Algebraic Manipulation Quotes

Through algebra you easily arrive at equations, but always to pass therefrom to the elegant constructions and demonstrations which usually result by means of the method of porisms is not so easy, nor is one's ingenuity and power of invention so greatly exercised and refined in this analysis.

We may always depend on it that algebra, which cannot be translated into good English and sound common sense, is bad algebra.

Indeed we may consider the engine as the material and mechanical representative of analysis, and that our actual working powers in this department of human study will be enabled more effectually than heretofore to keep pace with our theoretical knowledge of its principles and laws, through the complete control which the engine gives us over the executive manipulation of algebraical and numerical symbols.

The art of doing mathematics consists in finding that special case which contains all the germs of generality.

My algebra was relatively poor. I found it very difficult to use equations that substituted numbers - to which I had a synesthetic and emotional response - for letters, to which I had none. It was because of this that I decided not to continue math at Advanced level, but chose to study history, French and German instead.

The application of algebra to geometry ... has immortalized the name of Descartes, and constitutes the greatest single step ever made in the progress of the exact sciences.

Mathematicians are always playing tricks on each other. They're always pulling jokes on each other.

Grandad taught me that the alien signs and symbols of algebraic equations were not just marks on paper. They were not flat. They were three-dimensional, and you could approach them from different directions, look at them from different ways, stand them on their heads. You could take them apart and put them back together in a variety of shapes, like Legos. I stopped being scared of them.

If there are four equations and only three variables, and no one of the equations is derivable from the others by algebraic manipulation then there is another variable missing.

We cannot forbear suggesting one practical result which it appears to us must be greatly facilitated by the independent manner in which the engine orders and combines its operations: we allude to the attainment of those combinations into which imaginary quantities enter.

The fun little proofs that you can do with algebra - they are sort of like crowd pleasers in a way. Like, the .9 repeating equaling one. It doesn't take a lot of algebra to prove that, and it's really fun. It kind of wows people. It's like they're watching magic happen right before their eyes.

In the beginning of the year 1665, I found the method of approximating series and the rule for reducing any dignity of any binomial into such a series.

Von Neumann languages do not have useful properties for reasoning about programs. Axiomatic and denotational semantics are precise tools for describing and understanding conventional programs, but they only talk about them and cannot alter their ungainly properties. Unlike von Neumann languages, the language of ordinary algebra is suitable both for stating its laws and for transforming an equation into its solution, all within the "language."

I tell you, with complex numbers you can do anything.

I would advise you, Sir, to study algebra, if you are not an adept already in it: your head would get less muddy, and you will leave off tormenting your neighbours about paper and packthread, while we all live together in a world that is bursting with sin and sorrow.

What is algebra exactly; is it those three-cornered things?

Algebra messed up one of those divisions between things that help you make sense of the world and keep it tidy. Letters make words; figures make numbers. They had no business getting tangled up together.