Columnist (https://www.newscientist.com/article-type/columnist/) and Mathematics (https://www.newscientist.com/subject/mathematics/) How can you have a proof without proving anything? Mathematicians found a way and, in the process, came to blows over it – but 100 years on, this trick is a common part of modern maths, says columnist Jacob Aron By Jacob Aron (https://www.newscientist.com/author/jacob-aron/) 10 July 2026 https://www.facebook.com/sharer/sharer.php?u=https%3A%2F%2Fwww.newscientist.com%2Farticle%2F2532687-the-sneaky-maths-trick-for-solving-problems-without-answering-them%2Fhttps://twitter.com/share?url=https%3A%2F%2Fwww.newscientist.com%2Farticle%2F2532687-the-sneaky-maths-trick-for-solving-problems-without-answering-them%2Fhttps://api.whatsapp.com/send?text=The%20sneaky%20maths%20trick%20for%20solving%20problems%20without%20answering%20them%20https%3A%2F%2Fwww.newscientist.com%2Farticle%2F2532687-the-sneaky-maths-trick-for-solving-problems-without-answering-them%2Fhttps://www.linkedin.com/sharing/share-offsite/?url=https%3A%2F%2Fwww.newscientist.com%2Farticle%2F2532687-the-sneaky-maths-trick-for-solving-problems-without-answering-them%2Fhttps://reddit.com/submit?url=https%3A%2F%2Fwww.newscientist.com%2Farticle%2F2532687-the-sneaky-maths-trick-for-solving-problems-without-answering-them%2F&title=The%20sneaky%20maths%20trick%20for%20solving%20problems%20without%20answering%20themmailto:?subject=The%20sneaky%20maths%20trick%20for%20solving%20problems%20without%20answering%20them&body=How%20can%20you%20have%20a%20proof%20without%20proving%20anything%3F%20Mathematicians%20found%20a%20way%20and%2C%20in%20the%20process%2C%20came%20to%20blows%20over%20it%20%E2%80%93%20but%20100%20years%20on%2C%20this%20trick%20is%20a%20common%20part%20of%20modern%20maths%2C%20says%20columnist%20Jacob%20Aron%0D%0Aread%20more:%20https%3A%2F%2Fwww.newscientist.com%2Farticle%2F2532687-the-sneaky-maths-trick-for-solving-problems-without-answering-them%2Fhttps://www.newscientist.com/article/2532687-the-sneaky-maths-trick-for-solving-problems-without-answering-them/ How do you prove a proof? Sometimes, you don’t Lucidio Studio, Inc./Getty Images A mathematician opens her office door to find a small fire. Without panicking, she looks around the room and spots a fire extinguisher. “Ah, a solution exists!” she says, before closing the door and continuing on with her day. Simply knowing it is possible to extinguish the fire is proof enough that the problem can be solved – why bother to actually go through the motions to do it? This old joke sums up how a lot of modern mathematics gets done, thanks to a sneaky tactic for problem-solving: the non-constructive proof. More from New Scientist Explore the latest news, articles and features Sign up to our notifications for the latest news and updates. You can disable anytime.