Change the World

The world needs you. Really. Let's join forces and bring a truly customized interactive education to everyone on the planet!

Worst case: you'll gain a deeper understanding of the topics you think you know by explaining them.

Better (and more likely) case: Worst case + you'll help at least one other person understand a topic that they would not have otherwise.

Best case: Use your imagination :)

Lemma: The world needs change.

Proof. Say, for sake of contradiction, that the world did not need change. Let us say the health of the world is defined by a function $h(t)$, where $t$ represents the age of the world. By our assumption, $h'(t)$ is unnecessary. This means that $h'(0)$ is unnecessary, but $h'(0)$ is a real number and all real numbers are necessary. Hence, we have a contradiction. $\Box$

Let's change the world!

Websites like Expii are designed as vessels for giving back to the academic community, to allow people to continue learning and passing down knowledge to more eager students. In an ideal world this system would go on forever. You can contribute to the content base and/or use Expii to learn material independently or as a supplement for a class. Either way you are helping make the community of intellectuals stronger, so help out in whatever way you can!

What We Do

There are billions of children without any exposure to math. Of these, you must agree that many of them, if not all, have some sort of potential in problem-solving. There are millions of children stuck in a public school setting following standards unsuited for the appreciation of math. There are many others who have received a glimpse of what math can be like. The hopefuls - they are Ramanujans waiting for their Hardy, or some, waiting for a teacher to come along. And then there's us.

We need to give back to the world for these countless opportunities. We learn in the process. We feel happy, and that makes us learn even more. Consider the others.

If you're dizzy about public school math, take a break and think about public school something-else. Public school English, for example, has room for some teachers to make it really interesting. Now consider all things we accept as beacons of our math, and you will inevitably stumble upon the Art of Problem Solving. So the difference is problem-solving and thinking. You think in good English classes as well, and thus one consistency is established And we can go beyond that.

Now what is mathematical beauty associated with? Mathematical beauty can often appear in fractals, for example. Even when you spoil them, a flood of mathematical beauty is unleashed. Even when the pattern is revealed, you have to discover to comprehend. But to be consistent with our tendency to prefer rediscovery, we say that fractals are even more beautiful when rediscovered.

Is the beauty of a theorem different from that of a poem? I only have an opinion on this, and as with most mathletes, I am liberal and remain open to any opinions. My opinion is that the beauties of both are quite similar. They're both statements (a little flexibility with the poem), so it's not like we're going to say anything about how it relates to rediscovery. And then math and a language all take on structures... I encourage you to ask similar questions, such as those comparing the beauty of parts of mathematics to nature and the arts (including music).

Mathematics is just another structure that can be interpreted in a positive way or in a negative way, but discovery is the only way to guarantee proper extraction of its beauty.

Imagine that you are looking for a "subtheory" consistent with expressing individuality without money.

Now think about this. What would this subtheory be like?

Ironically because Jesus promoted helping the poor, you see many Christians spending money buying things that other people make claiming that it expresses themselves. When you think of Islam upholding this type of teaching, you're coming close. However, you're a mathlete, so you connect this with math, which immediately solves this problem. However much math has been developed, there's still infinite room for exploration and for one to express individuality, and there's always going to be enough for no one to be able to say that one is basically doing the same thing as another. Problems may be best be written for the public eye, but problem-solving is the key to individuality.

What's the difference between how the ancients learned and how public schools teach?

The ancients discovered. Public school standards force people into memorization.

Why was computation invented (besides bounds for inequalities)?

Computation was invented because people wanted to grade faster. If you look at certain computational tests, such as HMMT (Thank you, students of Harvard and MIT who are on expii!), you'll find traces of computation being quite creative. However, they had to write standardized tests quicker as well, and honestly American politicians decrease in mathematical creativity because of earlier generations of American politicians (<3 Garfield).

There is a lot of undiscovered mathematical potential among living organisms. What do we choose to do with it? We let them discover it.