Jack Dorsey is this kind of billionaire. At just 39, Dorsey is the CEO and co-founder of two of Silicon Valley's biggest players, Twitter, the social media platform, and Square, a mobile payments company. Together these companies have a market cap of $15.6 billion; Dorsey's personal wealth has been estimated at anywhere between $1.13 and $3.9 billion. And yet he has a reputation of being something of a minimalist. He has boasted about getting the bus to work, buying tickets in bulk, on a monthly pass, to save money. He once encouraged a start-up audience to drink only lemon water and red wine. At the San Francisco office of Square, where I recently met with him, he eschews anything as cumbersome as an office, or God forbid, a desk. "I walk around," says Dorsey, dressed in jeans, a no-name black sweater and orange high tops. "I meet people. I mainly work on my phone when I need to communicate."

Dorsey has blue eyes and a trim build; he is neatly bearded and immaculately coiffed, and resembles nothing so much as the world's richest hipster. He is best known for Twitter, which he helped found in 2006, and which now has 300 million users worldwide. Less well known is his financial technology, or "fintech", start up, Square, which he launched in 2009.

In late March, Dorsey will travel to Australia to launch Square's signature product, the Square Reader, a three-centimetre square piece of plastic that, plugged into the audio jack, turns any smartphone or tablet into a credit card processor. For small, artisanal businesses – food stands, personal trainers – this is a significant development. In the past such businesses would not have been able to accept payment by card, either because their credit history meant they didn't qualify, or because they found the conditions – rental of credit card terminals, long term binding contracts – too onerous. "It's all about economic empowerment," Dorsey says, nursing a half-drunk bottle of Kombucha Iced Tea. "It's about enabling people who were previously locked out of the economy to get up and running quicker and easier."

As the story goes, Dorsey came up with the idea with long time friend, Jim McKelvey, a computer scientist and artist who also ran a small glassblowing business. One day McKelvey got a call from a woman in Panama who was willing to pay $3000 for one of his works. Unable to accept her card, McKelvey missed out on the sale. It was, McKelvey has said, a lightbulb moment. (McKelvey has since stepped back from his involvement in the company.)

Dorsey has high hopes for his technology. "Payment is another form of communication," he told Vanity Fair magazine in 2011. "But it's never been treated as such. It's never been designed. It's never felt magical." I made plenty of payments in San Francisco with businesses that used the reader, and none of them felt particularly magical. And yet it has to be said that the reader is, without question, a formidable piece of engineering. Since starting as a point of sale device – a cash register in your hand – it has grown to include a range of backend services, including online invoicing and payroll functions, inventory management and business analytics, all of it bundled up in a chunk of plastic that costs $19. "When we started Square there was a lack of cohesion," Dorsey tells me. "There was a different company building every piece of the system. What we've done is put it all in one piece of software."

Dorsey is a big name, but success is by no means assured. The payments space is already crowded, and Dorsey's technology is, experts say, easily mimicked. "Also, I am not sure Jack fully understands the market here, or the banking system," says Jost Stollmann, CEO of Tyro, an Australian mobile payments operator. "He will find it difficult to make money, I think."

Dorsey seems serenely untroubled by this. Right now, he is looking forward to seeing Australia, which he has never visited. When I asked him what he expected, he replies: "Bliss."

Two-time drop-out and a fascinating character

Square is based in San Francisco's downtown, adjacent to the city's rundown Tenderloin district. (Twitter is in a separate building, 80 metres away.) Occupying five interconnected football pitch-sized floors, the offices, which house 1200 staff, are the very acme of IT chic, with acres of open space and polished glass. Bifurcating the building is a colossal vaulted staircase, 15 metres wide and 40 metres high, its steps marching skyward like those of a Mayan temple. As with Dorsey, the presiding aesthetic here is minimalism: the only non-work related items I spotted on people's desks were the odd box of tissues and a tube of hand sanitiser.

By all accounts, Dorsey is a generous employer. A programmer at his companies with just one or two years' experience can earn $150,000 a year, plus $500,000 in stock. "And the conditions are excellent," a former Twitter staffer tells me. "There's free food, free drinks, free gym and pool, gaming areas, lounges, in-house masseurs and a dry cleaning service. The company wants to keep the programmers in the building, working, for as long as possible. Need a meal? Eat at the in-house restaurant. Need to do your dry cleaning? Do it in the building."

