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Michael Atiyah
65 quotes
“Nobody succeeded until two of the most famous figures in mathematics appeared... Niels Abel and Évariste Galois.”
Michael Atiyah (1929–2019) said by 2019 at the latest wikiquote, CC BY-SA 4.0 source
“Galois... was... imprisoned... for radical views. ...[H]e was to take part in a duel, in which he was killed, but that... was an assassination plot. They covered it up. He was... murdered by the because of his radical opinions.., but the last night.., he stayed up... scribbling his notes which formed the foundations of modern mathematical theory, the theory of groups.”
Michael Atiyah (1929–2019) said by 2019 at the latest wikiquote, CC BY-SA 4.0 source
“Abel... died of tuberculosis before he could get his first job... These two figures are the pioneers of modern mathematics. All that we do... rests on their pioneering work. ...These ...are ...the two most romantic figures in the history of mathematics. We all dote on them. ...We all admire both of them... [T]hey showed... that an equation of degree 5 cannot be solved by... roots, but... you have to solve it by using more complicated... s.”
Michael Atiyah (1929–2019) said by 2019 at the latest wikiquote, CC BY-SA 4.0 source
“[[w:Elliptic function|[E]lliptic functions]]... have something to do with an ellipse... [I]f you go... to elementary calculus... you'll find formulas for the length of the arc of an ellipse. ...[E]lliptic functions come from that term.”
Michael Atiyah (1929–2019) said by 2019 at the latest wikiquote, CC BY-SA 4.0 source
“[T]he come from the circle and the s come from ellipses.”
Michael Atiyah (1929–2019) said by 2019 at the latest wikiquote, CC BY-SA 4.0 source
“[T]here are several circles you can draw in this picture. There is the circle round the outside which goes through the vertices and there's a smaller circle... inscribed to the pentagon.”
Michael Atiyah (1929–2019) said by 2019 at the latest wikiquote, CC BY-SA 4.0 source
“Imagination is a very important part of mathematics. I hope you all possess... imagination.”
Michael Atiyah (1929–2019) said by 2019 at the latest wikiquote, CC BY-SA 4.0 source
“[M]athematicians and codes are well connected in history. One of my predecessors at Oxford was the , Wallis, famous for his formula for pi, and... very popular with both sides in the Civil War... [L]ike von Braun after... [World War 2,].., captured by the enemy, he... went to work on doing codes the other way around. As a mathematician he could survive the civil war... comfortably. ...If you want to survive difficult times... be a mathematician.”
Michael Atiyah (1929–2019) said by 2019 at the latest wikiquote, CC BY-SA 4.0 source
“Poncelet discovered a beautiful theorem that if you have a ... whose vertices are on one ellipse, and whose sides touch another ellipse, then... if there is one solution, there are infinitely many solutions. ...This ...beautiful theorem ...used to be taught ...in schools where they taught geometry. ...[T]he two ellipses, you may think, look very different from two circles, but by elementary you can always move them so that ...they're both circles.”
Michael Atiyah (1929–2019) said by 2019 at the latest wikiquote, CC BY-SA 4.0 source
“I always want to try to understand why things work. I'm not interested in getting a formula without knowing what it means. I always try to dig behind the scenes, so if I have a formula, I understand why it's there. And understanding is a very difficult notion. People think mathematics begins when you write down a theorem followed by a proof. That's not the beginning, that's the end. For me the creative place in mathematics comes before you start to put things down on paper, before you try to write a formula. You picture various things, you turn them over in your mind. You're trying to create, just as a musician is trying to create music, or a poet. There are no rules laid down. You have to do it your own way. But at the end, just as a composer has to put it down on paper, you have to write things down. But the most important stage is understanding. A proof by itself doesn’t give you understanding. You can have a long proof and no idea at the end of why it works. But to understand why it works, you have to have a kind of gut reaction to the thing. You've got to feel it.”
