Prove that pi
is greater than 3.05.
A legendary exam problem, just one line long. Now that you're grown up — how would you solve it?
That problem you couldn't solve —try it once more.Math, as a liberal art.
There's no need to rush to the answer. On the train to work, in the quiet before sleep. Time spent with a single problem is the finest kind of learning. Infinite Math is a book of math problems, made for grown-ups.
Take on the legendary problems
of Japan's top universities.
“Is tan 1° rational?” “Prove that pi is greater than 3.05.” Problems that have been talked about for decades. Now it's your turn.
From university exams
to elementary school.
Good problems at every level across six categories: number theory, classic problems, and elementary, junior-high, high-school and university entrance exams. With a daily problem and five-problem sessions, it's perfect for relearning.
It doesn't end
with the answer.
Every problem comes with an explanation of the background and the thinking. For Pick's theorem or the bridges of Königsberg, touch the figure and see the “why” for yourself.
Get a pen
and some paper.
One problem from the app. Choose an answer and the explanation opens.
A Job Done by Two
A certain job takes A exactly 12 days alone and B exactly 4 days alone. If they do it together, in how many days will it be finished?
- IIs Pi Greater Than 3.05?Univ. of Tokyo
- IIIs tan 1° Rational?Kyoto Univ.
- IIICranes and TurtlesClassic
- IVThe Monty Hall ProblemProbability
- VThe Birthday ParadoxProbability
- VITower of HanoiClassic
83 problems in all, with more on the way
Frequently asked questions
How much does it cost?
It's free, and every problem is included. A banner ad is shown at the bottom of the screen.
What kinds of problems are there?
83 problems (as of October 2026, with more added over time) in six categories: number theory and puzzles, classic problems, and elementary, junior-high, high-school and university entrance exams — from cranes and turtles and the Monty Hall problem to the legendary exams of the Universities of Tokyo and Kyoto.
Can I enjoy it if I'm not good at math?
Yes. You just pick an answer from the choices, and every problem has an explanation of the background and the thinking behind it. Difficulty is shown with stars, from easy to very hard.
What should I do each day?
Take on the “Daily Problem,” a new one every day. When you want more, try a “Session” of five problems. Solved problems are recorded so you can aim to clear them all.
Which languages are supported?
19 languages, including English, Japanese, Chinese and Korean. The problems and explanations are translated too.
Is it available on Android?
Yes, it's on Google Play. It runs on iPhone with iOS 17 or later and on Android 8.0 or later.
Math, once more —
as a liberal art.
Infinite Math — math for curious grown-ups