Every true mathematician sees mathematics everywhere—in a child's swing or a pendulum, in the outline shape of a tree and that of its leaves, in the clouds

Il y a jusque dans les exercices des enfants ce qui pourrait arrêter le plus grand Mathématicien.

The genius is childlike. Like children he looks into the world as into a new creation and finds there a perennial source of wonder and delight.

The mathematician has reached the highest rung on the ladder of human thought.

Mathematics, and perhaps other sciences like physics, have the mission to prepare or improve the human brain, be it the brain of an individual or the collective brain of mankind, for developments yet to come. Just as animals play... in preparation for situations arising later in their lives, it may be that mathematics... is a collection of games. ...may be the only way to change the individual or collective human mind to prepare it for a future that no one can yet imagine. ...[L]ife appears inter alia as a sequence of chemical games... between individuals, or between groups... essentially of a mathematical nature... not... the von Neumann-Morgenstern theory of games, but more general games in the widest sense. This has perhaps... a direct biological role... a book... by... , ...Das Spiel (The Game) ...describes a number of mathematical games or puzzles and discusses the games molecules... play with each other. ... ...we have seen ...starting with a simple pattern and simple recursive rules can lead to unbelievably complicated configurations... that... defy analysis a priori.

The nice thing about mathematics is doing mathematics.

The kind of mathematics foisted on children in schools is not meaningful, fun, or even very useful. This does not mean that an individual child cannot turn it into a valuable and enjoyable personal game. For some the game is scoring grades; for others it is outwitting the teacher and the system. For many, school math is enjoyable in its repetitiveness, precisely because it is so mindless and dissociated that it provides a shelter from having to think about what is going on in the classroom. But all this proves is the ingenuity of children. It is not a justifications for school math to say that despite its intrinsic dullness, inventive children can find excitement and meaning in it.

Mathematical magic combines the beauty of mathematical structure with the entertainment value of a trick.

Mathematical magic combines the beauty of mathematical structure with the entertainment value of a trick.

I grew up in Cambridge in England, and my love of mathematics dates from those early childhood days.

Mathematics is the fruitful Parent of, I had almost said all, Arts, the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to Human Affairs. In which last Respect, we may be said to receive from the Mathematics, the principal Delights of Life, Securities of Health, Increase of Fortune, and Conveniences of Labour: That we dwell elegantly and commodiously, build decent Houses for ourselves, erect stately Temples to God, and leave wonderful Monuments to Posterity: That we are protected by those Rampires from the Incursions of the Enemy; rightly use Arms, skillfully range an Army, and manage War by Art, and not by the Madness of wild Beasts: That we have safe Traffick through the deceitful Billows, pass in a direct Road through the tractless Ways of the Sea, and come to the designed Ports by the uncertain Impulse of the Winds: That we rightly cast up our Accounts, do Business expeditiously, dispose, tabulate, and calculate scattered 248 Ranks of Numbers, and easily compute them, though expressive of huge Heaps of Sand, nay immense Hills of Atoms: That we make pacifick Separations of the Bounds of Lands, examine the Moments of Weights in an equal Balance, and distribute every one his own by a just Measure: That with a light Touch we thrust forward vast Bodies which way we will, and stop a huge Resistance with a very small Force: That we accurately delineate the Face of this Earthly Orb, and subject the Oeconomy of the Universe to our Sight: That we aptly digest the flowing Series of Time, distinguish what is acted by due Intervals, rightly account and discern the various Returns of the Seasons, the stated Periods of Years and Months, the alternate Increments of Days and Nights, the doubtful Limits of Light and Shadow, and the exact Differences of Hours and Minutes: That we derive the subtle Virtue of the Solar Rays to our Uses, infinitely extend the Sphere of Sight, enlarge the near Appearances of Things, bring to Hand Things remote, discover Things hidden, search Nature out of her Concealments, and unfold her dark Mysteries: That we delight our Eyes with beautiful Images, cunningly imitate the Devices and portray the Works of Nature; imitate did I say? nay excel, while we form to ourselves Things not in being, exhibit Things absent, and represent Things past: That we recreate our Minds and delight our Ears with melodious Sounds, attemperate the inconstant Undulations of the Air to musical Tunes, add a pleasant Voice to a sapless Log and draw a sweet Eloquence from a rigid Metal; celebrate our Maker with an harmonious Praise, and not unaptly imitate the blessed Choirs of Heaven: That we approach and examine the inaccessible Seats of the Clouds, the distant Tracts of Land, unfrequented Paths of the Sea; lofty Tops of the Mountains, low Bottoms of the Valleys, and deep Gulphs of the Ocean: That in Heart we advance to the Saints themselves above, yea draw them to us, scale the etherial Towers, freely range through the celestial Fields, measure the Magnitudes, and determine the Interstices of the Stars, prescribe inviolable Laws to the Heavens themselves, and confine the wandering Circuits of the Stars within fixed Bounds: Lastly, that we comprehend the vast Fabrick of the Universe, admire and contemplate the wonderful Beauty of the Divine 249 Workmanship, and to learn the incredible Force and Sagacity of our own Minds, by certain Experiments, and to acknowledge the Blessings of Heaven with pious Affection.

I enjoy being surprised by mathematics and its intrinsic difficulty. The moment I enjoy best is when the pieces of the puzzle fall into one coherent whole.

, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

[T]he one lesson that I drew from coming in from... lots and lots of detours. ...[T]he other side of the coin. ...I started doing mathematics seriously quite late ...That had interesting consequences. ...Most people in mathematics came into mathematics early ...typically in your teens ...[T]he phenomenon of exists ...only in music and mathematics. ...[C]hild prodegies exist primarily as performers, and the mathematical equivalent is problem solvers, rather than theory builders, and the music equivalent would be s. It's true that Mozart was a child prodigy in composition, but on the whole... performers and problem solvers are the dominant types of child prodigies... [T]his phenomenon only exists in music and mathematics, and correspondingly, they come in quite early... Innate or not... it involves a lot of ... Well, maybe there is such a thing as talent... but one necessary condition for a child prodigy... is... the... that could bear with long long long hours of enormous amounts of training, and sometimes it becomes an obsession. ...I'm aware that child prodigies exist in chess and in ... and in go and so on, but that's... a small variation on mathematics... I don't know about innateness and... I'm not sure about... talent. ...[T]he human brain is a very complicated machine and it would be very surprising if there is no... innate difference between one brain and another... after all, there are innate differences between one body and another... I have seen lots and lots of mathematics students... who are very talented... by the standard judgement... But ultimately... on the whole, I am simplifying... it's really the effort, and how much you really like the subject that made a difference as to ultimate success.