A Very Brief History of Very Large Numbers

What is the largest number of which you can conceive? This question has driven Greek mathematician Archimedes at a computer terminal.mathematicians and scientists for millennia, challenging the greatest minds of every era. In ancient India, a sacred text called the Yajurveda from around 1000 BCE named numbers based on the power of ten up to a quadrillion, or 1012. Building on these numbers, the Lalitavistana Sutra expanded these conventions up to a much larger number, 10421. In writings about the Buddha, Siddhartha Gautama, there is a famous story of him expressing his own mathematical abilities by naming all of the powers of ten up to 1053 in a competition with renowned mathematician Arjuna.

In Ancient Greece, the way that scholars described large numbers was by using powers of 10,000, a number that they called a “myriad.” Using this notation, Archimedes was able to describe numbers up to 1064, or a myriad myriad to the myriad myriadith power, in his work The Sand Reckoner. This system persisted into the Roman Era, with ancient Romans describing the number one million as,”decies centena milia,” or ten hundred thousand. The term million was invented around the 13th century, by combining the Italian word for a thousand, “mille,” with a suffix “ion” meaning to square the number.

In modern mathematics, scholars have been able to define very large numbers, the most famous of which may be the googolplex. A googolplex can be expressed as the decimal 1 followed by 10100 zeroes, a number that cannot be written. In “Cosmos: A Personal Voyage,” famed astronomer and mathematician Carl Sagan describes a googolplex in a spatial method that puts it in context. He proposed that if the observable universe is filled with particles that are 1.5 micrometers in diameter, a googolplex would represent all of the possible combinations to number and arrange all of those particles. This number would be much larger than the estimated number of atoms in the known universe which is thought to be around 1080.

All of these examples make it clear that humankind has long been fascinated with the idea of very large numbers, and the development of computing has had this idea at its core since the days of Ada Lovelace and Charles Babbage’s early computers. Lovelace’s “Analytical Engine” design would provide a method for the computation of the sums of the first n numbers, sometimes known as “Bernoulli numbers”, including their squares and cubes. This calculation was built on years of theoretical mathematics advanced by mathematicians such as Pythagoras, Takakazu, Archimedes, Aryabhata, and Abu Bakr al-Karaji, and launched the development of the modern computer as we know it today. 

As POLARISqb has developed our system for optimizing and searching large chemical libraries, the increased capabilities of quantum computing have led to some very large numbers of our own. Early in our company’s history, it was clear that we were dealing with numbers that were outstripping some very famous large numbers such as Avogadro’s Constant, which is 6.022 x 1023. Today scientists at our company are confident in saying that we are able to research up to 1030 distinct molecules, or one nonillion combinations, based on our fragment-based system and the abilities of quantum annealing computers to optimize very large combinatorial calculations. 

Why do we need to have so many molecules? After researchers find a druggable protein, the next step is to find a set of molecules that binds to the protein binding pocket. The more molecules included in the starting library of molecule candidates, the better the chance that one of them will become a drug. In the past, researchers were limited by computing power to look at only small libraries, making the process of finding preclinical candidates slower and more expensive. However, using QuADD on a quantum computer, researchers at POLARISqb are able to build and search this massive chemical space in less than a minute, rather than a matter of months or years. This kind of optimization holds the promise of accelerating drug discovery timelines by orders of magnitude for chemists around the globe, opening new doors that may lead to treatments and cures for diseases that affect billions.