main concepts scientists sections
Scientist

Emmy Noether

1882–1935 · Mathematics, theoretical physics
Emmy Noether — an outstanding German mathematician who revolutionized mathematics and theoretical physics. Her most famous work is Noether's theorem, which links the symmetries of physical systems to conservation laws. This theorem became a cornerstone of modern physics, especially in general relativity and quantum field theory. Despite obstacles as a woman in academia, she made fundamental contributions to abstract algebra and was renowned for her original thinking.

Biography

Born in Erlangen to mathematician Max Noether. She studied languages and planned to become a teacher, but later turned to mathematics. Studied at the University of Erlangen, where initially she only audited lectures because women were not allowed to be full students. Later moved to the University of Göttingen, where she worked with David Hilbert and Felix Klein. Due to discrimination, she was long unable to obtain a position, teaching under Hilbert's name. In 1933, being Jewish, she emigrated to the USA, where she taught at Bryn Mawr College and collaborated with the Institute for Advanced Study. She died in 1935 after an operation. Recognition came to her largely posthumously.

Key discoveries

💡 Despite being denied a paid position early in her career, she conducted seminars officially listed under Hilbert's name, and once even gave a lecture under his name when Hilbert himself was ill. Einstein called her 'the most significant creative mathematical genius thus far produced since the higher education of women began.'
"She regarded her methods as methods of work and thinking, which is why they had spread so imperceptibly everywhere."
Concepts
spacetime curvatureexpansion of the universe
Laws
Noether's theoremprinciple of least actionlaw of conservation of momentumlaw of conservation of energylaw of conservation of angular momentumlaw of conservation of electric charge
Scientists
Jacob BekensteinKarl SchwarzschildJoseph WeberAdam RiessChristian DopplerSaul PerlmutterKip ThorneMaarten Schmidt

Related articles

physics.data-an2008-05-222 minarXiv:0805.3464
Hidden Rhythms of El Niño: What Daily Data Reveal
A barometer on the island of Tahiti and a barometer in the Australian city of Darwin show different pressures. Subtract one from the other, and you get a number that climatologists call the Southern Oscillation Index. It changes every day, but within these daily jumps hide steady rhythms, just as the beats of a metronome hide within the noise of an orchestra.
Filippo Petroni·Marcel Ausloos
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Atmospheric and Oceanic Physics2008-10-212 minarXiv:0810.3882
Sunspots and the Paraná's Floods
The Paraná River behaves like a seismograph that records not the shaking of the ground but the pulse of the Sun. A century of daily water-level measurements at the gauging station in the city of Corrientes, 900 kilometers from the river's mouth, shows that when the Sun has many sunspots, the river floods more. This connection is neither accidental nor weak.
P. J. D Mauas·E. Flamenco·A. P. Buccino
Alain AspectAlbert EinsteinAnton ZeilingerSun
SimplePopularAdvanced
Atmospheric and Oceanic Physics2008-12-283 minarXiv:0812.4846
Climate seesaws that get stuck
A seesaw with two children rarely balances perfectly. It tips either left or right, pausing at the extremes for a moment before swinging back. The tropical Pacific behaves similarly: it either warms up off the coast of Peru (El Niño) or cools down (La Niña), and these states can last for months, sometimes over a year.
Tian Ma·Shouhong Wang
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Math Physics2009-03-122 minarXiv:0903.2106
An Air Pendulum Over the Pacific
In the 1920s, British meteorologist Gilbert Walker, trying to forecast monsoons in India, noticed a strange connection: when air pressure rises over the eastern Pacific, it falls over the western Pacific, and vice versa. It was as if a giant air pendulum were swinging along the equator.
Tian Ma·Shouhong Wang
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Atmospheric and Oceanic Physics2010-02-042 minarXiv:1002.1024
The Swing That Ignores the Push: Why the Annual Rhythm Produces a Three-Year Cycle
A swing builds up when you push it in time. But sometimes the person on the swing responds not to every push but to every third one, and the amplitude grows slowly yet inexorably.
A. Bershadskii
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systemsharmonic oscillator
SimplePopularAdvanced
Atmospheric and Oceanic Physics2010-02-262 minarXiv:1003.0028
El Niño's Seasonal Pulse: How Delayed Ocean Waves Lock the Phase
The ocean is like a pendulum with a memory. A push from seasonal winds returns not immediately but months later, when a wave crosses the Pacific. This delay, the authors argue, is what makes El Niño and La Niña repeatedly peak at the same time of year.
