...Once you entomb mathematics in an artificial language à la Hilbert, once you set up a completely formal axiomatic system, then you can forget that it has any meaning and just look at it as a game that you play with marks on paper that enable you to deduce theorems from axioms. You can forget about the meaning of the game, the game of mathematical reasoning, it's just combinatorial play with symbols! There are certain rules, and you can study these rules and forget that they have any meaning!
Gregory ChaitinRelated topics
certain formal game language mathematics meaning once paper play set study Hilbert RulesRelated quotes
I was early regarded as having unusual intellectual capacity. I was an omnivorous reader, and I added to that a desire to systematize my understanding. As a result, history, for example, was not merely a set of dates and colorful stories; I could understand it as a sequence in which one event flowed out of another. This sense of order crystallized during my high-school and college years into a predominant interest in mathematics and mathematical logic.
Kenneth Arrow
I must tell you that mathematicians are not scientists, they are artists.... Apart from the most elementary mathematics, like arithmetic or high school algebra, the symbols, formulas and words of mathematics have no meaning at all. The entire structure of pure mathematics is a monstrous swindle, simply a game, a reckless prank. You may well ask: "Are there no renegades to reveal the truth?" Yes, of course. But the facts are so incredible that no one takes them seriously. So the secret is in no danger.
Theodore Kaczynski
As a graduate student I studied mathematics fairly broadly and I was fortunate enough, besides developing the idea which led to "Non-Cooperative Games," also to make a nice discovery relating to manifolds and real algebraic varieties. So I was prepared actually for the possibility that the game theory work would not be regarded as acceptable as a thesis in the mathematics department and then that I could realize the objective of a Ph. D. thesis with the other results.
John Forbes Nash
His work, called Aryabhatiya, is composed of three parts, in only the first of which use is made of a special notation of numbers. It is an alphabetical system in which the twenty-five consonants represent 1-25, respectively; other letters stand for 30, 40, ...., 100 etc. The other mathematical parts of Aryabhatiya consists of rules without examples. Another alphabetic system prevailed in Southern India, the numbers 1-19 being designated by consonants, etc.
Aryabhata
Now what are we looking at right here? What's bang in the middle? Some people think that's mathematics there. Fine. But if maths is the study that best allows you to think your way to the centre, what're the forces you're investigating? Maths is totally abstract, at one level, square roots of minus one and the like, but the world is nothing if not rigorously mathematical. So this is a way of looking at the world which unifies all the forces: mental, social, physical.
China Miéville