The only way to comprehend what mathematicians mean by Infinity is to contemplate the extent of human stupidity.
I've approached music with the understanding that knowledge is available regarding tones and their effect upon the body. I think the father of that knowledge was the mathematician Pythagoras who lived several thousand years ago. Pythagoras was also a fine musician and he knew specifically what tones would affect which parts of the body.
Bertrand Russell started off as a mathematician and then degenerated into a philosopher and finally into a humanist; he went downhill rapidly!
I think we need more math majors who don't become mathematicians. More math major doctors, more math major high school teachers, more math major CEOs, more math major senators. But we won't get there unless we dump the stereotype that math is only worthwhile for kid geniuses.
I suppose that every age has its own particular fantasy: ours is science. A seventeenth-century man like Blaise Pascal, who thought himself a mathematician and scientist of genius, found it quite ridiculous that anyone should suppose that rational processes could lead to any ultimate conclusions about life, but easily accepted the authority of the Scriptures. With us, it is the other way `round
The total subject of mathematics is clearly too broad for any of us. I do not think that any mathematician since Gauss has covered it uniformly and fully; even Hilbert did not and all of us are of considerably lesser width quite apart from the question of depth than Hilbert.
Mathematicians, like cows in the dark, all look alike to me.
I began to research the concept of dimensionality from the point of view of quality, and not just quantity, as a mathematician might do. Taking my clues from the theosophical use made of the Vedantic levels of reality, I identified the western notion of Energy (as someting which is effecatious by means of motion), with the idea of Time. The more comprehensive dimension 'eternity' I defined as a form of energy which is efficacious without motion. In this manner I began to establish the qualities of dimensions and open out the seemingly monolithic concept of energy.
The method of Fluxions is the general key by help whereof the modern mathematicians unlock the secrets of Geometry, and consequently of Nature.
Mathematics has been called the science of the infinite. Indeed, the mathematician invents finite constructions by which questions are decided that by their very nature refer to the infinite. This is his glory.
Science is a differential equation. Religion is a boundary condition.
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