I want to talk about this. I know that YouTube has auto-generated captions if the uploaded video is in English. It would be so much more useful if they can also generate captions for other languages, for example, Filipino. Like that would be awesome. This post is actually generated from an audio file that I uploaded on youtube which I edited afterwards.
Anyway, this is the plan. It's really... I'm having a hard time just being spontaneous. I have a huge filter and I just can't spit things out. One other option is to write on the phone. But that's actually hard because the tactile feedback from typing with a physical keyboard is not there. It's hard. Talking is much more spontaneous. I overthink less when talking.
I've been wanting to post a tutorial video about proving. I missed proving so much. Say you know what you're trying to prove so you start with the given, right? You start with what you know based on the definitions. Then you come up with implications. From there you connect the dots.
So proving is like connecting the dots.
It's actually fun because you start from zero then you build up your case just like a lawyer does. You build up your arguments until you arrive at your "destination"
But it's really not that easy. Sometimes it's not straightforward. If you're a student, the professor gives the statement and you simply provide a proof. But when you're a researcher, it's actually your job to come up with conjectures. A conjecture is a statement that you think is right based on the patterns that you observe. You try a lot of examples then you check if it applies to other structures as well. You may use a software to check all the cases, if possible.
You have to make sure that your "guess" is not only applicable to a few examples. I know this does not really make sense because I'm talking in general. It would be awesome if I could give a specific example. Next time, I promise.
The point is that math is not only a science, it's an art. The common idea is that in math there is only one correct answer. And for the most part, that's true. Because, well, it's already been solved before. The author has already solved that problem before he included it in his book. But where's the fun in that? I think what's more fun is figuring out whether a statement is correct or not by trying out as many examples as possible. Then coming up with a conjecture and eventually proving it.
That's the fun part!
Although I should warn. Some conjectures are yet to be proven or disproven. See the Millennium Prize Problems, for example.
Anyway, this is the plan. It's really... I'm having a hard time just being spontaneous. I have a huge filter and I just can't spit things out. One other option is to write on the phone. But that's actually hard because the tactile feedback from typing with a physical keyboard is not there. It's hard. Talking is much more spontaneous. I overthink less when talking.
I've been wanting to post a tutorial video about proving. I missed proving so much. Say you know what you're trying to prove so you start with the given, right? You start with what you know based on the definitions. Then you come up with implications. From there you connect the dots.
So proving is like connecting the dots.
It's actually fun because you start from zero then you build up your case just like a lawyer does. You build up your arguments until you arrive at your "destination"
But it's really not that easy. Sometimes it's not straightforward. If you're a student, the professor gives the statement and you simply provide a proof. But when you're a researcher, it's actually your job to come up with conjectures. A conjecture is a statement that you think is right based on the patterns that you observe. You try a lot of examples then you check if it applies to other structures as well. You may use a software to check all the cases, if possible.
You have to make sure that your "guess" is not only applicable to a few examples. I know this does not really make sense because I'm talking in general. It would be awesome if I could give a specific example. Next time, I promise.
The point is that math is not only a science, it's an art. The common idea is that in math there is only one correct answer. And for the most part, that's true. Because, well, it's already been solved before. The author has already solved that problem before he included it in his book. But where's the fun in that? I think what's more fun is figuring out whether a statement is correct or not by trying out as many examples as possible. Then coming up with a conjecture and eventually proving it.
That's the fun part!
Although I should warn. Some conjectures are yet to be proven or disproven. See the Millennium Prize Problems, for example.
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