Writing is thinking distilled.
Writing necessitates vocalizing thoughts. Thoughts that may not be fully formed, in the sense of there perhaps being some dangling ends that you were unaware of. It’s awfully similar to actually doing things, as opposed to merely fantasizing about them. I think writing is to thinking the same as working out a math problem is to going to lecture. Sure, going to lecture can be helpful, but it is rare to be able to ace a midterm solely by going to class and listening to someone speak.
It’s similar to actually starting a company as opposed to signing up to go to yet another entrepreneurship workshop.
Writing often forces you to get into the nitty-gritty under the aegis of telling a story with no inconsistencies. It forces you to understand what you are trying to explain. This ties into why students are often encouraged to teach concepts to peers - time and again, vocalizing your thoughts has been shown to be an effective way of reinforcing understanding. Good thinking doesn’t happen by passive osmosis of other people’s good thinking, Alexey Guzey says. Good thinking is what makes people valuable, and in addition, it makes you look cool. There’s no reason to not want to be a good thinker.
Write about something you just learnt, when it is fresh in your mind, to prove to yourself that you understand whatever microaspect of the larger problem you are dealing with. By understand, I mean as close to objectively understand as possible. You would be completely okay with standing up on stage in front of a crowd of professors to give a short speech on the topic.
Write about things you feel shaky with. Write to create a strong foundation for yourself. This is the rationale behind my algorithms guide. In addition to practicing, documenting ideas that are new to you could only serve to help.
Write about ideas you have that you would like to test out in the real world. Regardless of why you feel that urge.
Write to get better at writing. Getting better at writing will force you to stop fooling yourself when you don’t understand something.
Write with consistency to force yourself to learn new ideas, new things to write about.
According to Alexey’s blog post about blog posts, which I highly recommend, a good question to ask yourself about your writing is would you save the post that you wrote to Evernote/whatevernote if you randomly stumbled upon it on the internet? I think that is poignant. Write in a way that is useful to people. Write in a way that you would find useful. Similar to what is often a rule of thumb for innovation - write for yourself. Write the posts you wish existed.