Ilya Zaliapin·Michael Ghil
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Dynamical Systems2011-09-132 minarXiv:1109.2818
Climate as a Road Map: Bifurcations and Resonances of El Niño
The Pacific Ocean does not breathe evenly but in bursts. Every few years, its warm waters stir, and then Australia suffocates from drought while Peru is flooded with rain. This phenomenon is called El Niño, and it resembles a traveler wandering along an invisible road map.
Bernd Krauskopf·Jan Sieber
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Popular Physics2011-11-112 minarXiv:1111.2845
Depth as a Measure of Natural Complexity
A team assembling a jigsaw puzzle from random pieces: how many simultaneous moves does it take to complete the picture? If the pieces are independent, they all go down at once. If each piece depends on the previous one, you have to work one at a time. So it is with systems: some states assemble instantly, others require a long sequential effort.
Jon Machta
Henri PoincaréEmmy NoetherJohn von Neumannuniform convergenceoptimization
SimplePopularAdvanced
Chaotic Dynamics2012-01-233 minarXiv:1201.4679
One-Third Resonance: Why Climate and the Sun Swing in Sync
A swing pushed once per second usually oscillates once per second. But if you push it harder and at the right rhythm, it can swing three times slower: one full swing for every three pushes. Physicists call this subharmonic resonance, and it seems to govern the most prominent climate and solar oscillations.
A. Bershadskii
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systemsharmonic oscillator
SimplePopularAdvanced
Atmospheric and Oceanic Physics2012-06-252 minarXiv:1206.5828
El Niño as Conductor: How Climate Ties Together Earth's Rotation and Carbon Dioxide
A vast tongue of warm water rises to the surface of the tropical Pacific, and the entire climate system begins to resonate in unison. This is El Niño, the most powerful natural climate oscillation, affecting weather from Australia to Alaska.
A. Mazzarella·A. Giuliacci·N. Scafetta
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Atmospheric and Oceanic Physics2014-11-042 minarXiv:1411.0815
Ocean Sloshing as a Clock: An El Niño Model via the Mathieu Equation
In 1981, the ocean off the coast of Peru behaved strangely. The warm current that usually arrives every few years changed its rhythm, and scientists still argue about what exactly shifted. A new study offers a simple answer: the ocean sloshes like water in a bowl that is rocked by tides and Earth's rotation.
Paul R. Pukite
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Atmospheric and Oceanic Physics2015-01-262 minarXiv:1501.06265
The Coast as Rain Conductor
The coast works like a conductor: it doesn't create the music, but it sets the rhythm and direction. Every morning, the sun heats the land faster than the sea, and warm air rises over the sand, pulling in a moist breeze from the ocean. By evening, the land cools and the wind reverses. This daily pendulum lines up clouds along the water's edge, like musicians following the baton.
Martin Bergemann·Christian Jakob·Todd P. Lane
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systemscontrol theoryprobability theory
SimplePopularAdvanced
Dynamical Systems2015-06-022 minarXiv:1506.00756
Rhythm Thrown Off by Wind: How Noise Blurs Oscillations
A pendulum swings steadily until gusts of wind disturb it. Each push shifts the rhythm slightly, and soon the beats no longer match the metronome. Natural oscillators live the same way: the heart, populations, climate cycles—they all oscillate, but randomness constantly interferes.
Stilianos Louca
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systemsharmonic oscillatornonlinear dynamicschaos theory
SimplePopularAdvanced
Dynamical Systems2015-11-233 minarXiv:1511.07472
The Pacific Pendulum: Why El Niño Erupts Once a Decade
The Pacific pendulum swings irregularly. Sometimes it barely trembles near the bottom, and sometimes it suddenly makes a giant sweep that disrupts weather across the planet. El Niño, the warm current in the equatorial Pacific, recurs every few years, but truly strong events happen once every 10–20 years, and until now no one could explain why they appear so irregularly.
Andrew Roberts·Esther Widiasih·Axel Timmermann·Christopher K. R. T. Jones·John Guckenheimer
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Geophysics2016-04-063 minarXiv:1604.01742
The Ocean Conducts Its Own Orchestra: How Nonlinear Analysis Reveals Hidden Rhythms of the Indo-Pacific
An orchestra without a conductor: the instruments set their own rhythm. That is how one might describe the climate system of the Indo-Pacific region, where sea surface temperatures oscillate across many time scales, from seasonal to multi-decadal. Previously, to hear a single instrument, you had to pre-tune filters, cutting off everything else.
