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20 questions · 12 almanac · 0 findings

Mathematical Analysis

Calculus-based study of limits, functions, and convergence.

Connects to Differential Geometry4 Topology3 Algorithms and Data Structures2 Chaos and Complex Systems2 Condensed Matter Physics2 Algebraic Geometry1 Comparative Anatomy and Morphology1 Everyday and Recreational Physics1 Fluid Dynamics1 History of Science and Scientists1 Nobel Science Prize History1
Almanac A Nautilus Shell Obeys the Same Math as a Soap Bubble
  • What did D'Arcy Thompson argue was shaping biological forms like nautilus shells and coral colonies, besides evolutionary history?
  • How did Thompson's background as a classicist shape the argument and style of On Growth and Form?
  • Why did biologists find On Growth and Form philosophically interesting but experimentally thin?
Almanac A Soap Film Proves Its Own Theorem
  • What contribution did Lars Ahlfors make to the theory of conformal mappings and complex analysis?
  • What is the Plateau problem, and how did Jesse Douglas solve it?
Almanac A Decade's Quiet Math, Finally Counted
  • What problem did Laurent Schwartz's theory of distributions solve for objects like the Dirac delta function?
  • Where do Schwartz's distributions show up in later mathematics and engineering?
Almanac Four Ways to Redraw the Map
  • What does the Atiyah-Singer index theorem connect, and why has it proven useful in physics as well as mathematics?
Almanac Geometry Interrupted by Martial Law
  • What is noncommutative geometry, and how did Alain Connes extend geometric thinking to settings where coordinates do not commute?
Almanac Four Medals, No Shared Ground
  • What are mean-field games, the area of nonlinear partial differential equations Pierre-Louis Lions was recognized for?
Almanac Eighty Years, Then a Woman Won
  • How did Martin Hairer's theory of regularity structures give rigorous meaning to equations physicists already used informally?
  • What kind of chaotic behaviour in dynamical systems did Artur Avila's research bring order to?
Almanac The Applied Mathematician Who Won Anyway
  • What is the theory of hyperbolic conservation laws and shock waves that Lax developed, and where is it used today?
  • Why was Lax's 2005 Abel Prize notable as a first for an applied mathematician?
Almanac When Waves Break, and When They Don't
  • What does it mean for a nonlinear wave equation's solution to 'blow up' in finite time?
  • What is a soliton, and how does it let a wave equation shed energy while the rest of the solution disperses?
  • Why is understanding wave-equation blowup practically important for modeling fluids and fields?