Timo Math

Hello

This is Timo from Taiwan. Welcome to my personal website. I’m a PhD student studying number theory. This is a place where I share some math content. Hope you find something useful!

Something I Write

Below are some materials written by me. If you have any questions or find some mistakes, please do not hesitate to contact me by email. Feel free to download the whole PDF files!

Expository Papers

• Cyclotomic Polynomial
• Dedekind’s Theorem on Galois Groups and Chebotarev’s Density Theorem
• Liouville’s Theorem on Diophantine Approximation and Liouville Number
• Proofs of the Infinitude of Primes
• Resultant and its Applications
• Special Zeta Values at Positive Even Integers (Classical Case and Function Field Case)
• The Transcendence of $e$
• Visualize the Gaussian Integers

High School Math

• Birthday Problem
• Christmas Stocking Theorem
• Simple Math Puzzles
  1. Covering the Plane with Lines
  2. Shifting Rooms Problem
• Visual Proofs
  1. Determine the Area by Determinant
  2. Pythagorean Theorem
  3. Sum of First $n$ Squares
• When Proofs Go Wrong
  1. Every Triangle is Isosceles
  2. Everyone Has the Same Birthday

Something Interesting

Webpages

• The Evolution of Trust
• Examples of eventual counterexamples
• Poring over Poncelet
• 27 Lines on a Cubic Surface (see here for interactive page)

Videos

• Approximating Irrational Numbers (Duffin-Schaeffer Conjecture) - Numberphile
• 1+1/2+1/3+…+1/n is NEVER an integer when n is bigger than 1
• Why do prime numbers make these spirals? | Dirichlet’s theorem, pi approximations, and more

Photos

• 3D-printed Klein bottle
• 3D-printed Sierpiński pyramid

Quotes

• “What we (mathematicians) do is to invent a language to describe what we discovered.” —Ngô Bảo Châu
• “There are five fundamental operations of mathematics: addition, subtraction, multiplication, division, and modular forms.”—Martin Eichler

Papers

• Proof of the Sheldon Conjecture (free access from the author’s webpage) Carl Pomerance and Chris Spicer. In: The American Mathematical Monthly 126.8 (2019), pp. 688–698.
• The Strong Law of Small Numbers Richard K. Guy. In: The American Mathematical Monthly 95.8 (1988), pp. 697–712.