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Equation Collections

Curated journeys and emotional collections — from equations that built civilization to the math behind AI.

Emotional collections

epic

Equations That Built Civilization

The formulas that redirected human history.

pythagorean theoremnewtons second lawmaxwell equationseinstein mass energy
cosmic

Equations That Took Us to Space

From Kepler to rockets to cosmology.

keplers lawstsiolkovsky rocket equationnewtons second lawhubble law
futuristic

Equations Behind AI

The mathematics powering modern intelligence.

gradient descenttransformer attentionshannon entropybayes theorem
organic

Equations Inside Your Body

Math governing life and health.

sir modelmichaelis menten equationhardy weinberg equationnernst equation
digital

Equations That Run the Internet

Bits, waves, and networks.

shannon entropypagerank equationmaxwell equationsfourier transform
gold

Equations Behind Money

Finance, risk, and markets.

black scholes equationbayes theoremcobb douglas
earth

Equations Behind Climate

Modeling our planet's systems.

navier stokes equationideal gas lawfriedmann equation
sonic

Equations Behind Music

Harmonics, Fourier, and synthesis.

fourier transformwave equation
velocity

Equations Behind Cars and Planes

Mechanics, fluids, and thermodynamics.

newtons second lawbernoulli equationideal gas lawdrag equation
living

Equations That Explain Life

Growth, genetics, and ecology.

logistic growthlotka volterra equationshardy weinberg equation
infinite

Equations That Explain the Universe

Cosmos from Big Bang to dark energy.

friedmann equationhubble laweinstein field equationsdrake equation
prestige

Equations Worth a Nobel Prize

Breakthrough formulas that changed science.

schrodinger equationeinstein mass energymaxwell equationsdirac equation
mission

Equations Used by NASA and ISRO

Space agency essentials.

tsiolkovsky rocket equationkeplers lawsnewtons second lawhubble law
flow

Equations Used in CFD

Computational fluid dynamics core.

navier stokes equationbernoulli equationreynolds number
engineering

Equations Every Mechanical Engineer Must Know

Core mechanical engineering toolkit.

newtons second lawideal gas lawbernoulli equationyoungs modulus
clinical

Equations Every Doctor Should Know

Clinical and physiological models.

sir modelmichaelis menten equationnernst equationbayes theorem
neural

Equations Every AI Engineer Must Know

ML and deep learning foundations.

gradient descenttransformer attentioncross entropy lossshannon entropy
intense

Equations That Scare Mathematicians

Infamous difficulty and open problems.

navier stokes equationdirac equation
mystery

Equations Nobody Fully Understands

Turbulence, quantum gravity, and more.

navier stokes equationeinstein field equations

Classic collections

Foundational Equations

The equations every scientist should know.

Euler's Identity

eiπ+1=0e^{i\pi} + 1 = 0

Pythagorean Theorem

a2+b2=c2a^2 + b^2 = c^2

Newton's Second Law

F=maF = ma

Bayes' Theorem

P(A∣B)=P(B∣A) P(A)P(B)P(A|B) = \frac{P(B|A)\, P(A)}{P(B)}

Shannon Entropy

H=−∑ipilog⁡2piH = -\sum_{i} p_i \log_2 p_i

Physics Giants

Equations that revolutionized our understanding of reality.

Mass-Energy Equivalence

E=mc2E = mc^2

Schrödinger Equation

iℏ∂ψ∂t=H^ψi\hbar \frac{\partial \psi}{\partial t} = \hat{H}\psi

Maxwell's Equations

∇⋅E=ρε0,∇×E=−∂B∂t\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}, \quad \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}

Universal Gravitation

F=Gm1m2r2F = G\frac{m_1 m_2}{r^2}

Planck's Equation

E=hνE = h\nu

Space Exploration

From Kepler to rockets to cosmology.

Kepler's Third Law

T2=4π2GMa3T^2 = \frac{4\pi^2}{GM} a^3

Tsiolkovsky Rocket Equation

Δv=veln⁡m0mf\Delta v = v_e \ln\frac{m_0}{m_f}

Rocket Thrust Equation

F=m˙ve+(Pe−Pa)AeF = \dot{m} v_e + (P_e - P_a) A_e

Hubble's Law

v=H0dv = H_0 d

Friedmann Equation

(a˙a)2=8πG3ρ−kc2a2+Λc23\left(\frac{\dot{a}}{a}\right)^2 = \frac{8\pi G}{3}\rho - \frac{kc^2}{a^2} + \frac{\Lambda c^2}{3}

Drake Equation

N=R∗⋅fp⋅ne⋅fl⋅fi⋅fc⋅LN = R_* \cdot f_p \cdot n_e \cdot f_l \cdot f_i \cdot f_c \cdot L

AI Revolution

The mathematics powering modern intelligence.

Gradient Descent Update Rule

θt+1=θt−η∇θL(θt)\theta_{t+1} = \theta_t - \eta \nabla_\theta L(\theta_t)

Transformer Attention

Attention(Q,K,V)=softmax(QKTdk)V\text{Attention}(Q,K,V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V

Cross-Entropy Loss

L=−∑iyilog⁡(y^i)L = -\sum_{i} y_i \log(\hat{y}_i)

PageRank Equation

PR(pi)=1−dN+d∑pj∈M(pi)PR(pj)L(pj)PR(p_i) = \frac{1-d}{N} + d \sum_{p_j \in M(p_i)} \frac{PR(p_j)}{L(p_j)}

Shannon Entropy

H=−∑ipilog⁡2piH = -\sum_{i} p_i \log_2 p_i

Life Sciences

Equations modeling living systems.

Hardy-Weinberg Equation

p2+2pq+q2=1p^2 + 2pq + q^2 = 1

Michaelis-Menten Equation

v=Vmax⁡[S]Km+[S]v = \frac{V_{\max}[S]}{K_m + [S]}

SIR Model

dSdt=−βSI,dIdt=βSI−γI,dRdt=γI\frac{dS}{dt} = -\beta SI, \quad \frac{dI}{dt} = \beta SI - \gamma I, \quad \frac{dR}{dt} = \gamma I

Lotka-Volterra Equations

dxdt=αx−βxy,dydt=δxy−γy\frac{dx}{dt} = \alpha x - \beta xy, \quad \frac{dy}{dt} = \delta xy - \gamma y

Logistic Growth Equation

dNdt=rN(1−NK)\frac{dN}{dt} = rN\left(1 - \frac{N}{K}\right)

Engineering Essentials

Core equations for building the physical world.

Ohm's Law

V=IRV = IR

Reynolds Number

Re=ρvLμRe = \frac{\rho v L}{\mu}

Young's Modulus

E=σε=FL0AΔLE = \frac{\sigma}{\varepsilon} = \frac{F L_0}{A \Delta L}

Lift Equation

L=12ρv2SCLL = \frac{1}{2} \rho v^2 S C_L

Drag Equation

D=12ρv2SCDD = \frac{1}{2} \rho v^2 S C_D