James Joseph Sylvester Quotes

In studying the action of the Analytical Engine, we find that the peculiar and independent nature of the considerations which in all mathematical analysis belong to operations, as distinguished from the objects operated upon and from the results of the operations performed upon those objects, is very strikingly defined and separated.

Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.

It is not of the essence of mathematics to be conversant with the ideas of number and quantity.

I turn aside with a shudder of horror from this lamentable plague of functions which have no derivatives.

I am interested in mathematics only as a creative art.

I still remember the realization in college at Flinders University in Australia that mathematics was not just an abstract game of symbols but could be used as a tool to analyze and understand the modern world.

You have to spend some energy and effort to see the beauty of math.

And what are these fluxions? The velocities of evanescent increments. And what are these same evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them the ghosts of departed quantities...?

Always be willing to look at both sides of the argument. Understanding the other side is the best way to strengthen your own.

The internet explodes when somebody has the creativity to look at a piece of data that's put there for one reason and realise they can connect it with something else.

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.

For some time now, I have been encouraging people to ask themselves why things look the way they do.

Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry.... if mathematical analysis should ever hold a prominent place in chemistry -- an aberration which is happily almost impossible -- it would occasion a rapid and widespread degeneration of that science.

Show Holmes a drop of water and he would deduce the existence of the Atlantic. Show it to me and I would look for a tap. That was the difference between us.

The object of the engine is in fact to give the utmost practical efficiency to the resources of numerical interpretations of the higher science of analysis, while it uses the processes and combinations of this latter.

Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.

When a truth is necessary, the reason for it can be found by analysis, that is, by resolving it into simpler ideas and truths until the primary ones are reached. It is this way that in mathematics speculative theorems and practical canons are reduced by analysis to definitions, axioms and postulates.

It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.

Writers themselves don't analyze what they do; to analyze would be to look down while crossing a canyon on a tightrope.

The person who did most to give to analysis the generality and symmetry which are now its pride, was also the person who made mechanics analytical; I mean Euler.

Mathematical Analysis is... the true rational basis of the whole system of our positive knowledge.

There's always a hole in theories somewhere if you look close enough.

I just want to take a realistic look now, now that we have enough distance.

We look at, the absurdity of the system provides us the most material. And that is best served by sort of the theater of it all, you know, which, by the way, thank you both, because it's been helpful.