and one of the things I'm in love with is not just mathematics my title actually is professor of applied mathematics and that word applied has has two meanings there's the 20th century meaning and 20th century meaning is applications has always been what Boeing would want you know let's let's use mathematics for an engineer to to build airplane design or submarine structures or or build buildings so mathematics has been applied using the tools of sines and cosines and functions for engineers and scientists and physicists so Einstein uses the mathematics and it's applied math but you know this amazing shift has happened in the 21st century in 21st century applied mathematics is no longer about subject it's not about differential equations or calculus it turns out every math you could ever imagine is applied math so if you care about numbers turns out that almost everywhere that numbers are multiplied together and factored into pieces is how data is encrypted when you swipe through a Visa card so the National Security Agency NSA they hire mostly math PhDs or number theorists number theory turns out to be useful for for people anywhere in the world today if you care about issues of chance and probability like how often do I get heads or tails in a simple coin toss or rolling dice it turns out that's the foundation of how you do prediction analysis for business you want to model these things because you have so much data coming in that you can't get anything 100% right so now data is almost going to be approximated you'd be happy to be 95% sure 90% sure something is gonna work because you have terabytes of data coming to you per second so now all of a sudden things that were known for probability turns out to be applied if you care about patterns of how molecules are organized and the structures and shapes of a rubik's cube for example turns out that's the foundation for quantum mechanic issues and foundations for chemistry so there's that almost every mathematical idea that you can think of turns out to be applied even from number theoretic 'el stuff and and what I care about is shape and a revolution happened related recently to the kind of shape I care about which is not geometric shape which talks about spheres and angles but topological shape and topology just means take off your classes if you take your glasses up how does the world look it looks fuzzy and then you roughly get the idea their shape but you don't get it perfectly and and it turns out there's and at Stanford there's a faculty named professor named Gunnar Carlson who I worked with and he was one of the founders of this field called topological data analysis so what he does is he looks at data and he takes up his glasses and he sees the data approximately in a fuzzy way and he's able to tell you what the overall shape of the data is in a fuzzy setting not on a perfect angular measurement setting but in a fuzzy setting and that helps a lot because most of the data that we get have noise in it all right no data that's coming to us is perfect a lot of people when they fill out their forms and you're watching Netflix and you're giving Netflix data if you're giving data from Amazon or Apple you don't fill out all the all the fields so they don't know everything about you there's all these holes missing and that that data has noise because you might maybe fill one or two things incorrectly so the fact you can take off your glasses and get a rough approximation of what's really going on is beautiful so using topological data analysis you could immediately tell whether you're normal or have type 1 or type 2 diabetes' really quickly you can quickly see that there are these three branches going on you're gonna fit in one of those things you don't need to know the exact geometry but that rough topology is really good so everything is applied that's why I love it