(See Corrections & Amplifications item below.)

It is the tool you wish you had in high-school math class.

Wolfram Alpha, a new search engine, has been assessed by Web watchers for its potential to compete with Google. But it's really a bigger threat to calculators -- and science and math curricula. Enter a chemical formula for, say, caffeine, and it will tell you everything from its molecular weight to its structure diagram. Enter a derivative, that fixture of calculus class, and it will determine the results, complete with a helpful "show steps" button.

Math teachers say the software, which takes elements from pricey proprietary programs and makes them freely available online, has the potential to give students empowering new tools. Some would argue too empowering. Lazy students could take shortcuts, while harried teachers get headaches redesigning their homework and tests in response to a moving target: The company behind Wolfram Alpha vows to keep expanding and improving it.

"Why bother learning information that can be Googled when needed?" asks Bruce Yoshiwara, a math professor at Los Angeles Pierce College. "And why master some mathematical algorithm, say long division, when computational power is always at hand?" Prof. Yoshiwara adds, "Wolfram Alpha should reinforce the millennial generation's devaluation of knowledge."

To Stephen Wolfram, the founder and chief executive of Wolfram Research, such questions mark progress, not a lack of work ethic from today's students. "If there's one constant to progress, it's that we get to automate more and more levels of stuff," Dr. Wolfram says. By automating the drudgery, Wolfram Alpha should open up possibilities for exploration on a deeper level, he says.

Or that's the idea, anyway. Mathematicians and statisticians who have taken Wolfram Alpha out for a test drive didn't always agree on whether its advent was a good thing for education, but nearly everyone found at least one problem with the search engine. Sometimes it was befuddled by certain queries. Other times it was clueless about important mathematical theorems and principles. It also lacks some important social statistics such as flu deaths or GDP by province.

That last group is hardly a fixture of math tests, but it is crucial to Wolfram Alpha's lofty long-term goal "to make all systematic knowledge immediately computable and accessible to everyone."

Browsing Results

Check out results for the queries below, in the Wolfram Alpha search engine. Note: Wolfram Alpha works best with the Firefox Web browser.

Plus, watch a Wolfram Alpha overview video.

For now, barely a month after its launch, Wolfram Alpha should be judged as a work in progress. It has received more than 100 million queries, according to Dr. Wolfram, and his team of "a couple of hundred people" working on the engine have been analyzing failures and making fixes.

One big stumbling block is guessing at users' intentions. For instance, the engine only understands English, but many users abbreviate months in other languages. And calculus fans seeking to calculate a derivative have used the word "derivate," which Dr. Wolfram is pretty sure isn't a word. He's willing to have his search engine interpret it like one, anyway.

The notion that students won't even have to know that the correct word is "differentiate," let alone calculate derivatives, is an exciting yet scary one for some instructors.

"Some students will figure out ways to come up with what appears to be their work, but isn't," says Colm Mulcahy, a mathematician at Spelman College. He notes that Wolfram Alpha works on some cellphones, and "the sad reality is that students use mobile phones in classrooms, more than we would like. It's been known to happen in testing situations."

Not everyone expects cataclysmic change. David Bressoud, president of the Mathematical Association of America, is skeptical. "There are so many ways students can get around doing the work themselves," says Prof. Bressoud, who teaches at Macalester College. He notes that students could also use those cellphones to seek answers from other students by text. And study-aid Web sites offer the answers to questions from popular math and science textbooks.

Previous technological advances caused educational upheaval. Calculators pushed some to chuck multiplication tables; graphing calculators later replaced graph paper. With time previously devoted to memorization and computation freed up, teachers shifted the focus to word problems and reasoning.

Now, with solutions to more-complicated problems at students' fingertips, teachers may have to start over once again.

"This is part of an accelerating trend," says John Dell, a physics teacher at Thomas Jefferson High School for Science and Technology in Alexandria, Va. "It no longer makes sense to teach students the arcane art of doing integrals. If you're an old educator and you really liked this part of teaching calculus, you're not going to like it."

Even as educators consider curriculum changes in time for the fall, Wolfram Alpha is itself adapting -- perhaps too fast for teachers to keep up. "However you set up your pedagogy, it could change tomorrow," says Maria Andersen, a mathematics instructor at Muskegon Community College in Muskegon, Mich. "It's a little frightening to a teacher trying to prepare good lessons."

Dr. Wolfram's new search engine is breaking new ground, some say, in the way it organizes and displays data. "When it matures sufficiently, perhaps several years from now, if it doesn't find what we want, what we want won't exist," says Donald Berry, chairman of the department of biostatistics at the University of Texas M.D. Anderson Cancer Center. He sees Wolfram Alpha as one potential way the Obama administration can realize its goal of computerizing and systematizing health records. Still, Prof. Berry calls Wolfram Alpha "sort of primitive" in its current form.

Dr. Wolfram says he is going to improve his computational engine. He estimates that Wolfram Alpha has been able to answer about 75% of queries in some way. The rest produce the frustrating message, "Wolfram|Alpha isn't sure what to do with your input." Sports statistics are a notable hole.

Successful searching is all relative. Type "gdp spain/Italy" and you get the ratio of the two nations' GDP. But type "10 lbs kgs" and you may be seeking a unit conversion, but instead the site multiplies 10 pounds by one kilogram, producing a nonsensical answer of "22.05 square pounds," whatever that means.

Dr. Wolfram wonders aloud what success rate his search engine will reach. "80%? 90%? 98%?" That is one query Wolfram Alpha can't yet answer.

Write to Carl Bialik at numbersguy@wsj.com

Corrections & Amplifications

The graphic that appears in this column showed the results of searching the Wolfram Alpha search engine for "C, E, G, B flat, D, F sharp and A." While the musical notation in the graphic correctly listed the notes returned by the search, the query given in the graphic neglected to include the G note.