Even if he hadn't started two of the biggest tech companies in the world, Dorsey would be a fascinating character. A two-time college drop-out, he has studied botanical illustration and dress making, and worked for a time as a massage therapist. According to the book Hatching Twitter by New York Times writer Nick Bilton, he was once so broke in his early twenties that he set up an auction on eBay where he offered to read the children's book Goodnight Moon to the highest bidder. (Four people took up the offer, one of them paying $100.) He has variously expressed a desire to be fashion designer and the mayor of New York. Observers describe him as "charming and smooth", petulant, pretentious, and "a really friendly guy". "Most people think he's arrogant," one former Twitter employee tells me. "Though that's not unusual in the Valley. All these big guys, they all think they are walking gods among men."

He is also, apparently, an idealist. Dorsey has long talked of Twitter as a force for good, for transparency and accountability. Twitter also encourages staff to take part in #TwitterforGood, which sees employees participate in charity work every couple of months. "I loved working there," says Ben Novakovic, who moved to San Francisco when We Are Hunted, the Brisbane based software start-up where he worked, was bought by Twitter in 2012. "You always had the feeling working there was meaningful and changing the world."

Uneven reputation

And yet Dorsey has an uneven reputation in the Valley, thanks to his role in the early days of Twitter. Dorsey was raised in St Louis, Missouri, the oldest of three brothers. His father, Tim, was an engineer who specialised in medical equipment; his mother, Marcia, stayed at home. As a boy, he had a speech impediment, and would spend hours in his room playing with the IBM PC Junior his father gave him for his eighth birthday; three years later, he got a Macintosh. In time, Dorsey borrowed his father's CB radio, which, when combined with a police scanner, allowed him to eavesdrop on the short burst transmissions from police and ambulance crews, the constant updates of what they were doing, where they were and where they were going.

Dorsey taught himself to code, and became a keen hacker. In 1999 he came to San Francisco, where he worked on a fledgling internet platform for dispatching taxis, couriers and emergency services. He also began sketching out a live blogging service where posts would appear in real time. After losing his job in the tech bubble, however, he returned in 2002 to St Louis, before heading back west in 2005, for second bite at San Francisco.

One day in 2005, while sitting in a cafe in the South Park neighbourhood, Dorsey met the well-known internet entrepreneur and pioneering blogger Evan Williams. Williams was then running a struggling podcasting start-up called Odeo, where he offered Dorsey a job as a coder. When Odeo folded in 2006, Williams encouraged his staff to brainstorm alternative ideas. Dorsey revisited his earlier work with dispatch systems and real-time communications. Together with other Odeo staffers, he married these with SMS, the phone messaging service. The result: a larval version of Twitter. (Dorsey called the platform Status, before Noah Glass, a long time Odeo employee, suggested Twitter.)

After some early hiccups, Twitter took off. By 2008, there were 1.2 million register users, sending 15 million tweets a month. But the company was in chaos. Dorsey became CEO, but proved comically out of his depth: the site's servers regularly crashed, costs blew out. According to Hatching Twitter, Dorsey alienated staff by ordering them around; in an effort to assert his power, he fired people at will – in one instance, Bilton says, while the employee was on holiday. While the engineers scrambled to keep the site afloat, Dorsey would leave the office early to attend yoga classes and sewing lessons. (He later told The New Yorker that he always resumed work later.) In late 2008, it was discovered that Twitter had no back-up. If the database went down, everything would be lost.

Perhaps most tellingly, Dorsey seemed constitutionally incapable of crediting others. "Jack was intellectually selfish," a long-time Silicon Valley insider and friend of Dorsey's told me. "If you look at his interviews from 2007 and 2008, it's all, 'I said this', and 'I did this'. There was never any 'we'. And so, you know, people didn't really care for him."

Dorsey was sacked in October, 2008, and Williams installed as CEO. (Dorsey was made a "silent chairman" – a symbolic role, with no voting rights or decision-making power.) Dorsey cast about for other projects, eventually coming up with the idea for Square. In Bilton's telling, he also began plotting his return to Twitter, holding back room meetings with board members and employees, and publically portraying himself as Twitter's sole creator. (Williams responded by shutting down his Twitter email account.) Thanks in part to Dorsey's efforts, Williams was in turn sacked as CEO, in 2010, and replaced by then COO Dick Costolo. In 2011, Costolo invited Dorsey back to Twitter, as executive chairman and chief product manager.

