#### by Rob Kirby

Morton Brown was born in the Bronx on 12 August 1931. His father, Irving Brown came from Romania, and owned and operated a fruit and vegetable store in Manhattan. His mother, Shirley Lehrman, was of Polish-Russian descent. Mort had an older brother, Jack, who went to engineering at NYU and the Navy.

Mort finished high school in June 1948, having skipped 7th grade. He went to the University of Wisconsin and first met R H Bing in spring 1950 in an elementary calculus class. Bing urged Mort to take his graduate topology course, which Mort did, but then he dropped out and retook it the following year, finding it much easier the second time. Mort finished his BS in 1953, after taking a one-semester break in order to, as he put it, figure out how to have a social life and also be a mathematician.

While still an undergraduate in 1952, Mort heard that countable
Hausdorff spaces were never connected, but he produced an example of
one anyway, putting an interesting topology on the positive integers.
It appeared as an abstract in *Bull. AMS* in 1953
[1],
but the
details were never published (this is the first example of Mort’s
reluctance to write up his work, and hence his debt to his
collaborators who usually did the lion’s share of the writing).

Bing encouraged Mort to give a short talk on his example at an AMS meeting at NYU in April 1953. Mort relates that he sat through the day’s talks, watching the audience grow until it was quite large. He was surprised there was so much interest in his example, but then the previous speaker, Sammy Eilenberg, walked out, after which the audience disappeared! Many years later, Eilenberg wrote to Mort asking for the details of his example (see [◊]; the precise date of this letter is not known).

Mort stayed on at Wisconsin for graduate work with Bing. In 1956 he married Kaaren Strauch, and they later had three boys, Aaron (1958), Alan (1959) and Carl (1961). Kaaren eventually became a Professor of Social Work at Eastern Michigan University.

Mort had the results of his PhD thesis by 1957, and took a job at Ohio State for 1957–58. Michigan then offered him a tenure-track job, but this required a PhD, so Mort had to actually write up his thesis. He partly chose Michigan because he wanted to work with Eldon Dyer who was being wooed by Michigan but did not in fact come.

In 1958 Barry Mazur found [e1], [e2] his striking proof of the Schoenflies Conjecture (modulo a small hypothesis, later removed by Marston Morse). Ed Moise said, according to Mort, that “Mazur went into the jungle with a string and caught the only lion that could be captured with a string.” Mort had, until then, never heard of the conjecture but started to think about it.

Mort found his proof of the Schoenflies Conjecture in early fall 1959, and showed it to Hans Samelson and Moise (who said that it “used mirrors”).

At an AMS meeting in Detroit around Thanksgiving, Mort met Henry Whitehead who had been working with M. H. A. Newman on the Conjecture. Mort explained his proof quickly in four steps and Henry said “wonderful.” Mort guessed Henry had not really understood the proof, until shortly afterward he heard Henry explain the proof with precision to someone else. Henry wrote to Newman to convey his excitement [private communication]: “Here is news which dwarfs everything else.” Newman discusses the Conjecture at length in [e3].

Mort published what he considers his two hardest papers in 1960:
“On the inverse limit of Euclidean __\( N \)__-spheres”
[3]
and
“Some applications of an approximation theorem for inverse limits”
[2].

The boundary of a smooth or PL manifold __\( M \)__ naturally has a “collar”
neighborhood of the form __\( \partial M \times [0,1] \)__. This is locally true
for a topological manifold by definition, but when Mort raised the
question of the existence of a topological collar, Whitehead said that
question was “very deep.” Nonetheless, Mort found a
proof
[4]
that in hindsight is quite easy. Add a collar to
__\( M \)__, and then push the collar into __\( M \)__ using a partition of unity and
the local collars.

Mort was at the Institute for Advanced Study in 1960 when he began collaborating with a Princeton graduate student, Herman Gluck, on the Annulus Conjecture and related issues. The Annulus Conjecture was well known to topologists like Whitehead, but it was Mort who coined the name after a conversation with Lee Rubel who emphasized the importance of a good name that people would easily remember.

The collaboration with Gluck led to a series of three *Annals*
papers on *stable* homeomorphisms
[6],
[7],
[5],
a name coined by Gluck for homeomorphisms which
can be factored into __\( h_1\circ h_2\circ \ldots \circ h_k \)__, where each
__\( h_i \)__ equals the identity on an open set __\( U_i \)__. They showed among
other things that the Annulus Conjecture held in all dimensions if and only if
all homeomorphisms of Euclidean space are stable.

These notions turned out to be very important in future work on triangulations of topological manifolds by Kirby and Siebenmann [e6] [e7]. In fact, these papers of Mort, together with Mazur [e1], Milnor’s paper on microbundles [e5], and Kister’s proof that topological manifolds have tangent bundles [e4], laid the foundations for later work on the structure of topological manifolds.

Two later papers,
[8]
and
[9],
concerned fixed points
of homeomorphisms of the plane, __\( \mathbb{R}^2 \)__. Consider an area preserving
homeomorphism of __\( \mathbb{S}^1 \times [0,1] \)__;
Poincaré
conjectured that it has two fixed points and proved some special cases.
Birkhoff
published a proof for the existence of one fixed point and in a later paper
corrected an error and claimed a proof for two fixed points. But
there was doubt in some quarters as to the accuracy of the second
paper. Brown and
W. Neumann
gave an elementary, detailed proof for two
fixed points which basically follows the outline of Birkhoff’s work,
and the authors describe their paper as mostly expository. A well
needed exposition.

Cartwright
and
Littlewood
showed that an orientation preserving homeomorphism of __\( \mathbb{R}^2 \)__
which leaves a compact, nonseparating continuum
__\( C \)__ invariant also leaves a point of __\( C \)__ fixed. Mort gives
a one-paragraph proof of this theorem
[9]
using a result of
L. E. J. Brouwer.