Euler’s Eyes is a free mathematics website, run independently since 2021. Its goal is simple: to explain mathematics step by step, from the basics to olympiad level, for people who are learning, with no sign-up and no payment.

What you will find here

  • History of Mathematics: the lives of the great mathematicians and the ideas they left behind, derived step by step, from Archimedes to Turing.
  • Mathematics for children: natural numbers, fractions, decimals and geometry, explained as simply as possible.
  • Pure mathematics: sets, relations and the foundations that hold up everything else.
  • Solved exams: OBMEP, ENEM, FUVEST and ITA (Brazilian olympiad and university entrance exams), question by question.
  • Interactive books: Trigonometry and The Semiotics of Mathematical Notation, with figures you can manipulate.
  • Study materials: solved exams as PDFs, to print and study offline.

All content is available in Portuguese, English, Japanese and Chinese. The site can also be used through the Euler Eyes app for Android.

Who writes it

The site is written and maintained by Hiro Watanabe. The texts, solutions and interactive books are original work. Everything is written first in Portuguese; the versions in other languages are translations.

How the content is made

  • Exam solutions are checked against the official answer key published by each exam board. Questions are reproduced with the exam and year indicated, for educational purposes.
  • Historical images and photographs come from Wikimedia Commons. Each chapter ends with credits for the images it uses.
  • Found a mistake? Write to us through the Contact page and include the page address. Corrections are made directly in the text.

Why “Euler’s Eyes”?

Leonhard Euler (1707–1783) lost almost all sight in his right eye around 1738 and, years later, developed a cataract in his left eye. Nearly blind, he kept working: about half of his work was written after that, often dictated from memory. The site’s name is a tribute to that way of seeing mathematics: clearly, even when the eyes fail.

How the site is funded

Euler’s Eyes is free and will stay free. Hosting costs are covered by Google AdSense ads and by voluntary support. Ads have no influence on what is published. The Privacy Policy explains what data the ads use and how to opt out of personalised ads.