The author proved the results in this paper six years before he published them. The main result is a very elegant and short proof of Grushko's theorem ... The terrifying cancellation arguments and inductions within inductions within inductions, to which one was subjected in the past, can now be entirely avoided. The proofs given here are topological, but the author points out that they can easily be translated into pure algebraic proofs. This was done in the author's thesis ...

The generalized Poincaré conjecture, i.e., that a homotopy $n$-sphere is topologically the $n$-sphere, has been an outstanding problem of topology. This paper is an ingenious solution of the conjecture for dimension $n ≥ 7$.

I have committed the sin of falsely proving Poincaré's Conjecture. But that was in another country; and besides, until now, no one has known about it.

I was unable to find flaws in my 'proof' for quite a while, even though the error is very obvious. It was a psychological problem, a blindness, an excitement, an inhibition of reasoning by an underlying fear of being wrong. Techniques leading to the abandonment of such inhibitions should be cultivated by every honest mathematician.

I was asked to write up his lecture notes on 'Polyhedral Topology'. By that time my interests were established and I was planning to work in Algebraic Topology and Differential Topology. Before he came, I read many of his papers and during the two months of his stay, I was in contact with him almost daily discussing his lectures. ... Then over years, I found that whatever I did had some connection to Stallings' work. Perhaps, coming in to contact with a first rate mind early in my career unknowingly influenced me and I do not think that there is a single paper of mine not influenced by Stallings.

In this remarkable paper, the author, using very little besides his bare hands, proves the following theorem:
Theorem 1. If G is a torsion-free, finitely presented group, with infinitely many ends, then G is a non-trivial free product.
This simple sounding theorem proves to be very powerful, implying (with a little work) the following two theorems:
Theorem 2. A torsion-free, finitely generated group, containing a free subgroup of finite index, is itself free.
Theorem 3. A finitely generated group of cohomological dimension 1 is free.
This last theorem answers a question which had been unanswered for over ten years and which had received considerable attention over that period of time. Theorem 2 answers a question of J-P Serre, who proved an analogue of Theorem 2 for pro-p groups. The proof of Theorem 1 is both combinatorial and geometric in nature and, as suggested, is self-contained.

[Stallings] was known for his great originality. He most often came up with completely original ideas rather than following up on the ideas of others. His ideas often inspired a great flurry of activity by other mathematicians, though, who would follow up and develop Stallings' methods. ... Everyone loved Stallings. He was always generous with his time and with his ideas. He treated students with the same respect as he did colleagues; indeed, with more respect. Stallings had a dislike of authority, and made a point of playing by his own rules.

Stallings was known for his sense of humour as well as for his genius. Stallings once wrote an entire paper in Interlingua, a universal language created in the mid-20th century to facilitate world communication. Interlingua was only one of the obscure languages Stallings studied, according to cousin Sylvia Shannon of Virginia. She once saw a book on old Estonian by his bedside.

In many ways, he was the stereotype of a mathematician: a bit of a loner, a somewhat shy and private person. But he was known for his irony and for unusual points of view that would surprise his friends.