How We Use Number Theory and Non-Euclidean Geometry In Medicine

We’d like to talk about data privacy, how WellAI is applying Number Theory and non-Euclidean geometry, and why they are so important in medicine.


For medical data privacy, blockchain technology is the best technology out there.  At WellAI, we are fortunate to have some of the original blockchain mathematicians.  That’s something we are very proud of.


In our ongoing educational series, Daniel Satchkov, head of machine learning at WellAI, explains why Number Theory and non-Euclidean Geometry are essential in medicine.




Let’s first explain why Number Theory is important in blockchain and bitcoin.


In the decentralized blockchain, everyone holds her own keys.  In bitcoin, if you lose your key, your money is gone.  But that could be fixed.  It’s not the biggest problem.


But the big advantage is that you have your private keys.  Moreover, your private keys don’t have to be tied to your identity.


Some people think blockchain is anonymous.  That’s not true.  It is pseudonymous meaning you can create the key, and every action of that key would be connected.


Blockchain private keys are related to Number Theory.  Number Theory deals with very-very large numbers, numbers not found anywhere in this universe.  The universe is huge.  But these numbers are much much larger.


You don’t need a central authority to create a bitcoin account.  There is no central authority in bitcoin.  You create your own key.  A bitcoin key is just a set of random numbers.  You are your own authority.


But if everyone is independently generating a bitcoin key what is the chance that two people may have the same key, and then someone may get access to someone else’s money?  Yes, strictly speaking, it’s possible.  In Meta, for example, there is a central authority, an IT department that makes sure no two accounts are the same.


But Number Theory deals with such big numbers that for all practical purposes it’s impossible for two people to randomly generate the same numbers.


Blockchain keys are a remarkable achievement of humankind.  Something that humans did for centuries for fun all of a sudden has this amazing application.


There are also some interesting applications in geometry.  The Russian mathematician Nikolai Lobachevsky, along with the Hungarian Janos Bolyai came up with non-Euclidean geometry.  In Non-Euclidean geometry parallel lines do cross.  At that time every scientist in the world was laughing at Lobachevsky and Bolyai.  But then the 20th century came along, and with space exploration non-Euclidean geometry became critical.


A field of medicine that cannot exist without non-Euclidean geometry is genomics.  A lot of genetic structures are best described with non-Euclidean geometry.


We are at the very beginning of understanding applications of mathematics and data science in medicine and other fields of life!


Stay healthy!  Stay knowledgeable about your health.


WellAI Team

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