Give a Counterexample

Have you noticed that disputes are often unconstructive, and the winner is the one who shouted louder or expressed themselves more assertively? But if we apply the laws of logic to our arguments, any disagreement can be resolved smoothly and elegantly. In mathematics, this technique has been honed to perfection.

Let’s start with a simple example. We often try to convey a certain message to the other person, but it can be challenging to do so. That’s when we resort to examples. We may say, “Women are capable of playing chess just as well as men. For example, the Hungarian chess player Judit Polgar won against the leading grandmasters and for a long time was ranked in the top ten of the world’s chess players.” If it were not for the specific example, the other person could easily answer: “No, I think otherwise.” But you have to agree that your argument sounds a lot more convincing when you back it up with an example.

A woman wearing a pink shirt.

Now consider a different scenario: your friend tells you that all soccer players are blond. How can you prove them wrong? The most sensible thing to do is provide a counterexample. Why? Because a single counterexample outweighs a thousand examples in favor of the original argument. 

Your friend may list dozens of blond soccer players, but you put an end to the dispute once you mention, for instance, the dark-haired Lionel Messi. Similarly, counterexamples hold a special place in solving mathematical problems. Do you still have doubts? We will prove you wrong.

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