Dorsey now found himself running both Square and Twitter. "The only way to do this is to be very disciplined," he told CNN, adding that he regularly put in 16-hour days.

It paid off. In 2013, Twitter held its IPO. At an opening price of $US26 a share the little blue bird suddenly became worth $US31 billion.

Silicon Valley fuels inequality

Such valuations are common in the Valley. Uber, the ride hailing company that has its offices in the same building as Square, is currently valued at $US51 billion ($68 billion). In 2014, Citigroup estimated Instagram, the photo sharing service, to be worth $US35 billion. Last year the Economist magazine valued the total value of Bay area tech companies at more than $US3 trillion. A recent explosion in the number of so-called "unicorns" – start-ups valued at $US1 billion or over – has even fuelled talk of a tech bubble.

Such wealth is having a profound effect on San Francisco. Locals complain of not being able to find a parking space, of previously affordable restaurants now packed with preppy-techies, and of skyrocketing rents. The cabbie who drove me from the airport lamented the "Manhattan-like" property prices. "The other night I picked up a couple who told me how lucky there were to have bought a house for $5 million."

Not surprisingly, San Francisco now has one of the highest levels of inequality of any major American city. Thanks to a well-documented housing crisis, the streets are awash with homeless people – crackheads, ice addicts, the physically and mentally ill. Meanwhile, tech workers on $US200,000 plus stock options breeze in like new age Brahmins, a class of high caste Ivy League graduates whose excesses have become legend; Halloween parties with acrobats and tigers; birthday get-togethers with ice sculptures and firebreathers. A Google office party featured a wave pool, so employees could go surfing in between cocktails.

"Don't get me wrong," my cabbie said. "They have rejuvenated the city, but they don't have any respect for it. They just want to make their money and leave."

Silicon Valley likes to spruik its philanthropic credentials. Tech moguls are known to have donated hundreds of millions of dollars of their own money towards a range of causes, from children's health to low cost transport. And yet the largesse goes both ways. When Twitter moved its headquarters from San Francisco's CBD to the Tenderloin district, in the city's north-east, they sold it as part of their social good agenda, as an effort to reinvigorate a flagging district; what they didn't say was that they received a $US22 million tax break for doing so.

I wanted to discuss all this with Dorsey, the role of Twitter as a force for good, Twitter as a window on the world, as he has described it. But Dorsey refused to go there. "I'm not talking about Twitter," he said, in his characteristic monotone, adding: "We're here to talk about Square." But what about transparency, I asked. What about openness and access?

"Apologies," he replied, tapping the lid of his ice tea on the table. (So sensitive were they about Twitter that I was not permitted to walk through the company's offices.) When, some moments later, I began asking another question that skirted into Twitter territory, his head of communications for Square, Katie Baynes, interrupted: "Either we talk about Square or we can stop the whole thing."

'Total junk'

Dorsey's reluctance to discuss Twitter is understandable. Once the darling of social media, the company has of late suffered a grievous battering. The stock tumbled 55 per cent in 2015, with analyst Trip Chowdhry of Global Equities Research calling it "total junk". User numbers – the metric most valued by Wall Street – have also stalled. At the time of Twitter's IPO, the company was billed by investors as the next Facebook; instead, Facebook has left Twitter in its wake, both in terms of revenue (Facebook made a $US3.69 billion profit in 2015; Twitter lost $US521 million), as well as users (Facebook had 1.49 billion active monthly users last year; Twitter had 316 million.)

One of Twitter's problems has been its size. Before Dorsey became CEO, staff numbers ballooned to more than 4000. When Stephen Phillips, co-founder of We Are Hunted, moved to San Francisco to work with Twitter in 2012, he was "astounded" by the number of employees. "I just couldn't believe it," he says. "I just thought, 'What are they all doing'?' And they were hiring 50 more programmers a month … It was like working in a bank. It had all the same bureaucracy, except they were 'cool'."

The company found it almost impossible to move quickly. "Twitter actually knows it can't innovate, even though they say they can," Phillips says. "The way they innovate is to wait for a start-up to design something new, and then they buy you out." (Twitter snaps up dozens of smaller companies every year.)

