  7. It is not the old boy’s network, it is called the invisible college, people who are in the know, and who know each other. It is not supposed to be biased. If Yoda or Spock were computer scientits, they would most likely be part of that invisible college, regardless of how he looked or where they came from … you get the jist of it …