Math AOK Web Page
LJA TOK
Vocab: EMPIRICAL
1.
derived from or guided by experience or experiment.
2.
depending upon experience or observation alone, without using scientific method or theory, especially as in medicine.
3.
provable or verifiable by experience or experiment.

​While some people claim mathematics to be discovered, others claim that it is invented, but neither view seems to be entirely satisfactory.
Mathematics itself is neither invented nor discovered, it is both. The was that we interpret numbers and signs and how we use mathematics is invented because if it was discovered in other places, they would have different symbols for addition subtraction and numbers. Mathematics itself and the laws involved in it are discovered because they are universally identical. Mathematics is similar to physics in this way in that no matter who you are or where you are in the universe, when you take two things and put two more things next to them, you have four things. This will ALWAYS be true, it is simply how the numbers are spoken and written that may change.
BIG WIG
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Pythagoras of Samos
Pretty much everyone who has taken high school algebra knows the name Pythagoras and his equation a squared plus b squared equals c squared. He is most famous for this equation but he had many other pieces of work in his lifetime. Pythagoras was a Greek philosopher and mathematician and founder of the religious movement Pythagoreanism. Another famous mathematician named Plato was the student of Pythagoras showing that his influence was indeed great. Pythagoras is less famous for his musical mathematical equations but they were his work. He could translate musical notes into mathematics. This idea came to him when he passed out in the blacksmith workshop and heard the musical and scientific notes of the anvil.
LINKING QUESTION
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Is the book of nature written in the language of math?
No, the book of nature is not written in the language of math, the book of math was written in the language of nature. Math is a concept that was created by man whereas nature was not. The reason so many of the equations that people form have so much in common with nature is because the equations are derived from nature. Mathematics would not be around without nature because mathematics is simply a part of nature. Nature is so much more infinitely complex than mathematics that to saw that the book of nature was written in the language of math would be an insult to the extreme diversity and complexity that nature encompasses.
GUIDING QUESTION​
If a hypothesis "fails" to what extent is it still relevant?
A hypothesis in science or math can never fail or succeed, it can only be supported or disputed. A hypothesis cannot be proven true or false through any means, the data taken to test the hypothesis does not prove anything, it just adds more data to the equation. If a hypothesis not supported by the data then it has not failed, it was just as helpful as if the hypothesis was supported. Perhaps a hypothesis that was disputed by the data was more helpful because getting an unexpected result may spur on research in that area. With disputes and disparities research and learning are more motivated than if everything were to have gone according to plan.
Max's Aok Math Page
Paradigm Shift
​Although there have been a few paradigm shifts in the study of mathematics, there are less than some of the other aspects of knowledge because of math being so linear. It is a very rare event that a mathematical equation is proven to be wrong. The paradigm shifts that occur in math are more to do with physics and how the world works than the actual math itself. We know know that the solar system in heliocentric but at one point this was not known. As soon as someone suggests something completely radical that changes the face of the field, a paradigm shift has occurred. The largest paradigm shift in the field of mathematics and physics was when Sir Isaac Newton invented/discovered the laws of motion. Newton had three laws of motion and they are very well known today because of how revolutionary they were. Newton elected to think outside of the conventional methods and ways of going about things in order to distance himself from the ideas and influences of others. This gave him a unique perspective and he was able to come up with these mathematical equations that changed the face of physics and math for the rest of human history. Perhaps in the years to come we will discover a way to exceed the speed of light and this may cause many more breakthroughs in all kinds of fields. It is almost impossible to know what the future holds in store for mathematics but we can be sure that it is not over yet.
Bio
My name is Max Shelbourne and I am a senior at Le Jardin Academy. My favorite past times and hobbies are paddling six man and one man Hawaiian Outrigger canoes, kayaking, reading, and playing video games. My most enjoyable classes are math, biology, and chemistry because I enjoy when there is a correct answer to a question. I like being able to memorize information and then recall it to solve problems.