A "shut up and calculate" timeline#

Last tended 2026-02-27

Intro: David Mermin speaks for the pragmatists#

One might say the Copenhagen interpretation of quantum mechanics—thank you Bohr and Heisenberg—spawned decades of angst among scientists. It was a marvel that notions of "observer," "measurement," and "wave" could so thoroughly elude a consensus explanation—or any explanation whatsoever that seemed even remotely intuitive.

But though there was angst and elusiveness in droves, in the end there could be really no dispute that the train had reached the station named "Utility". And so it was that in a 1989 article for Physics Today, David Mermin gave us the pithy advice:

Shut up and calculate!
...if the math works, the underlying "meaning" is secondary (or even a distraction).


I love this Mermin dictum, and it has caused me to ponder the many "shut up and calculate" events in science history where the "calculative" breakthrough preceded the conceptual "map" to underpin it.

A proposed timeline of such events#

Time Milestone Proponent(s) Context
150 CE – 1543 The Ptolemaic / Copernican Epicycles Claudius Ptolemy / Nicolaus Copernicus This is the one "ironic twist" entry in our list where those calculating took their conceptual premise—that everything orbits the Earth in perfect circles—as self evident. So they devised complex "circles within circles" math to accurately predict planetary positions—and calculated away.
1713 Universal Gravitation Isaac Newton In the 2nd ed. of Principia, Newton famously wrote "Hypotheses non fingo" (I frame no hypotheses) to shut down critics asking how gravity worked across a vacuum.
1884 – 1890s Maxwell’s Equations (Simplified) Oliver Heaviside (The "Maxwellians") Heaviside stripped Maxwell's 20 original equations down to 4. He famously dismissed the need for a "mechanical" understanding of the aether in this way: "Shall I refuse my dinner because I do not fully understand the process of digestion?"
1900 Planck’s Law Max Planck Planck derived a formula that perfectly matched blackbody radiation data, but only by assuming energy was "quantized"—an "act of despair" he couldn't physically justify at the time.
1916 Fine-Structure Constant Arnold Sommerfeld Identified as a "magic number" (approx 1/137) to fix the Bohr model's spectral lines. It remains the ultimate "plug it in because it works" constant in physics.
1925 Matrix Mechanics Werner Heisenberg An intentionally abstract formulation of quantum mechanics that discarded "visualizing" the atom entirely in favor of observable mathematical tables (matrices).
1926 Wave Mechanics Erwin Schrödinger Provided the Wave Function, which predicts probabilities with staggering accuracy, despite no consensus then (or now) on what the wave actually represents physically.
1928 – 1931 The Dirac Equation Paul Dirac Dirac trusted the math of his relativistic electron equation so much that he predicted the positron (antimatter) to explain a "negative energy" result he didn't initially understand.
2013 – Present The Amplituhedron Nima Arkani-Hamed / Jaroslav Trnka A geometric "jewel" that allows physicists to calculate particle interactions in seconds rather than months, even though we don't yet know how space and time "emerge" from it—and "emerging" really is the only way whatsoever to describe space and time's part in it.

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