Joanna Slawinska·Dimitrios Giannakis
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Atmospheric and Oceanic Physics2016-09-293 minarXiv:1609.09185
An Orchestra Without a Conductor: How the Ocean and Atmosphere Strike a Deal
In 1972, anchovies vanished off the coast of Peru. Fishermen were left empty-handed, and the world learned the word El Niño. Since then, scientists have been searching for ways to predict when that warm current will once again upend the planet's weather.
Dimitrios Giannakis·Joanna Slawinska
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Geophysics2016-11-242 minarXiv:1611.09167
The River That Refuses to Speed Up
The Paglia River behaves like a pendulum that resists being pushed. If a sudden influx of water pours in, the river does not keep gaining strength but quickly swings back to its usual level. This behavior is called antipersistence, and it was found in a twenty-two-year record of half-hourly discharge measurements near the Italian town of Orvieto.
Marcel Ausloos·Roy Cerqueti·Claudio Lupi
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Fluid Dynamics2017-05-173 minarXiv:1705.06207
An Orchestra Without a Conductor: Slow Rossby Waves Set the Climate's Rhythm
Over the tropical Pacific, air pressure breathes with periods from two to fourteen years. The barometer on Tahiti rises while it falls in Darwin, Australia, and the entire planet's climate shudders: El Niño arrives. Meteorologists call this the Southern Oscillation and have tracked it for 138 years, but until now they couldn't answer a simple question: where do such periods come from?
T. Elperin·N. Kleeorin·I. Rogachevskii
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Stellar2017-06-282 minarXiv:1706.09105
The Sun's Two Pendulums: How Coupled Oscillations Create a 90-Year Rhythm
Place two pendulums side by side and give one a gentle push; the other will soon pick up the rhythm. This behavior isn't limited to clocks on a shared shelf; it also applies to the plasma inside the Sun. In the star's convection zone, two huge ring-shaped flows circulate: one closer to the surface, the other deeper. Each oscillates with its own period—12.05 and 9.52 years.
Yasushi Muraki
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systemssolar cycle
SimplePopularAdvanced
Chaotic Dynamics2017-07-282 minarXiv:1707.09853
Two Ocean Pendulums Sing in Unison
Two pendulums hang from the same wall, with a spring stretched between them. Each on its own can swing or stay still, but connect them and a shared dance begins: one nudges the other, and oscillations spread through the whole setup. That's how the Pacific Ocean works, where two neighboring regions exchange heat through waves.
Chandrakala Meena·Elena Surovyatkina·Sudeshna Sinha
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systemschaos theory
SimplePopularAdvanced
Dynamical Systems2017-08-073 minarXiv:1708.02334
How an Orchestra Falls Apart: Chenciner Bubbles in a Climate Model
The conductor of an orchestra gradually loses control of the tempo. First, the second violins fall slightly behind, then the cellos speed up, and soon every musician is playing in their own rhythm, even though a minute ago they all followed the same melody.
Andrew Keane·Bernd Krauskopf
Emmy NoetherLev Landauspontaneous symmetry breakingFourier series
SimplePopularAdvanced
physics.gen-ph2017-09-212 minarXiv:1709.07146
An Ocean Thermometer Instead of a Barometer: A New Take on Climate Indices
For a century, climatologists have measured the ocean's pulse with a barometer. Indices like El Niño or the North Atlantic Oscillation are built on atmospheric pressure differences between two points, and then we wonder why rivers don't obey.
Jishi Zhang·Jingrong Lu·Haidong Huang·Xiaoning Liu·Yafeng Zhao·Zhiyang Wang·Jinlei Mo
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Atmospheric and Oceanic Physics2018-03-232 minarXiv:1803.08909
El Niño and the Indian Monsoon: A Connection Under Pressure
The dance between two partners, the ocean and the sky, has been going on for thousands of years. El Niño warms the Pacific, and usually at the same time seasonal rains over India weaken. But in recent decades, the rhythm seems off: rains don't always respond to the warm current.
Mátyás Herein·Gábor Drótos·Tamás Bódai·Frank Lunkeit·Valerio Lucarini
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Atmospheric and Oceanic Physics2018-05-152 minarXiv:1805.05525
The Cold Dance Around Antarctica: A Wave That Never Stands Still
It takes eight years for a wave to circle Antarctica. It carries warmth and cold in turn, and sea ice advances and retreats with its crests. Previously, researchers caught this wave using different methods and saw either a propagating signal or a frozen dipole. Now it's clear: the dipole is just a snapshot of the wave when it stretches between two oceans.
