Stephen Wolfram had a dream: to invent a search engine that could work stuff out for us. Alex Bellos meets the scientist who might just change the way we use the internet

The British scientist Stephen Wolfram has a clear vision for the future – a vision that dates back to his childhood in the 1960s and 70s. In those days, we didn't prophesise that computer technology would bring us convenient ways to shop, or new ways to talk to our friends in short sentences. The dream was much grander – that computers would work out stuff for us, a bit like Hal in 2001: A Space Odyssey (without the murderous intent).

It was with this aspiration that Wolfram launched Wolfram|Alpha, a website that aims to be able to answer any factual question asked of it. Wolfram says he wanted to create an "insanely ambitious thing, like the science fiction computers of old". Currently, for example, when we want to know something on the web, our default action is to Google it, but this just searches for words rather than calculating answers, so leads you only to what has already been written, which may or may not be what you want to know. Wolfram|Alpha, on the other hand, is an attempt to change the way we interact with knowledge on the web, to make the web more intelligent – by providing bespoke, freshly computed answers from a curated database of sourced facts.

When Wolfram|Alpha was launched in 2009, it was initially hailed a Google-killer. Users flocked to the site to ask it the sort of question you ask Google, but when it didn't do what they wanted, they grumbled and didn't return. Some users, for example, typed in their own names, and the engine failed to give any response. Or they asked a complicated question, didn't get an answer and so felt it wasn't intelligent enough. Wolfram has said the site went live because it was at the stage in development when it needed to understand the sorts of questions people would ask it – the hype, he says, was useful, even if the site didn't live up to users' initial expectations. "If you look at most web phenomena – Google, Facebook – you only tend to know about them when they have gotten pretty big," he says. "We happened to launch with a big spike."

In the last year and a half, however, Wolfram|Alpha has been growing steadily and now contains about 10 trillion data points, making it, Wolfram claims, the largest integrated data set in the world. Its strongest areas are in science – you can ask it to solve difficult mathematical problems, give you maps of the night sky or break down chemical compounds. It will also cross-reference socioeconomic data, give you 23 rhymes for the word "cat" and complete the saying, "A penny earned..." It can't answer every question you ask it – but it can already do a lot.

Wolfram believes it is inevitable that people will increasingly want the internet to provide them with correct answers to questions – rather than, as with Google, providing a selection of pages you have to read before deciding whether or not they are relevant. "People's expectation [for expertise] is just going to go up."

Indeed, the move from searching to question-answering explains the recent rise in popularity of the website Quora, which has 7.6m page views a day. In Quora, users submit questions and answers, and vote on which answers are best. But Quora relies on human responses coming in when users take the time, whereas Wolfram|Alpha's are computer generated and delivered in two seconds.

Wolfram, 51, has long been one of Britain's most intriguing scientific figures. He published his first academic paper while a schoolboy at Eton in the 70s. At 20, he had a PhD in physics, by 22 he was the youngest person to win a MacArthur "genius" award and, by his mid-20s, was at the elite Institute for Advanced Study at Princeton, whose alumni include Albert Einstein and Kurt Gödel.

An illustrious academic career beckoned, but an interest in computer programming superseded Wolfram's interest in physics and he moved into business. He wrote the technical software Mathematica, which launched in 1988 and is still widely used throughout science and industry. Thanks to Mathematica, his company Wolfram Research has been nicely profitable, which has allowed him time and money for his other projects.

One of these was his 2002 book A New Kind Of Science, about how very simple rules can produce great complexity. "The thing I tend to do is take these big complicated things and try to drill down to get the fundamental components underneath," he says. "With Wolfram|Alpha it's the same thing. There's all this stuff, all this knowledge in the world. How can one organise thinking about this in such a way that it's actually finite enough to build a coherent system?"

We meet at the headquarters of Wolfram Research in Champaign, Illinois. (The neighbouring town, Urbana, is where Hal famously became operational.) He runs the company remotely from Boston – via daily conference calls – but has flown to Champaign for some end-of-year meetings. "It's very disorientating doing these meetings in person," he says as we sit down.

Wolfram is an idiosyncratic mixture of Eton-educated CEO and deep scientific thinker, supremely self-confident and tirelessly curious. He certainly sees himself as an important player in the grand sweep of history – which is just as well, since if he weren't so self-assured, he wouldn't take on such audacious projects. "What [we are] trying to do is to take knowledge from throughout history and automate it. That seems like an important step in the progress of technology."

But how do you go about such a mammoth task? Wolfram had a base on which to start – Mathematica, which already contains a lot of scientific data and algorithms for making computations with that data. On top of this, the task has been to fill the Wolfram|Alpha database with as much information as possible: including government statistics, live feeds from weather stations, data about earthquakes, figures from financial markets, whatever is out there and available. Among the 500 staff at Wolfram Research, there are PhDs in subjects including astronomy, physics, biology and engineering, and individuals are encouraged to suggest, contribute and curate data from their areas of expertise.

Yet this is a project that stems from the brain of Stephen Wolfram and is very much shaped in his image. He has an oak tree in his backyard, for example, and it was this that made him think it would be interesting to input data on trees. "Pretty soon, we were talking to the guy who is the world authority on tree growth. And he said, 'Look, we've got this database with a million trees in it – we'd love to just give it to you and maybe you can do something interesting.'"

