Fields Medal: June Huh

[Music] in mathematics you want to know what is true and why it's true it's often hard to go straight from where you are to where you want to go [Music] each one of us has to find our own way the boundary between knowing and not knowing is so clear in mathematics you can almost see this mysterious region that our brain secretly operates if you think about something long enough you cross that line of understanding [Music] when i was young math was like a far away land surrounded by giant walls that i could not climb i

grew up in korea and i dreamed of becoming a poet to express the inexpressible [Music] i eventually learned that mathematics is a way of doing that now i am a professor of mathematics at princeton university i do research in combinatorics my way was to build spaces from combinatorial objects once you have a space to move around you can use your geometric intuition to extract information hidden in the original combinatorial structure a good example of my work is the proof of the darling wilson conjecture that's an old question and the easy special case of it is

the following problem in plain geometry take a finite set of points on a plane and connect every pair of points by a line do we always get at least as many lines as points dowling and wilson predicted that the answer is yes for points in an arbitrary dimension comparing the number of planes of a given dimension with that of a complementary dimension connected by part of the initial point set the conjecture can be formulated purely in the realm of discrete mathematics but it's hard to prove within that same realm so my collaborators and i imagine

the space whose geometry untangles that difficulty this imagine space has properties that are very similar to spaces that are familiar and more visible to us and those properties allowed us to answer the original question using a totally different type of intuition this is what happened in the case of road dust conjecture and darling wilson's conjecture and to a large extent mason's conjecture [Music] i construct and analyze and wander in the geometric realm of my imagination and when it becomes three o'clock i go to pick up my kids from the elementary school [Music] it really wakes

me up my wife naong is the most important person in my life she's my friend and companion and sometimes a teacher she's always there for us my older son dan we do a little bit of math together is it 30 yep can i start here no you're not done yet he enjoys posing problems and watching other people solve them it's like a puzzle and there's great joy in it high five okay my younger son sol he just started walking [Music] after dinner we change into our pajamas and go to bed [Music] and then we repeat

the whole thing [Music] there is beauty in this repetition [Music] we are truly very lucky princeton is one of the best towns in the world to be a mathematician and it's a peaceful place to raise our children every one of my works could not have been done without the help and influence of my collaborators being a part of a giant network of very good people gives me the freedom that i could not imagine before i became a mathematician on clear days i can see that i'm a small and simple part of a big and complex

ancient structure in some mysterious way we are connected to each other and we grow from that connection you