Larry Page, a computer science PhD student, submitted a patent for internet search based on an obscure piece of mathematics. The most relevant websites were found more quickly and accurately thanks to the method known as PageRank. The patent was sold in 2005 for more than $1 billion. The net worth of Page's company is over $1tr.
The mathematics described in the patent were created by someone other than Page or Brin. The equation they used is at least 100 years old. Chinese mathematicians used similar methods more than two thousand years ago. Page and Brin realized that by calculating the stationary distribution of a matrix they could find the most popular sites more quickly.
Applying the correct equation can change the world we live in.
The most recent example of a piece of mathematics transforming tech is the PageRank story. In 2015, three engineers used the idea of gradient descent to increase the time viewers spent watching YouTube by 2,000%. The service was transformed from a place we went to for a few funny clips to a major consumer of our viewing time by their equation.
The financial industry has been built on variations of the diffusion equation, attributed to a variety of mathematicians including Einstein. Logistic regression was developed by Sir David Cox in the 50s and is used by professional gamblers to ensure they win.
There is good reason to think that there are more billion-dollar equations out there. Where to look for the next one is the question.
There are a few candidates in mathematical work in the 20th century. One of the ways in which patterns can be self-similar is through the use of fractals, patterns that are repeated on many different levels, like the shape of a broccoli head. There was some excitement about applications that could store data more efficiently after mathematicians developed a comprehensive theory of fractals. A small community of computer scientists started showing how mathematical fractals can produce amazing, weird and wonderful patterns after interest died out.
Chaos theory is a field of mathematics that is looking for a money-making application, like the butterfly effect, in which if a butterfly flaps its wings in the Amazon, we need to know about it in order to predict a storm in the North Atlantic. The theory tells us that in order to accurately predict storms, we need to know about every tiny air disturbance on the planet. It is an impossible task. Chaos theory points towards repeatable patterns. The Lorenz attractor is a model of the weather that produces regular and recognisable patterns despite being chaotic. It may be time to revive these ideas given the uncertainty of the times.
Self-propelled particle models describe movements similar to those of bird flocks and fish schools. I use these models to better coordinate tactical formations in football and to scout players who move in ways that create more space for themselves and their teammates.
Current reinforced random walks capture how ants build trails and the structure of transportation networks. Today's computers have central processing units that make computations and separate memory chips to store information, but this model could take us to new forms of computation in which computation and memory are part of the same process. The new computers would benefit from being distributed. Difficult computational problems could be broken down into smaller sub-problems and solved more quickly.
Whenever there is a breakthrough application of an equation, we see a lot of imitations. The current boom in artificial intelligence is driven by two equations that are put together to create a neural network. History shows that the next big leap forward doesn't come from using the same mathematical trick. It came from a completely new idea, read from the more obscure pages of the book of mathematics.
The challenge of finding the next billion-dollar equation isn't simply knowing every page of the book. Brin was persuaded by Page to help him find the math to solve the problem. You don't need to be a mathematical genius to use the subject. You just need to know what equations can and can't do.
There are many hidden intellectual and financial resources in mathematics. It is up to us to find them. The next billion-dollar equation is being searched for.
The Ten Equations that Rule the World: And How You Can Use Them Too was written by David Sumpter.
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