The summer months saw a sharp drop in user interest in Wolfram Alpha, the online “computational knowledge engine” that calculates everything from planetary distances to cholesterol levels and generates (from the topics it knows) customized charts and graphics not available from general search engines. In the peak days after the May 15 launch, traffic soared to around 2.8 million daily visitors–but then hit a trough of 200,000 in July, according to the company. But now, with traffic now drifting back toward the 300,000 mark, the site is pinning its hopes partly on a new application programming interface (API) to leverage the online tool in websites, online publishing, desktop applications and mobile devices. An iPhone app will be one of the early examples.

It will be interesting to see how third-parties leverage the depth of Wolfram Alpha’s knowledge in math, science, geography, and engineering beyond the simple search-engine-like interface that now confronts users. Right now, the engine has a ways to go to meet the goal of its brainchild, the physicist Stephen Wolfram, to “make all systematic knowledge immediately computable and accessible to everyone.”

The rebound toward 300,000 visitors may reflect a back-to-school bump, with students seeing the engine as a great tool for doing their math and science homework, according to Schoeller Porter, who heads up Wolfram’s API program. (Indeed, the engine is throwing a homework day event next week to promote further such use.) “We had an enormous launch with a huge amount of interest and a lot of traffic. The traffic fell off, and we fully expected that; it was a nice relaxation for us, and it let us fix code and put in new features,” he told me this morning. “It followed a kind of—I won’t say overhyped–but a well-hyped launch.” Wolfram Alpha is built on Mathematica–Stephen Wolfram’s comprehensive repository of mathematical and scientific formulae–and fed by datasets curated by Wolfram Research.