ESP Biography



HENRY WILLIAMS, Columbia freshman studying CS, math and physics




Major: CS/Physics/Math

College/Employer: Columbia

Year of Graduation: 2022

Picture of Henry Williams

Brief Biographical Sketch:

Not Available.



Past Classes

  (Look at the class archive for more.)


The Foundation Crisis in Mathematics in Splash 2018 (Nov. 17 - 18, 2018)
For centuries, mathematics was considered to be the most stable and deductive reasoning, which gives results with absolute certainty, it was long believed that mathematical knowledge was beyond doubt. But at the end of the 19th century and the beginning of the 20th, several developments shook our faith in the unshakable nature of mathematical reasoning. The emergence of non-Euclidean geometry undermined absolute acceptance of the theory of space and shape that had reigned since classical Greece. Gregor Cantor’s work on the nature of infinity forced us to rethink our sense of numbers. And Kurt Gödel’s incompleteness theorem cast doubt on the possibility of a completely well-grounded notion of mathematical truth. In this class, we will explore the fundamental philosophical uncertainty in mathematics, and hopefully I will convince you that the math you have known and loved your whole life is built on shaky ground. This class will include discussions on the philosophy of math and whether it is grounded in the real world, or own minds, or somewhere far stranger.


Neon Genesis Evangelion: A Dialectic in Splash 2018 (Nov. 17 - 18, 2018)
What is Evangelion? A cult phenomenon 90s anime which ran out of money and ideas? An overhyped robot show that was just a vehicle for a lonely man's insecurities? Or a misunderstood masterpiece of modern culture? In this talk, we will discuss how a strange Japanese cartoon two decades old might have startling implications for your life and the nature of the human spirit. Evangelion is a show about middle-school kids getting in big "robots" and saving the world. It is also a deconstructive subversion of anime itself, a terrifying exploration of the mentality of such child soldiers and the fundamental brokenness of human relationships. Expect to leave singing the words "come, sweet death."


A Headfirst Dive Into "Mathematical Logic" in Splash 2018 (Nov. 17 - 18, 2018)
The meaning of term "Mathematical Logic" is fairly non-trivial. Mathematical logic is, on the one hand, the study of the logic of mathematics rigorizing the notions of "proof" and "example" in the framework of formal logic. But Mathematical logic is also the application of mathematical methods to logic using tools such as induction and set theory to proof meta-theorems about logic. It is even the application of logic to solving (somewhat) concrete math problems. In this course we will discuss all these flavors of mathematical logic as we introduce the basic concepts of completeness, consistency, satisfiability, and categoricity, discuss foundational results linking model theory (the study of examples) to proof theory (the study of formal proofs), then investigate the limitations of first-order logic, and finally prove Godel's momentous incompleteness theorem of first-order arithmetic. On the way, we will naturally develop foundational ideas about the theory of computation and how decidability and incompleteness are intricately linked. Time permitting, we will discuss applications of mathematical logic to problems in algebraic geometry such as the Ax-Grothendieck theorem and Lefschetz principle.


A Rigorous Development of Classical Mechanics in Splash 2018 (Nov. 17 - 18, 2018)
This class will discuss classical mechanics from a fairly abstract perspective. We will first introduce the Lagrangian formalism and discuss the principle of least action, its motivation, and its consequences. Next, using the Lagrangian perspective, we will develop the Hamiltonian framework which elegantly formalizes and extends the notions of momentum and energy. From there, we will discuss the theory of canonical transformations leading to Hamilton-Jacobi theory. If time permits, we will investigate advanced topics such as adiabatic invariants and show how Hamilton-Jacobi theory is the "ray-optics approximation" to the Schrodinger equation and how this insight lead Schrodinger to develop quantum theory. Along the way, we will discuss Noether's theorem on the connection between symmetries and conservation laws from each of these perspectives since each one gives their own flavor to this wonderful theorem.


A Treatise on the Modern Meme in Splash 2018 (Nov. 17 - 18, 2018)
To meme or not to meme, that is the question: Whether ‘tis nobler in the Sub to repost The gifs and jokes of yester year Or to create OC against the sea of reposts And in downvoting end them. To OC–to post; To post perchance to meme–ay there’s the sub, For in that post of OC what memes may come, When we have shuffled off this bottom text, Must give us pause–But that the dread of spici’r OC, That undiscover’d board, for whose born no memelord returns, puzzles the will, And makes us rather post the memes we have Than create others we not of? Thus Four Chan doth make normies of us all.


Casual Conversation on Concurrency in Splash 2018 (Nov. 17 - 18, 2018)
You and your homies are given a group project so you split up the work into tasks and let each person pick what they want. The due date arrives and your group unveils their masterpiece. But pride turns to horror when you realize that everybody chose the same task! Sound familiar? Well ... no ... not to me either. Come for a casual introduction to how computers know how "not to be that guy" by managing parallel operations and concurrent execution.