Physics & Chemistry

08/24/2026

George Green was a baker and grain miller who became an important mathematician largely through self-study.

He was born in England in 1793 and spent most of his life working in his family business while studying mathematics in his spare time.

He had very little formal education, so it is not fully known how he learned advanced mathematics. Despite this, he developed ideas that later became important in mathematical physics.

In 1828, he published an essay that introduced what we now know as Green’s theorem. In simple terms, Green’s theorem connects what happens along the boundary of a closed region with what happens throughout the area inside it. Instead of calculating certain quantities only along the boundary, we can calculate them by considering the corresponding quantities over the entire region. Green’s theorem is closely related to the divergence theorem and Stokes’ theorem.

Green’s life also shows that important mathematical work can come from people working outside traditional academic settings.

08/24/2026

08/24/2026

Quantization of the Electromagnetic Field ✍️

It explains how light, which once seemed like a smooth and continuous wave, can also behave as a collection of tiny packets of energy called photons. Imagine the electromagnetic field as a vast invisible ocean. In classical physics, this field can carry energy in any amount, but quantum theory reveals that its energy is exchanged in discrete, indivisible steps.

When the electromagnetic field is quantized, each allowed mode of the field behaves like a quantum oscillator. It cannot possess just any arbitrary energy; instead, its energy comes in specific levels. The smallest excitation of a mode is observed as a photon, with its energy determined by the frequency of the electromagnetic wave.

These photons are not simply tiny pieces of light traveling independently—they are quantum excitations of the underlying electromagnetic field. This explains phenomena such as the photoelectric effect, spontaneous emission, and the quantum behavior of light.

Scientists use the quantization of the electromagnetic field as the foundation of quantum electrodynamics (QED), one of the most successful theories in physics. It provides a powerful framework for understanding how light interacts with matter and reveals that beneath the smooth waves of classical electromagnetism lies a world governed by discrete quantum energy.

08/23/2026

On the left is Niels Bohr, one of the pioneers of quantum mechanics. On the right is Albert Einstein, known for his theory of relativity. This photograph was taken in December 1925 at the home of physicist Paul Ehrenfest in Leiden.

Einstein disagreed with the probabilistic nature of quantum theory and famously said, “God does not play dice.” Bohr responded, “Einstein, stop telling God what to do.”

Their disagreement became one of the most important debates in the history of physics. Although they strongly disagreed, they respected each other and continued to engage seriously with each other’s ideas.

08/23/2026

Relativity Numerical.

08/23/2026

Imagine these four in their prime, sitting for the IMO and Putnam with no preparation.
Who scores highest?

08/22/2026

Who's this decimal person?

08/22/2026

Geometry alone can force fluids to obey a one-way rule.

In a Tesla valve the channel’s fixed loops and islands create almost no resistance in the forward direction: fluid glides through smoothly. Reverse the flow and the same geometry spins the fluid into opposing vortices that collide and cancel net progress—no moving parts required.

This pure shape-based rectification now appears in microfluidic chips, battery cooling loops and pulse-jet engines where reliability without wear is essential.

08/21/2026

Eugene Paul Wigner, who knew both Albert Einstein and John von Neumann, made a striking comparison between them. He said:

“I have known a great many intelligent people in my life. I knew Max Planck, Max von Laue, and Wemer Heisenberg. Paul Dirac was my brother-in-Iaw; Leo Szilard and Edward Teller have been among my closest friends; and Albert Einstein was a good friend, too. And I have known many of the brightest younger scientists. But none of them had a mind as quick and acute as Jancsi von Neumann. I have often remarked this in the presence of those men, and no one ever disputed me. [...] But Einstein's understanding was deeper than even Jancsi von Neumann's. His mind was both more penetrating and more original than von Neumann's. And that is a very remarkable statement. Einstein took an extraordinary pleasure in invention. Two of his greatest inventions are the Special and General Theories of Relativity; and for all of Jancsi's brilliance, he never produced anything so original.”