Michael Atiyah (1929–2019) first seen 2016 wikiquote, CC BY-SA 4.0 source
Recorded in: Siobhan Roberts, Michael Atiyah’s Imaginative State of Mind (March 3, 2016) @QuantaMagazine.org Atiyah's response to: Is there one big question that has always guided you?
“Let me go back to the history of 2 dimensional surfaces. ...The great Gauss ...laid the foundations for modern differential geometry. ...Niels Henrik Abel ...studied s and showed for the first time that equations of degree 5 and more cannot be solved in terms of radicals, square roots... [etc.] [H]e brought into the theory of geometry, the complex variables... arising in polynomial equations. ...Bernhard Riemann ...whose collected works occupy one slim volume, but each chapter ...covers whole regions of mathematics.., brought the modern notion of topology into the game, to add to the differential geometry and the algebraic geometry of Gauss and Abel. These are... the three great figures in the [19th century] history of geometry...”
Michael Atiyah (1929–2019) said by 2019 at the latest wikiquote, CC BY-SA 4.0 source
“s, [in] our 2 dimensional study, is a... simple story. The surfaces are all characterized topologically by... the genus. When the genus is 0 the surface is the surface of a sphere, when it's 1, it's the surface of a .., when it's greater than or equal to 2, that's everything else... [T]hese surfaces... can have... metrics describing geometry, and they are characterized by having 0 curvature in the... torus (the torus is flat, in the sense like a ); the sphere, which has positive curvature which curves one way; and the surfaces of negative... [curvature], which curve the other way; where Gauss curvature takes values either zero, plus or minus.”
Michael Atiyah (1929–2019) said by 2019 at the latest wikiquote, CC BY-SA 4.0 source
“As civilization developed, it got new tools. ...Archimedes was supposed to have drawn in the sand ...then they had discovered chalk... [etc.] ...Then we had telescopes.., microscopes, computers ...All these advances in technology, which come indirectly out of the advances in science.., provide... new opportunities. You can look further.., or at things of a very small scale... [W]ith computers we can handle all this information and data at incredible speeds... [W]e have powerful [technological] tools which assist, (I don't say they replace traditional ways of thinking and doing.., but) they... expand your scope. You get new material for each generation... to work on.”
Michael Atiyah (1929–2019) said by 2019 at the latest wikiquote, CC BY-SA 4.0 source
“The is a very important step forward. ...The ...lines which form an outside pentagon ...starting at one point and taking one step [one vertex] at a time at the ...[correct] angles ...after 5 steps you get back to where you started. Supposing you take 2 steps [2 vertices] at a time. That's the... [pentagram] line. You go around that 5 times and... what have you got in the middle? ...Another pentagon. ...[I]f you did it again and... keep going... the pentagon will keep recurring. ...That's why you can't solve the [[w:Quintic function|[quintic] equation]]s. It's as simple as that. If you try it with the or s this doesn't happen. ...[T]his central ...[polygon] only appears at 5.”
Michael Atiyah (1929–2019) said by 2019 at the latest wikiquote, CC BY-SA 4.0 source
“[L]et's stick to odd numbers ... ...means 7-sided figures. ...We have ...on the outside, 7 points .., the vertices ...of a regular ...heptagon. That's going one step [one vertex] at a time... Now let's go 2 steps [vertices] at a time... the... line goes round, and comes back... and you get... another figure. ...You can ...draw a circle through ...vertices ...They will be concentric circles. ...[F]or the heptagon you will find the outside circle and ...two other ones. For the case of the pentagon we had one... big pentagon and a small pentagon. Here you'll find three, and that number keeps going up. If you went up to the next level... you can guess the formula. You'll find all these nested circles... Do I want to look at the circle that circumscribes, or that's inscribed? They're both there, but if you drew them all, the picture would get very complicated. I leave that to your imagination.”
Michael Atiyah (1929–2019) said by 2019 at the latest wikiquote, CC BY-SA 4.0 source