Quotable Mathematics

"Statistical methods are tools of scientific investigation. Scientific investigation is a controlled learning process in which various ...

"[…] data analysis in the context of basic mathematical concepts and skills. The ability to use and interpret simple graphical and nume...

"The discrepancy between our mental models and the real world may be a major problem of our times; especially in view of the difficulty...

"Data are generally collected as a basis for action. However, unless potential signals are separated from probable noise, the actions t...

"[...] any hope that we are smart enough to find even transiently optimum solutions to our data analysis problems is doomed to failure,...

"In every branch of knowledge the progress is proportional to the amount of facts on which to build, and therefore to the facility of o...

"Automatic design has the computer do too much and the human do too little, whereas automatic programming has the human do too much and...

"A special role is played in the theory of metric spaces by the class of open spheres within the class of all open sets. The main featu...

"I consider it as one of the most important steps made by Analysis in the last period, that of not being bothered any more by imaginary...

"From its beginning critical point theory has been concerned with mutual relations between topology and geometric analysis, including d...

"It is possible that analysis in the large may eventually reduce to topology, but not until topology has been greatly broadened. It i...

"As for methods I have sought to give them all the rigour that one requires in geometry, so as never to have recourse to the reason...

"I see with much pleasure that you are working on a large work on the integral Calculus [...] The reconciliation of the methods which y...

"The first step, whenever a practical problem is set before a mathematician, is to form the mathematical hypothesis. It is neither need...

"Often I have considered the fact that most of the difficulties which block the progress of students trying to learn analysis stem from...

"While those whom devotion to abstract discussions has rendered unobservant of the facts are too ready to dogmatize on the basis of a f...

"[...] if the behavior points for the entire control surface are plotted and then connected, they form a smooth surface: the behavior s...

" A giant component is a connected component whose size is on the same order of magnitude as the size of the whole network. Network per...

"The equation e^πi+1 = 0 is true only by virtue of a large number of profound connections across many fields. It is true be...