ESP Biography

ÁLVARO DÍAZ RAMOS, Aspiring researcher studying math and philosophy.

Major: Mathematics, Philosophy

College/Employer: Stanford

Year of Graduation: 2026

Brief Biographical Sketch:

Álvaro Díaz Ramos is a senior studying mathematics and philosophy at Stanford University. He has conducted research in model theory and set theory at UCLA and the Hebrew University of Jerusalem, and after graduation, plans to pursue a PhD in mathematics focusing on set theory. He is interested in ontology and the foundations of mathematics, and has previously worked on stability theory and order theory. In his free time, he likes to read, travel, do pull-ups, and listen to reggaeton. Fun fact: he holds citizenship in three countries!

In 2025-2026, Álvaro serves as a member of Splash leadership.

Past Classes

(Clicking a class title will bring you to the course's section of the corresponding course catalog)

X8241: Mathematical Abstraction in Splash Fall 2025 (Nov. 15 - 16, 2025)

In this semi-philosophical, semi-mathematical course, you will learn about what exactly mathematicians spend their days doing. I will discuss the well-known concept of "abstraction", and illustrate how all of mathematics emerges as a result of looking at the world around us and abstracting away!

M8160: An Introduction to Modern Infinity: Transfinite Numbers and the Strange Arithmetic of Linear Orders in Splash Spring 2025 (May. 24 - 25, 2025)

This class will introduce two modern approaches to formalizing the concept of infinity in mathematics. We will first explore ordinal numbers through the framework of axiomatic set theory, then move on to Conway’s surreal numbers. Along the way, we’ll explore the counterintuitive arithmetic of linear orders. Throughout the class, we will see how new and classic paradoxes of infinity reappear in these novel settings.