Secret

Mathematics

Mathematics is like exploring a scifi alien space with its exotic rules. I am interested in many of the fundamental workings of various mathematical theories and formulations so as to better understand the alien space that is associated with the mathematical concept, which is useful as a guide to find more efficient and inspiring computational methods to further explore unknown territory in mathematics and facilitate mathematical education to make people less fear of maths

One of my major personal research interest is

1. Nonstandard but valid ways in problem solving. For example, solving a counterexample finding question by deriving the constraint relation that the counterexample satisfy, and

2. Explore new mathematical objects by systematically causing proofs to break by modifying its underlying axioms.

http://i.stack.imgur.com/RU3Js.png

My questions tend to be quite philosophical and concern more about the global view of things, thus I often have trouble finding my path to explore them, or in other words, tend to lost my way in the alien space easily, as my math skills is not very advanced and i am still actively learning from others

Some of my questions are related to optimization, however the major motive of asking such questions is usually just exploring a mathematical object by walking around it, the analogy for this is "I am a tourist, how can I reach a certain interesting landmark?" and not because of having an optimization problem to be solved

Science Education

The importance of the role in education in advancing science is well recognised. In the context of mathematics, I am interested in, if possible, obtaining and building "lossless representations" of a given mathematical concept, including proof structures and strategies.

A lossless representation is a non word based information communication method (such as pictures, graphs etc.) that contains sufficient information to allow many subtleties and exceptional cases of a field of study (which is usually overlooked by analogies and only apparent in the more rigorous) to be covered, the the point that theoretically the field of study (or aspects of it) can be derived by manipulation of this representation.

These representations were believed to be slightly easier to obtain in the domain of mathematics due to far fewer criteria need to be satisfied (only need to be able to derive all properties of the mathematical object, including proof strategies, identities and relations)

As a result,

1. Visualisation and

2. Ability to explain the concept losslessly to a layman such that they can easily understand it, arosing their interest and be able to experiment on it by start performing qualitative and semiquantitative computations using it

are important considerations

My current personal research interest in this field is

1. Tensors, Linear maps and matrix visualisation
Top Questions

Are there mathematical objects that have been proved to exist but cannot be described in words?

asked May 16, 2015 at 16:24

Ordinal tetration: The issue of ${}^{\epsilon_0}\omega$

asked Jun 7, 2017 at 15:20

Trying to identify a film with a calligraphic style magic

asked Jan 23, 2017 at 21:55

How were vector calculus nabla ∇ identities first derived?

asked Feb 8, 2015 at 5:31

Example of algebraic structure that is non distributive for BOTH distributive laws and how to do computation in them?

asked Apr 1, 2015 at 12:55

0 to the power of 0, what does the essential discontinuity actually look like?

asked Nov 23, 2014 at 5:19

What is the most efficient and safest way to communicate with an alien should first contact occur?

asked Nov 28, 2016 at 15:28