One of the first things Dorsey did when he became CEO in late 2015 was slash 336 jobs – about 8 per cent of its workforce. (In February this year, four senior executives also left, having either resigned or been sacked, depending who you talk to.) Dorsey has since rushed through a range of product improvements, including a new function called Twitter Moments, which collects, or curates, tweets around four main categories: "news", "sports", "entertainment" and "fun". There was also an (extremely confusing) experiment with reversing the chronology of tweets, and, most recently, talk of expanding the platform's signature 140-character limit to 10,000. Dorsey also announced plans to invest more heavily in Periscope, a live video-streaming app that the company bought in 2015. (Unfortunately, when the company used Periscope to live stream its earnings call in February, the image appeared upside down and sideways to many viewers.)

Implementation has been patchy, especially with Moments, which puzzled many users and failed to impress investors. As the American tech writer Om Malik recently put it in The New Yorker, "The disconnect between Moments and Twitter Stream is evidence of a company that has been lazy in its product thinking".

Twitter isn't about to fold any time soon: it has $US3.5 billion in cash reserves, which, at its current rate of spending, is enough to keep the company afloat for 412 years. But investors don't want companies to merely float; they want them to take off. "Jack had a huge first mover advantage with Twitter, and everyone else was just left behind," says Stollmann. "It was a land grab model. As long as you grow, this is fine, you get lots of latitude. But as soon growth begins to flat line, investors say 'show me the money.' "

Implausible as it sounds, Twitter now finds itself a takeover target. "Everyone is talking about it in the Valley," an industry insider says. "It's one of the most discussed topics; who will own Twitter." Google and Microsoft are thought to be the most likely buyers.

Dorsey seems wounded by talk of a takeover. (He has previously described Twitter as one of his two "babies", the other being Square.) I raised it with him, but he says only that "I'm not going to comment on speculation".

'If anyone can resurrect Twitter, it's Dorsey'

There is one facet of Twitter upon which Dorsey's return has had an immediate and tangible impact: morale. Dorsey enjoys an almost guru-like status in Silicon Valley – the prodigal son, returned to save his sinking ship. "If there is anyone who can figure out how to resurrect Twitter, it's Dorsey," Malik wrote recently.

As the co-founder, Dorsey has a unique mandate for change. He is also a good motivator. In January, he used the company's bi-weekly "Tea Time" meeting to address the staff in what appears to have been a Jim Jones-style pep talk. No sooner had he walked off stage than employees hit the Twittersphere: "Best teatime ever. love this company, this product, this team," gushed one. "Because what Twitter makes happen will be remembered for generations, and I want to say I was there", tweeted another. "I love this company. @jack knows how to inspire a room of thousands …" And: "I joined Twitter because there is no other platform as powerful or as inspiring. I can't imagine a world without Twitter."

The reality is more complex. "There are two camps within Twitter," I am told. "There are those people who have really drunk the Kool-Aid and regard Jack with an almost religious fervour and consider him close to Steve Jobs and the second coming of Christ. Then there are the others who don't know but hope that is true, because they have equity and they are hoping Jack will turn the company around and they will all become millionaires."

Dorsey is fond of hiking. He is fond of Socrates ("The only true wisdom is in knowing you know nothing," he once tweeted). He is also fond of poetry: after buying a house near the Golden Gate Bridge, in 2012, for a reported $US10 million (minimalism only goes so far), he tweeted a line from Pablo Neruda: "I need the sea because it teaches me."

He is not so fond of losing. Given Twitter's travails, it's tempting to see Square as a road to redemption. "I started Square after Twitter," he explains, "and I learned after that founding, and of course you bring all of what you learn into what you do next." Twitter was synonymous with management dysfunction, but Square has been different. Despite the odd wobble – in 2013, Square COO Keith Rabois left the company after becoming the subject of a sexual harassment claim – Dorsey has put together what most observers agree is one of the strongest leadership teams in the Valley.

The Square Reader has been available in Canada for four years and in Japan for three. The company says there are now more than 2 million merchants using the technology; the company estimates it would have processed $US38 billion in transactions for 2015. Dorsey is upbeat about Australia. "Australia has adopted [new] technologies faster than the United States, so we're pretty excited about that," he says.

Dorsey has one of the biggest brains in Silicon Valley, with the vision to match. And he's a survivor. But can he transform the way Australians buy and sell? Can he surmount perhaps the greatest challenge of his career, and make paying for a sausage roll a "magical" experience? To paraphrase tech writer Malik, if anyone can do it, Jack can.