"On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols’ […]. Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient." (Jean Dieudonné)
"As the mind learns to understand more complicated combinations of ideas, simpler formulae soon reduce their complexity; so truths that were discovered only by great effort, that could at first only be understood by men capable of profound thought, are soon developed and proved by methods that are not beyond the reach of common intelligence. The strength and the limits of man." (Nicolas de Condorcet)
"Imagination, as well as reason, is necessary to perfection in the philosophical mind. A rapidity of combination, a power of perceiving analogies, and of comparing them by facts, is the creative source of discovery." (Sir Humphry Davy)
"Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two faculties, which we may call intuition and ingenuity. […] The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasonings." (Alan Turing)
"Number is limited multitude or a combination of units or a flow of quantity made up of units; and the first division of number is even and odd." (Nicomachus of Gerasa)
"On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols’ […]. Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient." (Jean Dieudonné)
"Since primes are the basic building blocks of the number universe from which all the other natural numbers are composed, each in its own unique combination, the perceived lack of order among them looked like a perplexing discrepancy in the otherwise so rigorously organized structure of the mathematical world." (H Peter Aleff,"Prime Passages to Paradise")"
"When any principle, law, tenet, probability, happening, circumstance, or result can in no way be directly, indirectly, empirically, or circuitously proven, derived, implied, inferred, induced, deduced, estimated, or scientifically guessed, it will always for the purpose of convenience, expediency, political advantage, material gain, or personal comfort, or any combination of the above, or none of the above, be unilaterally and unequivocally assumed, proclaimed, and adhered to as absolute truth to be undeniably, universally, immutably, and infinitely so, until such time as it becomes advantageous to assume otherwise, maybe." (Charles E Rhodes)
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