A Treasure Trove of Mathematics Websites

I would like to recommend a website for learning mathematics: Project Euler.

Named after Euler himself, this site clearly isn’t ordinary. It hosts thousands of math problems, from easy to highly challenging, with new problems published every week (all following the Project Euler style). Every problem requires computer programming to solve, appealing to those who have an interest in both mathematics and coding. It’s perfect for students whose curiosity isn’t satisfied by basic coursework, adults whose careers are not primarily math-related but who have an interest in the subject, and professionals who want to keep their problem-solving skills and mathematics proficiency at the cutting edge.

Founded in 2001, the site now boasts over one million registered users from every country worldwide. There are no restrictions on programming languages for solving problems—users have collectively employed 113 different programming languages to tackle these math challenges.

Interestingly, to register as a member, you must first solve a relatively simple math problem. Only after submitting the correct answer can you complete the registration. Incorrect answers will prevent registration.

If a number is the square of a positive integer, it is called a perfect square or simply a square number. For example, 25 is a square number because 5² = 5 × 5 = 25, and it is also an odd square number.

The first five square numbers are: 1, 4, 9, 16, 25. The sum of the odd square numbers among them is 1 + 9 + 25 = 35.

Here’s the problem: What is the sum of all odd square numbers among the first 932,000 square numbers?

This problem is quite simple—typical of high school math competitions—and can be solved using a summation formula. However, manually calculating it by hand is practically impossible to get right; programming is essential. Of course, programming is a mandatory requirement for registration on this site since every other problem depends on computational methods. We won’t provide the answer here, but as a hint, the correct answer has 18 digits.

The site does not recommend using AI to answer these problems because the development of skills comes through the process of solving them. Having AI directly provide the solution would render the site meaningless. Moreover, the website has an automated detection system: if it detects AI-assisted answers, similar to platforms like Zhihu, it will mark the answer with a “Cheating” label and may permanently ban the user.

Once registered, users can also view other members’ solutions to the problems; without registration, only the problems themselves are accessible.

Website: Project Euler