Auguste Comte Quotes

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

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.

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.

Aspiring to these wide generalizations, the analysis of quadratic functions soars to a pitch from whence it may look proudly down on the feeble and vain attempts of geometry proper to rise to its level or to emulate it in its flights.

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.

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.

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.

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.

The tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds the linking bridges and gives the ever more reliable forms.

It is the invaluable merit of the great Basle mathematician Leonard Euler, to have freed the analytical calculus from all geometric bounds, and thus to have established analysis as an independent science, which from his time on has maintained an unchallenged leadership in the field of mathematics.

I have to admit that he was not bad at combinatorial analysis - a branch, however, that even then I considered to be dried up.

All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.

The mathematical difficulties of the theory of rotation arise chiefly from the want of geometrical illustrations and sensible images, by which we might fix the results of analysis in our minds.

Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane.

The Holy Ghost is the Spirit of the Lord, and issues forth from himself, and may properly be called God's minister to execute his will in immensity.

People who have intended and loved what is evil in the world intend and love what is evil in the other life, and then they no longer allow themselves to be led away from it. This is why people who are absorbed in evil are connected to hell and actually are there in spirit; and after death they crave above all to be where their evil is. So after death, it is we, not the Lord, who cast ourselves into hell.

Revenge is an infection of the spirit.

Man can never come up to his ideal standard. It is the nature of the immortal spirit to raise that standard higher and higher as it goes from strength to strength, still upward and onward. The wisest and greatest men are ever the most modest.

Nature is the symbol of Spirit.

Poverty continues to exist. Its appearance seems to be relentless in evidencing itself not only to all the things we experience here in America, but certainly what we see globally. And I don't see anywhere any philosophical analysis that suggests we know how to get out of this.

Too much hard luck can create a permanent meanness of spirit in any creature.

There are no people on earth in whom a spirit of enthusiastic zeal is so readily kindled, and burns so remarkably, as Americans