“Theory” vs. “Theorem” – Difference Explained (8 Helpful Examples)

The words “theory” and “theorem” sound very similar to one another. And they are often used in similar fields, but what exactly is the difference between the two of them? In this article, we’ll analyse what separates the two, and what are some examples of each of them.

What Is The Difference Between “Theory” And “Theorem”?

A theory is a statement that is not 100% guaranteed to be true, however, there is enough evidence to justify believing it to be so. A Theorem is a statement that can be proved using axioms- like a mathematical formula.

For example, we have the THEORY of evolution. But Pythagoras THEOREM.

What Is The Difference Between "Theory" And "Theorem”?

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Theory

What Is A Theory?

When you hear the word “theory”, it can make people feel rather passionate, with phrases such as “that’s only a theory”. And yes, a theory is a statement that is not entirely guaranteed to be true. However, for a statement to become a theory, there does need to be some kind of evidence.

Some theories, such as evolution, are very difficult to prove. Due to our lack of time travel. However, the evidence from fossils and the consent of the scientific community is proof enough that it’s an idea that should be taken seriously.

A theory that is lacking in evidence is a hypothesis.

Hypothesis Vs Theory Vs Law – Difference Explained

In science, there are three common terms that some people get mixed up. These terms are “hypothesis”, “theory”, and “law”. Let me illustrate with an example.

Let’s say you’re on a walk and your metal detector finds a box, and within it is an old-looking photograph of Winston Churchill talking to Hitler. You might come up with a hypothesis that Churchill tried to stop the war via negotiations.

If you give the evidence to historians, they might gather more evidence, and agree. This then becomes a theory.

If you then invent a time machine and travel to find the theory to be true, you could call it a fact. In science, “facts” are sometimes called “laws”.

“In Theory” – What The Common Idiom Means

One phrase that you might have heard is “in theory”. This is not completely in line with the scientific use of the word, yet it does merge into it.

When someone says “in theory”, they refer to what should be but probably isn’t. For example, if I’m waiting for a bus, I might say “In theory, the bus will be here in 5 minutes. But knowing the current system, it will probably be closer to ten”.

Examples Of Popular Theories

Let’s take a look at some common theories that you might be familiar with.

  • Black Holes

Nobody has ever seen one in real life, they’d be dead if they did. But black holes are tears in a space that suck everything into them, including light.

  • Evolution

To put it bluntly, evolution is the idea that we evolved from apes to become human. It states that all living things started as microorganisms.

  • Relativity

Einstein’s theory that time moves slower if you move faster.

  • Gravity

The concept that gravity is part of the earth, and it’s the reason why things fall to the centre when you drop them.

4 Sentences That Use The Word “Theory”

  1. “I am a Christian, but I still think the theory of evolution still holds true. I can’t accept that all of that evidence is for nothing”

  2. “I have a theory that my brother is scared of cats and that’s why he doesn’t want to come round my house. But I might be wrong?”

  3. “Scientists are coming up with a new theory about why our skin starts to wrinkle when we get older. If their research goes well, they could end up finding a cure for ageing

  4. “The police had a theory about who killed all those people. But there was still not enough evidence for a conviction”.

Theorem

What Is A Theorem?

A theorem might sound similar to a theory, however, the two are unrelated.

A theorem is a fact proved via a chain of reasoning. When you combine arguments to come to a conclusion, the final conclusion is a theorem. IF all of the facts in the argument are true, then the theorem must also be true. However, as we’ll see later, whether the facts are true or not can be disputed.

A quick example of a theorem….

  • Each person will want 2 cans of coke at the party.
  • 5 people are coming to the party tomorrow.
  • 2 times 5 is 10
  • Therefore, I will need 10 cans of coke for the party tomorrow.

4 Sentences That Use The Word “Theorem”

  1. “When I was at school, I remember learning all about Pythagoras theorem. It was incredibly dull, but now that I’m an adult, I’m glad I learnt about it”

  2. “I started believing in God when I looked at Descartes Ontological Theorem. It just all clicked into place and started to make sense to me once I had finished reading his work”

  3. “All mathematics is just a string of philosophical theorems. Unlike other forms of philosophy however, there is no way we can question mathematics”

  4. “My maths teacher tried to teach us this new theorem that he had discovered. But we didn’t understand it because we were all twelve”.

Examples Of Common Theorems

And now, here are three theorems that you may be familiar with.

Pythagoras Theorem

a2+b2=c2

This is the idea that if you make squares from all three sides of a right-angled triangle, the area of the two shorter sides will add up to the area of the longest side.

Descartes Ontological Theorem.

God is perfect. Existence is better than non-existence. Therefore God exists.

The area of a circle.

Take the length from the middle of the circle to the edge and square it. Multiply that number by pi. And you have the area of the circle.

Conclusion

And that is the difference between a theory and a theorem. Hopefully, now you have a slightly better idea about how the two are separate and next time you need to, you’ll know which phrase to use.

As a general rule of thumb, science tends to prefer theories. However, mathematics tends to prefer theorems. But there are plenty of examples that break this rule.

The question you need to ask yourself is “have I deduced this from other facts? Or have I seen evidence towards this fact?”