Check out the latest article in my newsletter: The new book TOC: linkedin.com/pulse/new-book-… via @LinkedIn
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Projecting 2D closed curves into 1D time-domain waveforms & their live superposition
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Four equations. The complete map of physical reality.
Schrödinger’s equation tracks how a quantum wave function evolves in time under the Hamiltonian. Maxwell’s equations link electric and magnetic fields to charge, current, and light.
Einstein’s field equation equates spacetime curvature to the stress-energy tensor of matter. Dirac’s equation unifies quantum mechanics with special relativity for spin-1/2 particles and predicts antimatter.
They remain the sharpest language we have for how the universe actually works.
Check out the latest article in my newsletter: The new book TOC: linkedin.com/pulse/new-book-… via @LinkedIn
exp(\pi\sqrt(-1))=\pm\pi/2, fixed point...
In April 1975, Martin Gardner published an April Fool's mathematical hoax claiming that this expression was exactly an integer, supposedly following a conjecture by Srinivasa Ramanujan.
It was false—but the number was close enough to fool readers. The near-integer phenomenon had actually been observed by Charles Hermite in 1859, before Ramanujan's work.
This number misses an integer by just 0.00000000000075.
2D complex plane is special...
x² + y² = z² possesses infinitely many solutions in positive integers, the Pythagorean triples. Raise the common exponent by one, or by any larger amount, and those positive integer solutions vanish entirely.
The equation xⁿ + yⁿ = zⁿ therefore changes character with the size of n. For n = 1 the solutions are immediate; for n = 2 they are classical and abundant; for every integer n greater than 2 they do not exist at all. Pierre de Fermat noted the claim in the margin of his copy of Diophantus around 1637; Andrew Wiles supplied the proof in 1995.
Check out the latest article in my newsletter: Laplace operator and analytic functions in polar coordinates linkedin.com/pulse/laplace-o… via @LinkedIn
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A musical chord reaches us as one sound, yet contains several frequencies.
The Fourier transform reveals them. It takes a signal described in time and expresses it in terms of frequency.
The same sound, viewed through a different mathematical lens.
Spider move of a spiderweb... (plus/minus virus)...
Matter doesn't just collide; it rewrites its own fundamental code.
In strong interactions, a proton (uud) and neutron (udd) swap identities. A proton spawns a d + d̅ pair, ejecting the d̅ with a u quark to emit a π⁺ meson, becoming a neutron.
The target neutron absorbs this π⁺. A d quark annihilates with the incoming d̅, absorbing the u quark to emerge as a proton.
Reality is bound by this elegant, endless exchange of existence.
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The Navier-Stokes equations are among the most important — and most challenging — equations in physics. So, what makes them so difficult? And how could a new OpenAI proof finally resolve the problem? Watch our new video: youtube.com/watch?v=PsWR1rQE…
Researchers create DNA computer that performs 100-bit calculations without electricity — molecular system uses self-assembling strands to perform computing tomshardware.com/tech-indust…