Xinyang Wang·Dimitrios Giannakis·Joanna Slawinska
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Instrumentation2018-05-233 minarXiv:1805.09058
The Forest That Sometimes Falls Silent, Sometimes Sings: The Dynamics of the Drake Equation
The Galaxy is a forest where birds don't start singing right away. First, trees must grow — stars, around which planets eventually appear. The Drake equation counts how many birds might be singing in this forest right now, but it implicitly assumes that their number doesn't change: as many as there are, that's how many there have always been.
A. D. Panov
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Machine Learning2019-02-262 minarXiv:1902.10697
A City as a Single Organism: Water and Electricity Breathe in Unison
Every morning in six American cities, from Chicago to Minneapolis, faucets open at the same time coffee makers switch on. Water and electricity flow through pipes and wires like two connected vessels in the city's body. In the past, utilities monitored these flows separately, as if the organism had no common circulatory system.
Renee Obringer·Rohini Kumar·Roshanak Nateghi
Emmy NoetherHenri PoincaréJohn von NeumannDynamical SystemsWater
SimplePopularAdvanced
Atmospheric and Oceanic Physics2019-09-032 minarXiv:1909.05096
Seasonal Climate Seesaw: How El Niño and the Indian Ocean Dipole Are Linked
On a playground, two swings stand side by side. One child pumps on their own, while the other barely moves until the first gives a push with their foot. Something similar happens in the tropical Pacific and Indian Oceans, except instead of children, there are warm and cold masses of water.
Woosok Moon·John S. Wettlaufer
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Dynamical Systems2019-11-272 minarXiv:1911.12144
The Noise That Conducts the Ocean
Every few years, the Pacific Ocean rearranges itself: warm water from the east flows toward the coasts of South America, and weather goes haywire for six months. This is El Niño, and its arrivals cannot be predicted precisely, even though there is a rhythm to them. A model with 930 variables shows that noise is to blame—random gusts of wind acting like an invisible conductor.
Alexis Tantet·Mickaël Chekroun·J. David Neelin·Henk Dijkstra
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systemschaos theoryharmonic oscillator
SimplePopularAdvanced
Atmospheric and Oceanic Physics2020-01-152 minarXiv:2001.09757
Three Oceanic Conductors Control Iran's Rains
In 2019, northern and southwestern Iran received 50% more rainfall than usual, and rivers overflowed their banks. A year earlier, in 2018, rainfall was 53% below normal, and fields cracked under drought. Such swings are not random; they are responses to three distant oceanic pulses that set the rhythm for Iran's rains.
Majid Dehghani·Somayeh Salehi·Amir Mosavi·Narjes Nabipour·Shahaboddin Shamshirband·Pedram Ghamisi
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
stat.ME2020-07-013 minarXiv:2007.00267
Causality That Flips Sign: How Regimes Shape Connections
In a tropical forest, the dry season gives way to the rainy season, and with the weather, the rules of life change: some animals go into hibernation, while others come out of hiding. Likewise, in complex systems, from climate to economics, the links between processes are not set in stone. They depend on a hidden "regime" that itself switches from time to time.
Elena Saggioro·Jana de Wiljes·Marlene Kretschmer·Jakob Runge
Emmy NoetherHenri PoincaréJohn von NeumannDynamical SystemsMarkov chainMarkov chains
SimplePopularAdvanced
Atmospheric and Oceanic Physics2020-07-233 minarXiv:2007.15637
El Niño vs. Solar Panels
Over the Pacific Ocean, giant seesaws swing back and forth. Warm water pushes against the coasts of South America, and El Niño begins; a few years later, the ocean surface cools, and the seesaw tips the other way, into La Niña. These oscillations last for years and reshape cloud cover, rainfall, and wind across an entire continent.
Thiago B. Murari·Aloisio S. Nascimento Filho·Marcelo A. Moret·Sergio Pitombo·Alex A. B. Santos
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Atmospheric and Oceanic Physics2020-09-142 minarXiv:2009.09902
The Climate House of Cards: Where Does the Stability Limit Lie?
Imagine a house of cards where each card supports the others. One wobbles, and the neighbors start to lean. Earth's climate system works similarly: ice sheets, ocean currents, tropical forests, all are connected. If one element crosses a threshold, it can drag the rest down with it.
