Our trip down mainframe lane starts and ends, not so surprisingly, with IBM. Back in the 1930s, when a computer was actually a fellow with a slide rule who did computations for you, IBM was mainly known for its punched-card machines. However, the transformation of IBM from one of the many sellers of business machines to the company that later became a computer monopoly was due in large part to forward-looking leadership, at that time going by the name of Thomas Watson, Sr.
The Harvard machine was a manifestation of his vision, although in practical terms, was not a technological starting point for what followed. Still, it is worth looking at, just so we can see how far things have come.
It all began in 1936, when Howard Aiken, a Harvard researcher, was trying to work through a problem relating to the design of vacuum tubes (a little ironic, as you will see). In order to make progress, he needed to solve a set of non-linear equations, and there was nothing available that could do it for him. Aiken proposed to Harvard researchers there that they build a large-scale calculator that could solve these problems. His request was not well-received.
Aiken then approached Monroe Calculating Company, which declined the proposal. So Aiken took it to IBM. Aiken's proposal was essentially a requirement document, not a true design, and it was up to IBM to figure out how to fulfill these requirements. The initial cost was estimated at $15,000, but that quickly ballooned up to $100,000 by the time the proposal was formally accepted in 1939. It eventually cost IBM roughly $200,000 to make.
It was not until 1943 that the five-ton, 51-ft. long, mechanical beast ran its first calculation. Because the computer needed mechanical synchronization between its different calculating units, there was a shaft driven by a five-horsepower motor running its entire length. The computer "program" was created by inserting wire links into a plug board. The data was read by punched cards and the results were printed on punched cards or by electric typewriters. Even by the standards of the day, it was slow. It was only capable of doing three additions or subtractions per second and the machine took a rather ponderous six seconds to do a single multiplication. Logarithms and trigonometric calculations took over a minute each.
As mentioned, the Harvard Mark I was a technological dead-end, and did not do much important work during the 15 years it was used. Still, it represented the first fully-automated computing machine ever made. While it was very slow, mechanical, and lacked necessities like conditional branches, it was a computer, and represented a tiny glimpse at what was yet to come.