[see also: original]
He was the first to propose a complete theory of triple intersections.
Because N. Wiener is recognized as the first to have constructed such a measure, the measure is often called the Wiener measure.
Let $S_i$ be the first of the remaining $S_j$.
The first two are simpler than the third. [Or: the third one; not: “The first two ones”]
As a first step we shall bound $A$ below.
We do this in the first section, which the reader may skip on a first reading.
At first glance, this appears to be a strange definition.
The first and third terms in (5) combine to give ......
the first author = the first-named author
First, we prove (2). [Not: “At first”]
We first prove a reduced form of the theorem.
Suppose first that ......
His method of proof was to first exhibit a map ......
In Lemma 6.1, the independence of $F$ from $V$ is surprising at first.
It might seem at first that the only obstacle is the fact that the group is not compact.
[Note the difference between first and at first: first refers to something that precedes everything else in a series, while at first [= initially] implies a contrast with what happens later.]