David Hilbert

"Mathematics reveals the harmonious structure underlying all of reality."

"One must balance rigor with intuition in mathematical work."

"The foundations of mathematics must be both solid and flexible."

"In mathematics there are no shortcuts to success."

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

"A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street."

"Problems are the lifeblood of mathematics."

"One cannot escape the feeling that these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser even than their discoverers."

"Music is the pleasure the human mind experiences from counting, without being aware that it is counting."

"The further the spiritual evolution of mankind advances, the more certain it seems to me that the path to genuine religiosity does not lie through the fear of life, and the fear of death, and blind faith, but through striving after rational knowledge."

"Whenever I feel the need to exercise, I lie down until it goes away."

"The true spirit of delight, the exaltation, the sense of being more than Man, is the touchstone of the highest excellence."

"Every mathematical problem possesses beauty and intellectual intrigue."

"We cannot think about fundamental things in the world without using mathematics."

"Certainty about mathematical truths is the only certainty we can claim."

"The infinite! No other question has ever moved so profoundly the spirit of man."

"A proof should be like a clear window pane."

"There is no ignorabimus in mathematics; we must know, and we shall know."

"Every real number can be understood through the structure of mathematics."

"Geometry will not hold a candle to poetry once we understand both."

"The most beautiful experience we can have is the mysterious."

"My work always tries to unite the truth with the beautiful; when I had to choose one or the other, I usually chose the beautiful."

"If I were to awaken after having slept for a thousand years, my first question would be: has the Riemann hypothesis been proven?"

"The problems of mathematics are the poetry of logical science."

"What is the magic by which we can make a difficult problem disappear by reformulating it?"

"Mathematical thinking is not about numbers; it is about patterns, structures, and relationships."

"The conviction that every mathematical problem must be solvable is a powerful driving force for the researcher."

"In my belief, axioms, like the basis of a house, must be carefully chosen so that the entire structure stands firm."

"To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination."

"The principle of the mathematical proof is its integrity and its inevitable conclusion."