Ask a factual question of Siri, Apple's virtual assistant, and chances are the maverick British computer scientist and entrepreneur Stephen Wolfram is responsible for the answer. For when posed a question such as: "How far is it to Mars right now?", Siri turns to WolframAlpha, the answer engine developed by Wolfram through his US-based private company, Wolfram Research. It puts together answers based on information in thousands of external datasets vetted for their quality by Wolfram Research (in contrast, search engines such as Google traditionally provide only a list of web links that may contain the answer). "I don't view it as being clever," says Wolfram of his product, which he also licenses to the DuckDuckGo search engine (a deal with Bing recently ended after several years and one with Google fell apart). "I view it as being a big pile of engineering."

Wolfram had a certain notoriety before WolframAlpha. He was the child genius who turned his back on a promising academic career in particle physics to make a fortune as the creator of the software package Mathematica, widely used in science and engineering. And he was the author of a provocative 2002 work promising a revolution in how we understand the universe. The book, A New Kind of Science, theorises that the wonders of the natural world, from the great complexity in biology to the apparent randomness in physical systems, can be captured by simple rules. "I've never seen a more comprehensive theory or one that has incited so much irritation in the academic class," writes Margaret Wertheim in her 2011 work Physics on the Fringe. She calls Wolfram "by far the most famous outsider physicist today".

Not that he appears bothered. "I've been lucky enough to build a consistent stack of technology and science over the course of about 35 years," he says. "I have built tools that have let me do science. And from the science I have understood things that have let me build more technology."

He is also a self-described "information pack rat". For the past 25 years, he has been collecting all sorts of systematic information about himself. He records his every keystroke, every step and – at least sometimes – a picture every 30 seconds using a life-logging camera. He now uses it to answer "random, whimsical questions" about himself such as the chances he'll be on the phone at 9pm (39%).

Wolfram, 54, was born in London and grew up in Oxford, winning a scholarship to Eton. His father was a textiles businessman who wrote novels; his mother a philosophy professor at Oxford University. His interest in science began early, ignited by the space programme, and by his early teenage years he had read his way through a variety of college physics textbooks. As the age of 15, he published his first scientific paper, in the field of particle physics. "I wasn't really interested in the exercises in the textbook," he says.

He entered Oxford University at 17 without A-levels and left around a year later without graduating. He was bored and he had been invited to cross the pond by the prestigious California Institute of Technology (Caltech) to do a PhD. "I had written a bunch of papers and so was pretty well known by that time," he explains. He received his doctorate in theoretical physics in 1979, aged 20, and joined the faculty. At 22, he won a lucrative MacArthur Fellowship, becoming the then youngest winner of the "genius grant".

Yet his time at Caltech was short-lived. His interest in computers had led him to develop a software program for performing algebra. A dispute with the institute over commercialisation broke out and in 1982 he left, taking a position at the renowned Institute for Advanced Study (IAS) in Princeton.

Here, his work took a new direction that had begun at Caltech: studying very simple computer programs known as cellular automata, which had been pioneered in the 1950s but fallen into obscurity. What structures and patterns could they generate and what might that reveal about the origin of complexity in the universe? Using computer simulations, Wolfram was determined to find out.

In 1984, he finally "grokked" what he calls rule 30 – a particular cellular automaton that with enough iterations produced an intricate and seemingly random pattern, resembling that on the cone shell. He soon found several other automaton rules that produced similar results. Simplicity could spawn complexity, he concluded.

Soon, he and others were showing that, from snowflake growth to fluid turbulence, cellular automata could model the behaviour of many complex systems in nature. He left the IAS to set up the first research institute for the burgeoning field, which he called complex systems research, at the University of Illinois at Urbana-Champaign.

But he soon became frustrated. Other researchers didn't seem to grasp the message about just how powerful cellular automata could be to unlocking the secrets of the world. "I decided plan B is just to build the best tools I can and to do the science myself," he says.

The tool was Mathematica, software that performs a range of computational operations using symbolic language. In 1987, he founded Wolfram Research to bring it to fruition and a year later he quit academia to head the company and launch the first version. It made him a multimillionaire and provided a powerful tool to continue his experiments in cellular automata.

In 1991, armed with his computer, Wolfram withdrew from the world to take forward his discoveries, becoming a scientific recluse for more than a decade. "What I thought was going to be a year-long sabbatical to investigate turned into 10 and a half years," he says. The result, A New Kind of Science, self-published and intended for a general audience, ran to more than 1,200 pages.

The book presented an empirical study of the automata, showing that instead of producing fairly simple behaviour, as might be expected, they produced patterns of great complexity and randomness. He presented new accounts of space and time, the laws of thermodynamics, the origin of life, the creation of the universe and the existence of free will based on it. "Everything is reducible to these simple computational processes," he says.

It became a bestseller and received much press attention but was also heavily criticised. Not only were many scientists staggered by what they saw as hubris but they disagreed with his expansive claims and felt he had inadequately credited prior work. It would never have survived the ordinary peer review, so they claimed. "He tried to publish a manifesto rather than a contribution to the scientific process," sums up Henrik Jensen, a complex systems scientist at Imperial College, London.

Now, 12 years on, it seems the critics are ahead. "Scientists have not taken much notice of Wolfram's ideas," writes Wertheim in her book. Wolfram begs to differ. New ideas in science take time to win acceptance, he says, citing Einstein's theory of relativity. "In a dozen years, I think the absorption of NKS in mainstream science is going very well indeed." There are "thousands" of academic papers that explicitly say they use it, he says, and scientists now often build models based on programs rather than mathematical equations, which is a transition NKS has helped to achieve.

Yet perhaps the book's single greatest impact was on Wolfram himself, because it led him to his next project. Since his school days, he had dreamed of building a system that could answer questions based on all the information in the world. But he had always assumed the feat would require building a brain. The book convinced him such lengths weren't necessary: he just needed computation. The result was WolframAlpha, launched in 2009 and which he estimates has tens of millions of users ranging from students to engineers to financial analysts to policy-makers."It is nice to do useful stuff," he says. "I'm interested in turning ideas into real things." In 2012, Wolfram even added "Personal Analytics for Facebook", which allows users to visualise their networks, friends and site activities.

As to his next swing from technology back to science, his fantasy at least is to find a theory to explain all of physics – the so-called grand unifying theory of everything. Wolfram thinks it could be but a handful of lines of code. "Maybe I'll succeed, maybe I'll fail," he says. "The early signs are very encouraging."

His toolbox recently gained a new piece of technology that might help. He unveiled what he modestly calls the Wolfram Language, a computer programming language that combines Mathematica and WolframAlpha along with other elements (a preliminary version has been incorporated into the Raspberry Pi low-cost computer aimed at teaching children to learn to program). "The main point is to automate as much of the process of programming as possible and to build in as much knowledge about computation and about the world as possible," he says. "It really is going to be quite transformative."