Modern machine learning research has demonstrated remarkable achievements. Today, we can train machines to detect object

This concept is called bootstrapping, and many of these startups are sought after due to their ability to create revenue, cash flow, and product-market fit without needing investor cash.

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pecial gratitude to Stephen Wolfram, Jeremy Sykes and Mads Bahrami for ensuring that Cut-the-Knot stays alive and that this book sees the day. Additional thanks to Paige Bremmer,Glenn Schloebo, and other members of Wolfram Media for editing the manuscript.

Your relationship will never be the only thing that matters in your life, but you’ll face situations in which you must decide that it matters more than anything else. Margie confirms:

As a direct competitor of Salesforce, Zoho competes differently by using two tactics for its growth. They focus on offering a freemium with all the bells and whistles to help entice customers to switch over to their full suite of products eventually.

For Andy, the “stuff that was miserable” led him to marrying Sharleen, a relationship he describes as “so rock solid that I can have this memory lane conversation with my ex-fiancée, and I know we’re not gonna have a fight about this.”

Looking at the 2019 Forbes Cloud 100 list, we see that over 90% of this list have raised some kind of funding to kickstart their business. This leaves a smaller subsection of startups that have raised no money.

For Andy, the “stuff that was miserable” led him to marrying Sharleen, a relationship he describes as “so rock solid that I can have this memory lane conversation with my ex-fiancée, and I know we’re not gonna have a fight about this.”

Starting off with an older name on the list, Zoho is known as the CRM with everything. Having launched in 1996, Zoho was launched when there weren’t that many software companies in India.

“You put the ‘We’ above the ‘I.’ At a certain point, you’re willing to say, ‘Even though I’m angry, even though I’m hurt, this “We” is the cup that we both drink from, and we want to keep it filled. If I’m vengeful or spiteful, I’m not going to have anything to drink. So let’s keep nourishing this cup.’”

“The importance of the relationship always took precedence over everything else. The relationship is like the queen bee. Nothing else matters. Protect the queen. Even if I was resolute, ‘I am right and she is wrong,’ I was like, ‘Is it really important enough to cause a fracture?’ And it wasn’t. Ever.”

Put the power of your money back in your hands. The most accessible act of rebellion to modern-day consumption that we can engage in on a daily basis is how we choose to spend our cash.

We have some guidance from mathematics. In a 1989 paper, mathematician George Cybenko, then a researcher at the University of Illinois in Urbana, proofed the Universal Approximation Theorem: for any continuous function f, there exists a single-layer neural network that can approximate f arbitrarily well, as long as the activation function of that network is sigmoid-like.

“It was still a very new concept. We thought given the number of software India uses, there must be a huge opportunity. This was the driving force though the product has evolved over the years.” — says Vembu

Even if some of these have done smaller raises down the line, these startups have retained majority control of their own company and have since either been acquired, IPOed, or still going full steam ahead. This list will go through some of the startups that have managed to achieve this.

A lot of these advancements are powered by deep learning, in particular deep neural networks. Yet, the theory behind deep neural networks remains poorly understood. Sure, we understand the math of what individual neurons are doing, but we’re lacking a mathematical theory of the emergent behavior of entire network. What makes deep neural networks so powerful?