Wolfram|Alpha is not just intended to be a massive database of random facts, though – the facts need to be able to "talk" to each other, so they can be used in computations. For example, if you enter the question, "What was the weather in London on the day Prince William was born?" the site needs to be able to link weather information with biographical information. If you ask, "What is the distance to the moon divided by the length of the Amazon river?" it needs to link astronomical with geographical data. (The answers, by the way, are rainy and overcast with an average temperature of 16C and, currently, a ratio of 63.07.) To merge different data sets together, information must be coded in clever ways when it enters the database. Since this coding is one of the things that Mathematica has been doing for more than two decades, Wolfram has an advantage over other sites that may share some of the same information. If, say, you ask the site for "bananas UK", you get a graph of UK banana consumption from 1961 to 2007, as well as the curious fact that we rank 43rd globally in per capita banana consumption. (If you put "bananas, UK" in Google, you are led to the charity site "Bonkers about Bananas".)

Perhaps the most intellectually challenging issue for Wolfram|Alpha is how to understand the queries that come in. Unlike Google which, given a word or a sequence of words, trawls the web for pages containing those words, Wolfram|Alpha needs to understand the content of the question. "People have been trying to solve the [natural language understanding] problem for a long time, and it has generally been very difficult," Wolfram says. "Well, it turns out that it was a lot easier than we thought."

Not even a man as bullish as Wolfram would claim to have solved the problem of how to make computers understand natural language, but what he has done is devise methods to link the computable information he has to what people write in the input box – which can be full sentences, mathematical symbols, broken English, key words or mixtures of all four. The technology is still a work in progress, though, and one of the most frustrating aspects of using Wolfram|Alpha is the "computer says no" moment – you know it has the information you want, but it does not understand your question. For example, if you type in "sex", it will give you lots of fascinating information about the word, such as its Scrabble score, movies with "sex" in the title and its frequency in the English language (1,173rd most common when written, 1,218th when spoken). But if you are more specific, and type in "frequency of word sex when written", it thinks you are talking about frequency and tells you that the standard unit is the hertz.

So far, the questions that Wolfram|Alpha is most accomplished at answering correctly are in mathematics and science. If one of the aims of the site is to extend the range of problems that you can solve without using paper and pen – in the way that the pocket calculator meant you didn't need to know how to do long division any more – then Wolfram|Alpha has already been successful. There is now a swath of tricky maths questions that it will answer instantly. A-level calculus homework has effectively been made obsolete.

Would Wolfram feel a sense of shame if, as a result of his website, fewer people learned how to perform certain mathematical operations by hand? "There was a time when we had to cut feathers to make our own pens. Gradually more levels of civilisation and automation happen, and this is another such layer," he says. "What should happen is that you can build on to what is now automated and do the next level of stuff, where you need to add the human touch." It also cuts both ways since, if calculus is mechanised, this opens up new worlds for students for whom solving problems by hand was too difficult.

Speaking to Wolfram, it is impossible not to be infected by his enthusiasm. But while he may be guided by his intellectual ambitions, he is also a businessman. Wolfram|Alpha may appear to be a philanthropic project but, he says, it is already profitable. He has signed a deal with Microsoft's search engine Bing – a direct rival to Google – which uses Wolfram|Alpha embedded in its results page. And, he says, more deals will be announced soon.

After its wobbly start, Wolfram|Alpha now receives about 20 queries per second, which works out at almost 2m a day. (This makes it only the 3,304th ranked site on the web, according to Wolfram|Alpha's search engine.) Every week new data is added, and questions that come in shape its direction. (When one of the most popular queries was "penis size", one researcher at Wolfram Research duly spent a day and a half compiling authoritative global data on that.) Highly requested areas such as sports, music and cars are being developed and, it is hoped, will come online this year.

In 1993, when Wolfram was already an established figure in the tech industry, a young student called Sergey Brin spent a summer as an intern at Wolfram Research. A few years later Brin founded Google, and the men are still in touch. I ask Wolfram if he is worried that Google might try to copy Wolfram|Alpha. He doubts it would happen. "The things that made Wolfram|Alpha possible for us were a somewhat unique convergence of circumstances: Mathematica, a collection of very eclectic people. And it's a private company, so I can decide to do something completely crazy with it. It's not clear you can buy it, so to speak."

He adds that he recently found an old email from Brin saying that the only way to make progress in software was to give stuff away. "I thought that was funny. At the time, that wasn't my way of thinking at all."

And is it now?

"Yeah, a little bit. We shall see whether it turns out. I would expect Wolfram|Alpha to emerge as one of the pillars of the internet world. But whether it comes with a giant money machine or a small money machine, I can't say yet."

Recently, Wolfram was looking through a little physics notebook he wrote when he was 12. He saw lists of data and formulae. "It was, in a sense, Wolfram|Alpha 1972 and I'm like, 'Oh my gosh, I've been doing the same project all my life!'" It's a project that will never be finished, but along the way it may just change our experience of how we use the web.

Questions that only Wolfram|Alpha can answer…

1 You meet a distant relative, and discover they are your great-grandfather's sister's grandson's cousin. If you input "great-grandfather's sister's grandson's cousin", it will show you the family tree, tell you the relative is a second cousin once removed and you have a "blood relationship fraction" of 1/128.

2 You want to find the share price of a certain stock on a certain day, so you type: "Price of Nike stock on the day Wayne Rooney was born." The answer is $0.86, and the site also gives you the graph of the stock's performance a year before and a year after 24 October 1985.

3 You wonder how big Walmart is compared with UK GDP. Type "What is Walmart revenue as a fraction of UK GDP?" The answer is 0.186, plus a graph showing the change from 1985 to 2010.

4 You're arguing with friends about last year's blockbuster movies. Type in "Social Network, Inception, Harry Potter And Deathly Hallows box office". You get a timeline of earnings and a list of comparative data on total receipts, rank, screens and average take per screen.

5 What's interesting about the number 76577655163 – randomly plucked from your brain? The website tells you it is a prime number, that it is roughly 0.26 x the number of stars in our galaxy, 0.72 x the number of people who have ever lived and 12 x the number of people alive today.