The difference between what you gave and what they did is you used different words in the definition from the description. They literally just use the same word

The difference between what you gave and what they did is you used different words in the definition from the description. They literally just use the same words in the name as in the definition. Their statement in your terms would be more like, "Mathematical Physics is a method of exploring the world of physics by means of modern mathematics," which is a useless statement. By no means am I saying this field is worthless or a scam, I'm just saying those definitions are completely useless and circular.