David Hilbert

"The axiomatic method is suited to every science in which we wish to impart systematic knowledge."

"I have always thought that the greatest danger comes from underestimating the vastness and subtlety of mathematical ideas."

"The edifice of mathematics will grow to the height that we give it."

"One must always be prepared to discard one's preconceived opinions."

"The growth of mathematics comes from a genuine need for new methods."

"The most important principle in the development of mathematics is the principle of generalizing a particular case."

"I am sure that this problem, too, will enjoy the same beneficial influence that the effort to solve it will have on the development of mathematical science."

"Let us take as our guiding light the simple principle that pure mathematics is the study of what may be deduced from abstract concepts."

"A complete solution to any problem of import should be possible."

"Consistency and completeness are the hallmarks of rigorous mathematics."

"We want mathematics to be a unified edifice, not a collection of scattered facts."

"The question of the foundations and the ultimate meaning of mathematics remains open."

"Every genuine creation must shake the existing order in some way."

"The mathematical understanding of a phenomenon is attained only when we are able to reduce it to an abstract logical system."

"One should always prefer a true statement that disturbs to a comfortable falsehood."

"The beauty of a mathematical proof lies in its elegant simplicity."

"Mathematics knows no races or geographic boundaries."

"I have devoted myself to mathematics not for the glory but for the infinite joy it brings."

"The abstract and the concrete are always intertwined in the mathematical process."

"To understand the world, one must learn its mathematical language."

"Every mathematical truth is immutable and eternal."

"The most successful attack on a problem is often a change in perspective."

"Geometry is frozen music."

"The profound study of nature is the most fertile source of mathematical discovery."

"One's purpose in life should be the pursuit of understanding."

"A problem well-stated is half-solved."

"The spirit of mathematics is the capacity for finding order in chaos."

"We are not here to teach mathematics, but to teach thinking."

"The human spirit takes pleasure in symmetry."

"Logic is the hygiene of the mathematician."