Research is formalized curiosity. It is poking and prying with a purpose.

I want to make my own discoveries…….penetrate the evil which attracts me

I thought fit to... explain in detail in the same book the peculiarity of a certain method, by which it will be possible... to investigate some of the problems in mathematics by means of mechanics. This procedure is... no less useful even for the proof of the theorems themselves; for certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards... But it is of course easier, when we have previously acquired, by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.

[W]hen I did my PhD, it was in very very pure mathematics and I still love that field, ...algebraic topology ...but then ...I started moving into more physical subjects and... started doing experiments... I thought this was an opportunity. Until then I had lots of... friends and family who were not scientists, and who didn't have any mathematical background, but... with pure mathematics it's very difficult to convey the excitement of computing s... [W]ith physics I decided that every time I finish a project, write a paper or even figure out something, I should design a toy that... captures... joy that I have had, and can share it with people... [T]hen it became quite successful, and it became the other way around. Now I look around and... realize that there's science all around and so I start from the toys... I try to... discover one every month... I was given most of them because my good friends send me toys... but I have... stumbled on... 1/3 of them myself, and... depending on the public lecture... I got... maybe a dozen and... try to tell a story. ...[S]ome of the collections are more cohesive stories than others, but ...whatever I take, I start seeing connections ...And as with the larger nature, so with my toy collection, there are lots and lots of inner connections that I'm waiting to discover; and I usually can.

Research is creating new knowledge.

A good means to discovery is to take away certain parts of a system to find out how the rest behaves.

Research is formalized curiosity. It is poking and prying with a purpose. It is a seeking that he who wishes may know the cosmic secrets of the world and they that dwell therein.

The aim of research is the discovery of the equations which subsist between the elements of phenomena.

Scientists work by a combination of intuition and insight in trying to understand a question.

I shall often discuss mathematical discoveries... I shall try to make up a likely story how the discovery could have happened. I shall try to emphasize the motives underlying the discovery, the plausible inferences that led to it... everything that deserves imitation.

You see, I went on with this research just the way it led me. That is the only way I ever heard of true research going. I asked a question, devised some method of obtaining an answer, and got — a fresh question. Was this possible or that possible? You cannot imagine what this means to an investigator, what an intellectual passion grows upon him! You cannot imagine the strange, colourless delight of these intellectual desires!

Mathematicians are coming up with s that they use in their actual mathematical research. And these, like , I think is the name of one of them ... these are actually like s that have been engineered in a way that they can actually be used by working mathematicians to check the work they're doing.

This [experimentation] is the custom—and properly so—in those sciences where mathematical demonstrations are applied to natural phenomena, as is seen in the case of perspective, astronomy, mechanics, music, and others where the principles, once established by well-chosen experiments, become the foundations of the entire superstructure.

Study a field in which you can apply mathematics and have the conclusions validated or refuted by contact with free markets or physical reality.