"Recently a conversation with Prof. Huffman here indicated that he has recently been working on a machine with similar objectives."
A more thoughtful presentation might replace the second "recently" with "lately" or similar.
Beyond English department embroidery, there's little to fault with Nash's composition. His argument develops logically, his sentences parse correctly, he sticks to the primary points, and he's clear both about the potential significance and the nature of the mechanics involved.
This particular English department suggestion made me laugh out loud. How is it that adjectives became spin one-half particles? There are two distinct recent events in his sentence (the work and the discussion about the work). You suggest his presentation is weak because the cognitive Boson (recentness) wasn't recast as Fermionic when appending the -ly affix. When writing to the NSA, which is notorious for using seven levels of Fraktur script to distinguish algebraic levels, one presumes they can't keep two verb instances straight in a simple English sentence.
In high school I was given a composition exercise to write a paragraph on camera assembly. We were given the steps as a mishmash. It was an exercise in achieved logical order.
My solution:
The A goes into the B.
The B goes into the C.
The C goes into the D. ...
QED.
I varied the "goes into" part appropriately. In fact, I wrote very nice sentences. What I did not vary was beginning every sentence with "The". My English teacher was so annoyed with my stylistic uniformity he docked me severely. I could only raise my eyebrows and file his feedback in my Twilight Zone folder. We weren't given any objective function on the benefits of faux variation of form upon correct assembly, yet we were expected to engage in the art of embroidery nevertheless.
Nash made a pretty good start there. If he had received a one sentence answer (with or without confounding word repetitions) explaining that the class of LFSR ciphers (or whatever refined class is most suitable) are known to have a weak of the following nature, expressed perhaps with a supplemental equation or three, it would have been very interesting to read Nash's next response.
The next NSA response (if they were willing to engage in such a dialog) would likely have been "you're still on the right track, but the bar is higher yet".
One needs to realize that Nash is precisely the person the NSA doesn't wish to encourage to clear any bars for which they do not yet know the solution, as he was not of the right temperament to nurture in house, and not in any way predictable out-of-house.
Pedantic interjection: Oh look, I did something terrible and inconsistent with my compound adverbial prepositions in my previous sentence. Here I'm using my hyphens as instruction prefetch markers to the front-end sentence parser ("in house" hardly needs a hint as situated).
If I were in the NSA, however, I would use a regular hyphen where it appears as a prefetch hint, and a Fractur hyphen when used in a capacity that maps into the semantic parse tree. That place is packed with pedants. If you don't keep your levels straight, conversation degenerates and no ciphers are broken.