“The study of mathematics is like climbing up a steep and craggy mountain; when once you reach the top, it fully recompenses your trouble, by opening a fine, clear, and extensive prospect.” (Tyron Edwards, “The New Dictionary of Thoughts: A Cyclopedia of Quotations”, 1948)
“Creating a new theory is not like destroying an old barn and erecting a skyscraper in its place. It is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting point and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part of our broad view gained by the mastery of the obstacles on our adventurous way up.” (Leopold Infeld, “The Evolution of Physics”, 1961)
“The tantalizing and compelling pursuit of mathematical problems offers mental absorption, peace of mind amid endless challenges, repose in activity, battle without conflict, ‘refuge from the goading urgency of contingent happenings’, and the sort of beauty changeless mountains present to senses tried by the present-day kaleidoscope of events.” (Morris Kline, “Mathematics in Western Culture”, 1964)
“Nature’s beauty dies. The day dawns when the nautilus is no more. The rainbow passes, the flower fades away, the mountain crumbles, the star grows cold. But the beauty in mathematics — the divine proportion, the golden rectangle, spira mirabilis — endures for evermore.” (Henry E Huntley, “The Divine Proportion: A Study in Mathematical Beauty”, 1970)
"Mathematicians get a different kind of pleasure from the illumination of solving a problem, when what was once mysterious and obscure is made plain. Revealing the hidden connections in a situation is delightful - like reaching the top of a mountain after a hard climb, and seeing the landscape spread out before you. All of a sudden, everything is clear! If the result is extremely simple, so much the better . To start with confusing complexity and transform it into revealing simplicity is a marvellous reward for hard work. It really does give the mathematician a 'kick'!" (David Wells, "You Are a Mathematician: A wise and witty introduction to the joy of numbers", 1995)
“There is a strong parallel between mountain climbing and mathematics research. When first attempts on a summit are made, the struggle is to find any route. Once on the top, other possible routes up may be discerned and sometimes a safer or shorter route can be chosen for the descent or for subsequent ascents. In mathematics the challenge is finding a proof in the first place. Once found, almost any competent mathematician can usually find an alternative often much better and shorter proof. At least in mountaineering we know that the mountain is there and that, if we can find a way up and reach the summit, we shall triumph. In mathematics we do not always know that there is a result, or if the proposition is only a figment of the imagination, let alone whether a proof can be found.” (Kathleen Ollerenshaw, “To talk of many things: An autobiography”, 2004)
“Where things get really interesting is when unexpected bridges emerge between parts of the mathematical world that were remote from each other in the mental picture that had been developed by previous generations of mathematicians. When this happens, one gets the feeling that a sudden wind has blown away the fog that was hiding parts of a beautiful landscape. In my own work this type of great surprise has come mostly from the interaction with physics.” (Alain Connes [in “The Princeton Companion to Mathematics” Ed. by Timothy Gowers et al, 2008])
“It may be permissible to compare mathematical research with the opening up of a mountain range. There will always be the people whose principal interest it will be to try their ability in advanced mountaineering. They will go for the most difficult summits. Others will see their aim in making the mountain range accessible as a whole, by building convenient roads along the valleys and across the passes. They will also reach the summits eventually, but mainly for the sake of the beautiful views, and, if possible, by cable car.” (Hans Hermes)
“My approach to research consists in looking to the mathematical landscape, taking notice of the things I like and judge interesting and of those I don’t care about, and then trying to imagine what should be next. If you see a bridge across a river, you try to imagine what lies on the other shore. If you see a mountain pass between two high mountains, you try to imagine what is in the valley you don’t see yet but secretly know must be there.” (Enrico Bombieri)
"The scientific life of mathematicians can be pictured as an exploration of the geography of the 'mathematical reality' which they unveil gradually in their own private mental frame." (Alain Connes)
“There is a strong parallel between mountain climbing and mathematics research. When first attempts on a summit are made, the struggle is to find any route. Once on the top, other possible routes up may be discerned and sometimes a safer or shorter route can be chosen for the descent or for subsequent ascents. In mathematics the challenge is finding a proof in the first place. Once found, almost any competent mathematician can usually find an alternative often much better and shorter proof. At least in mountaineering we know that the mountain is there and that, if we can find a way up and reach the summit, we shall triumph. In mathematics we do not always know that there is a result, or if the proposition is only a figment of the imagination, let alone whether a proof can be found.” (Kathleen Ollerenshaw, “To talk of many things: An autobiography”, 2004)
“Where things get really interesting is when unexpected bridges emerge between parts of the mathematical world that were remote from each other in the mental picture that had been developed by previous generations of mathematicians. When this happens, one gets the feeling that a sudden wind has blown away the fog that was hiding parts of a beautiful landscape. In my own work this type of great surprise has come mostly from the interaction with physics.” (Alain Connes [in “The Princeton Companion to Mathematics” Ed. by Timothy Gowers et al, 2008])
“It may be permissible to compare mathematical research with the opening up of a mountain range. There will always be the people whose principal interest it will be to try their ability in advanced mountaineering. They will go for the most difficult summits. Others will see their aim in making the mountain range accessible as a whole, by building convenient roads along the valleys and across the passes. They will also reach the summits eventually, but mainly for the sake of the beautiful views, and, if possible, by cable car.” (Hans Hermes)
“My approach to research consists in looking to the mathematical landscape, taking notice of the things I like and judge interesting and of those I don’t care about, and then trying to imagine what should be next. If you see a bridge across a river, you try to imagine what lies on the other shore. If you see a mountain pass between two high mountains, you try to imagine what is in the valley you don’t see yet but secretly know must be there.” (Enrico Bombieri)
"The scientific life of mathematicians can be pictured as an exploration of the geography of the 'mathematical reality' which they unveil gradually in their own private mental frame." (Alain Connes)
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