"The trouble with integers is that we have examined only the very small ones. Maybe all the exciting stuff happens at really big numbers, ones we can't even begin to think about in any very definite way. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions."
About Ronald Graham
Ronald Graham — Life and Legacy
Ronald Graham was a distinguished mathematician whose innovative work spanned various areas, including combinatorics and computer science. He is particularly noted for his contributions to Ramsey theory, which investigates conditions under which order must appear in mathematical structures. Graham famously stated, 'Mathematics is the art of giving the same name to different things,' reflecting his belief in the creative nature of mathematics. This perspective underscores his approach to problem-solving and abstraction, where he often sought to unify disparate concepts through elegant solutions. His insights into algorithms have also shaped modern computational practices, emphasizing that 'The only way to learn mathematics is to do mathematics.' This philosophy highlights the importance of hands-on experience in mastering mathematical concepts. Graham's legacy continues to influence both theoretical and practical aspects of mathematics, inspiring future generations of mathematicians and computer scientists alike. His quotes resonate with those who appreciate the interplay between creativity and logic in the mathematical realm.
Quote collection
Ronald Graham quotes
13 quotes — follow a thought to its full quote page.
"Math is sometimes called the science of patterns."
"Juggling is sometimes called the art of controlling patterns, controlling patterns in time and space."
"Someone has remarked that 'An ideal math talk should have one proof and one joke and they should not be the same'."
"Incidentally, when we're faced with a "prove or disprove," we're usually better off trying first to disprove with a counterexample, for two reasons: A disproof is potentially easier (we need just one counterexample); and nitpicking arouses our creative juices. Even if the given assertion is true, our search for a counterexample often leads to a proof, as soon as we see why a counterexample is impossible. Besides, it's healthy to be skeptical."
"It wouild be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, 'Yes, it is true, but you won't be able to understand the proof.' John Horgan."
"AB=1/4((A+B)^2-(A-B)^2) is an amazing identity, and unfortunately, I have to remind my current students how to prove it."
"I was reminded of the Sydney Harris cartoon that said 'adding two numbers that have not been added before does not constitute a mathematical breakthrough'."
"Someone has said that all the great jugglers are dead."
"A lot of the high-level sports are really in your mind."
"Well, as you know, there are 24 hours in every day. And if that's not enough, you've always got the nights!"
"Some people think that mathematics is a serious business that must always be cold and dry; but we think mathematics is fun, and we aren't ashamed to admit the fact. Why should a strict boundary line be drawn between work and play? Concrete mathematics is full of appealing patterns; the manipulations are not always easy, but the answers can be astonishingly attractive."
"The ultimate goal of mathematics is to eliminate all need for intelligent thought."