 In mathematical writing, as in other scientific writings, we often use a style that's referred to in Latin as prualis mudestii, which again, this is a Latin phrase here, it basically means plural modesty, okay? What that means is that in mathematics, we actually use the pronouns we and us instead of things like I and me or you, right? We use the plural first person pronoun, we, us, our, we don't use I, me, mine, we don't use you, your, things like that. And why do we do that? Now, be aware in writing, it's very common to use the first person plural pronouns when writing, like for example, there's the example of the editorial we, there's an example of the royal we, in mathematics, the motivation is a little bit different as again, it's this plural modesty, this modest we is what we're using in the situation. And why do we do that? Well, the idea is if I was constantly writing I, I, I, me, me, my, my, it makes it sound very, very possessive, like this is my knowledge, I own mathematics, ha ha ha. Also it might come off as arrogant, like I have proven this. And the hubris can just become an obstacle to reading here. So it just to avoid the arrogance, it can be problematic if you write I and me all the time. On the other hand, though, if I'm constantly writing you, like if I'm using second person pronouns here, I say I'm writing a mathematical proof and I'm like you now see this, that's a little bit presumptuous, right? How do I know what you are understanding? Like I write a good proof, but if you don't understand it, and I'm saying you understand it, but you don't, it's like I don't understand that. You don't know me. You don't know who I am. You know, there's a weird awkwardness going on there as well. So we try to avoid second person pronouns when possible. Some people try to use the words like one, like we could say something like oh, and by this result, one can then see that the statement P is true. You can do that. Avoid some of the awkwardness that I'm supposing that you've understand what I just said now, but still it's informal because you're not referring to anyone specifically. It's just this generic bean who may or may not exist. And it still has a little bit of awkwardness to it as well. Instead, what we can do is by using we and us, because in this situation who are the we equals the author who wrote, but it also includes the reader. And so we can actually think of as when we're writing mathematics that the author and the reader are in the journey together hand in hand where the author is just guiding the reader as they're trying to understand these mathematical principles. And so this tip for writing, I want to present this video is to always use first person plural pronouns. So a bad example would be say something like the following because n equals 2k plus one, I see that n is odd. No, no, no, no, no, don't use I. Instead, we could say something like because n equals 2k plus one, we see that in his odd. We do it together. I, the author, you, the reader, just like with this video here, you'll often be referring to us. We're on this mathematical journey together. And while the author is probably more experienced on the topic being described, the learner, the reader can join with the author in discovering this mathematics together. And so by all means, this idea of pluralist modesty, I think I was mispronounced that, oh well, by the plural modesty here, we do this journey together and actually makes mathematical writing much more inclusive than any other method if I use different schemes to describe pronouns here. All right. And so that does bring us to the end of lecture 23. Thanks for watching. If you learned anything in these videos, please like them, subscribe to the channel to see more videos like this in the future. Share these videos with friends and colleagues so that they can learn about this stuff too. And as always, if you have any questions, feel free to post them in the comments below and I'll be glad to answer them as soon as I can.