The general rule used in English when making the comparative form of an adjective is to add the suffix –er to the base form for adjectives with one or two syllables, while you add more before the adjective when it has three or more syllables. So, because simple is composed of two syllables, the proper comparative form would be simpler.
The grammar rules of English are simpler than I thought! ✔
This sentence is grammatically correct and simpler was used properly. But, the beauty of the English language is that it often doesn’t follow its own rules! The word simple is one such case. It is used less commonly, but more simple is also correct, as can be seen in Oxford Learner’s Dictionary.
I thought English grammar was more simple when I first started learning it. ✔
To sum up, you can use both simpler and more simple freely.
Find me a simpler solution. ✔
Find me a more simple solution. ✔
However, if you are writing in an official capacity, try to use simpler. Because more simple is a non-standard form (even Microsoft Word will underline it as grammatically incorrect), people may not have come across it and can perceive it as incorrect. Explaining to your boss or clients that simpler and more simple are equally as valid is an unnecessary task that you can avoid by using the former.
A Couple of Additional Things to Look Out For
Regardless of whether you will be using simpler or more simple in your writing, there are a few additional things you should look out for, both from a grammatical and stylistic perspective.
You should be consistent in your texts, so, if you started out with simpler, use that form until the end. The same goes for more simple. This is also true for the superlative forms you use. You form a superlative by adding the suffix –est to the base, or most before the adjective, and the article the. Thus, you either get the simplest or the most simple.
If the comparative form you are using is simpler, the superlative is the simplest. For more simple, the superlative is the most simple. This is a stylistic choice, but your writing will be better if you stay consistent. Thus:
Running is simpler than walking, but crawling is the most simple. ✘
Basic trig is simpler than advanced trig, but counting is the simplest. ✔
Basic trig is more simple than advanced trig, but counting is the most simple. ✔
Both the suffixes –er and –est, and the words more and most are intensifiers; they should not be used together in the same phrase.
A browser game is more simpler than a regular computer game. ✘
Making coffee is the most simplest thing ever! ✘
Although, if you do make this mistake, you will be in good company. In Shakespeare’s play Julius Caesar, Marc Anthony says: “This was the most unkindest cut of all.” Still, maybe avoid intentionally breaking the double intensifier rule until you’ve written one or two world-renowned plays yourself. Once you have, don’t forget to mention us in the acknowledgments. Good luck with your writing!