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Emmy Noether’s revolutionary theorem explained, from kindergarten to PhD

A century ago, Emmy Noether published a theorem that would change mathematics and physics. Here’s an all-ages guided tour through this groundbreaking idea.

emmy noether

One hundred years ago, on July 23, 1918, Emmy Noether published a paper that would change science.

She was 36 at the time, working as an unpaid “assistant” under a male colleague because the University of Göttingen did not allow women to become professors. The paper, titled Invariante Variationsprobleme, contained a theorem that launched abstract algebra and linked two fundamental concepts in physics: symmetry and conservation laws.

Her insight was so profound that physicists are still unpacking its implications. “It’s hard to overestimate the importance of Noether’s work in modern physics,” says theoretical physicist Ruth Gregory, a professor at Durham University and a Visiting Fellow at Perimeter.

But what does Noether’s theorem actually tell us? The answer is both intuitive and complicated.

Kindergarten: So, what is Noether’s big idea?

We could think of no one more capable than Chris Ferrie to give an entry-level intro to Noether’s theorem. Ferrie is a quantum physicist with a side-project authoring science books for babies, including Quantum Physics for Babies, General Relativity for Babies, Optical Physics for Babies, and more.

With the help of his sons Max and Wes, he turned Noether’s groundbreaking idea into child’s play — and came up with possibly the most intelligent use of a fidget spinner to date.

High school: How does that link to science?

When Perimeter Director Neil Turok set out on a cross-Canada tour as part of the country’s 150th centenary in 2017, his goal was to inspire young people about the power and joy of science. In his talk, called “We Are Innovators,” Turok described Noether as a “hero” of both science and humanity, whose brilliance was all the more remarkable given the barriers she had to overcome. In this excerpt, Turok demonstrates concepts of Noether’s theorem with a frisbee and a mug, and explains why Noether herself remains an inspiration.

Watch Neil Turok’s full talk, “We Are Innovators”

Undergrad I: What, exactly, is a symmetry?

Noether’s theorem holds implications for many areas of science, including astrophysics and particle physics. Mathematician and cosmologist Ruth Gregory delivered a talk about Noether at Perimeter during the 2015 Convergence conference. First, Gregory takes a closer look at symmetries.

Undergrad II: How does that relate to conservation?

Okay, so there are all different kinds of symmetries in science. What does it mean to say symmetries are inextricably linked to conservation laws? Below, Gregory explores the connection.

Post-graduate: A clue to new science

Noether’s theorem also helps researchers find what cannot be seen. These “hidden symmetries” might not have been found without Noether’s theorem. Below, Gregory explains how Noether’s insights were vital to the development of modern particle theory.

Watch Ruth Gregory’s full talk

PhD: Bring in the field equations.

Feeling well-versed in the concepts underlying Noether’s theorem? Dive in a little deeper with this clip from University of Minnesota math professor Peter Olver, who also spoke about Noether’s influence during the 2015 Convergence conference. Here’s a taste:

Watch Peter Olver’s full talk 

A Force of Nature

Given her incredible contributions to science — particularly amid the obstacles in her way — Emmy Noether was truly a force of nature. Celebrate the accomplishments of Noether and other pioneering women of science by downloading our free “Forces of Nature” poster series. 

women of science

 

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