Nico Wunderling·Maximilian Gelbrecht·Ricarda Winkelmann·Jürgen Kurths·Jonathan Donges
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Atmospheric and Oceanic Physics2020-12-093 minarXiv:2012.04996
How Soil Breathes: Nonlinear Rhythms of Global Moisture
Soil breathes. The top layer of the earth takes in moisture after rain, then releases it into the air, much like lungs inhale and exhale. This inhalation and exhalation happens everywhere on the planet, but its rhythm is not uniform: in some places it is fast and steady, in others irregular and deep.
Diego Bueso·Maria Piles·Gustau Camps-Valls
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Atmospheric and Oceanic Physics2020-12-183 minarXiv:2012.09858
El Niño: A Pendulum Rocked by Seasonal Gusts
In the tropical Pacific Ocean lives a pendulum. Its position is the water temperature in the Niño 3.4 region, and gravity is the annual cycle that pulls the system toward warm or cold extremes. Random wind gusts strike the pendulum, and each hit either amplifies the swing or damps it.
L. T. Giorgini·W. Moon·N. Chen·J. S. Wettlaufer
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Atmospheric and Oceanic Physics2021-01-123 minarXiv:2101.04521
The Monsoon's Icy Pulse: How Cloud Ice Predicts Rain
Every summer, a giant atmospheric engine unfolds over India: moist ocean winds bring the rains that sustain crops and the lives of two billion people. But this engine sputters, and forecasting it a season ahead remains elusive. Models give only rough answers, and a monsoon forecast error can cost millions of tons of food.
Ushnanshu Dutta·Anupam Hazra·Subodh Kumar Saha·Hemantkumar S. Chaudhari·Samir Pokhrel·Mahen Konwar
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Atmospheric and Oceanic Physics2021-04-073 minarXiv:2104.02902
El Niño in a New Light: Operator Spectroscopy of Climate
The ocean off the coast of Peru warms and cools, and with it the whole planet runs a fever: rains flood deserts, and tropical forests dry out. This is El Niño, the most noticeable climate oscillation after the changing seasons. For half a century, it has been described by a single number: the water temperature in a small square of ocean.
Gary Froyland·Dimitrios Giannakis·Benjamin Lintner·Maxwell Pike·Joanna Slawinska
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Atmospheric and Oceanic Physics2021-04-152 minarXiv:2104.07174
Three Rhythms of El Niño: A Model of Complexity
An orchestra of three conductors governs the Pacific climate. The first conductor is intraseasonal wind bursts, blowing now from the west, now from the east, like random plucks on strings. The second is the interannual ocean dynamics, slowly rocking warm and cold waves.
Nan Chen·Xianghui Fang·Jin-Yi Yu
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
Atmospheric and Oceanic Physics2021-04-263 minarXiv:2104.12306
Monsoon Season: How a Single Index Captures India's Mosaic
Every summer, the same scene unfolds over India: clouds driven from the ocean by the wind release their rain, and how that rain falls on the fields determines the harvest for more than a billion people. Meteorologists have long tried to reduce this mosaic to a single number, the all-India rainfall index, which averages millimeters across the country.
Spencer A Hill·Adam H Sobel·Michela Biasutti·Mark A Cane
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced
stat.ME2021-12-093 minarXiv:2112.04843
The Uneven Pulse of Time: How Irregular Measurement Rhythms Skew Conclusions and What to Do About It
Imagine an interpreter who gets distracted by every rustle in the hall. The more rustles, the more errors in the translation, even though the meaning of the speech hasn't changed. The same happens with data: if measurements are unevenly spaced, standard analytical tools start "hearing" changes that never occurred in the underlying process.
Tobias Braun·Cinthya N. Fernandez·Deniz Eroglu·Adam Hartland·Sebastian F. M. Breitenbach·Norbert Marwan
Emmy NoetherJohn von NeumannLeonhard Eulerstochastic processes
SimplePopularAdvanced
Atmospheric and Oceanic Physics2022-06-143 minarXiv:2206.06649
Three Pendulums on a Shared Spring: How a Simple Model Explains El Niño's Whims
Three pendulums hang from a long rope attached to the ceiling. One swings fast, another slow, and the third sometimes freezes and then lurches. But the rope is shared, so each jerk of one is felt in the motion of the others.
Nan Chen·Xianghui Fang
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
SimplePopularAdvanced