Not alone in among any list of top mathematicians, Fefferman was a child prodigy. He received degrees in mathematics and physics at the University of Maryland at age 17. He received his Ph.D. in Mathematics at Princeton University in three years and by 22 he was full professor at the University of Chicago, the youngest full professor ever in the United States. At the ripe old age of 24, he returned to Princeton as full professor and has been there since. In 1984, he became Herbert Jones Professor of Mathematics at Princeton. Not surprisingly, the prodigy Fefferman won the Fields Medal in 1978.

Fefferman’s work in mathematics is focused primarily on partial differential equations, having unknowns that require modeling. Partial differential equations often have useful applications in computer models of complex systems, like weather forecasting and climate change. In addition to his career working out important results in partial differential equations, Fefferman has been extraordinarily prolific in diverse topics in the study of mathematics, from the mathematics involved in financial prediction, to fluid dynamics in, say, turbulent systems (i.e., chaos theory) to the study of neural networks in computer science (neural networks are an important topic in machine learning).

In addition to the Fields Medal, Fefferman won the Wolf Prize in Mathematics in 2017, and is a fellow of the National Academy of Science as well as the American Academy of Arts and Sciences.

**Featured in Top Influential Mathematicians Today**

According to Wikipedia, Charles Louis Fefferman is an American mathematician at Princeton University, where he is currently the Herbert E. Jones, Jr. '43 University Professor of Mathematics. His primary field of research is mathematical analysis.

- Hp spaces of several variables
- Weighted norm inequalities for maximal functions and singular integrals
- Some Maximal Inequalities
- The Bergman kernel and biholomorphic mappings of pseudoconvex domains
- Inequalities for strongly singular convolution operators
- the uncertainty principle
- The Ambient Metric
- The Multiplier Problem for the Ball
- Nodal sets of eigenfunctions on Reimannian manifolds
- Monge-Ampere equations, the Bergman kernel, and geometry of pseudoconvex domains*
- Characterizations of bounded mean oscillation
- Wave packets and fourier integral operators
- Geometric constraints on potentially singular solutions for the 3-D Euler equations
- On the Bergman kernel and biholomorphic mappings of pseudoconvex domains
- A note on spherical summation multipliers
- Parabolic invariant theory in complex analysis
- $Q$-Curvature and Poincaré Metrics
- C., L^2 cohomology and index theorem for the Bergman metric
- Honeycomb Lattice Potentials and Dirac Points
- Pointwise Convergence of Fourier Series
- Testing the Manifold Hypothesis
- On the convergence of multiple Fourier series
- Fundamental solutions for second order subelliptic operators
- On Local Solvability of Linear Partial Differential Equations
- Interpolation between ^{} spaces: the real method
- On the divergence of multiple Fourier series
- Ambient metric construction of Q-curvature in conformal and CR geometries
- Relativistic Stability of Matter - I
- Higher order commutator estimates and local existence for the non-resistive MHD equations and related models
- Can one learn history from the allelic spectrum?
- A sharp form of Whitney's extension theorem
- Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
- Strictly pseudoconvex domains in $C^n$
- Whitney’s extension problem for $C^m$
- Nodal sets for eigenfunctions of the Laplacian on surfaces
- Correction to "Monge-Ampere Equations, the Bergman Kernel, and Geometry of Pseudoconvex Domains"
- Hölder estimates on domains of complex dimension two and on three dimensional CR manifolds
- Lp bounds for pseudo-differential operators
- Growth of solutions for QG and 2D Euler equations
- On positivity of pseudo-differential operators.
- Finite time singularities for the free boundary incompressible Euler equations
- A weighted norm inequality for singular integrals
- EXISTENCE & SMOOTHNESS OF THE NAVIER–STOKES EQUATION
- Whitney’s extension problems and interpolation of data
- Wave Packets in Honeycomb Structures and Two-Dimensional Dirac Equations
- The uncertainty principle and sharp gårding inequalities
- On the energy of a large atom
- C m extension by linear operators
- Breakdown of Smoothness for the Muskat Problem
- Regularity of Coupled Two-Dimensional Nonlinear Fokker-Planck and Navier-Stokes Systems
- On the Dirac and Schwinger Corrections to the Ground-State Energy of an Atom
- On the Collapse of Tubes Carried¶by 3D Incompressible Flows
- Nodal Sets of Eigenfunctions: Riemannian Manifolds With Boundary
- Interpolation and extrapolation of smooth functions by linear operators
- Hölder estimates on CR manifolds with a diagonalizable Levi form
- On Squirt Singularities in Hydrodynamics
- Local Existence for the Non-Resistive MHD Equations in Nearly Optimal Sobolev Spaces
- Fitting a Cm-smooth function to data, III
- Fitting a $C^m$-Smooth Function to Data II
- Asymptotic neutrality of large ions
- Eigenvalues and eigenfunctions of ordinary differential operators
- A Generalized Sharp Whitney Theorem for Jets
- Growth and geometry of eigenfunctions of the laplacian
- Edge States in Honeycomb Structures
- Aperiodicity of the Hamiltonian flow in the Thomas-Fermi potential.
- The thermodynamic limit for a crystal
- Honeycomb Schrödinger Operators in the Strong Binding Regime
- The Density in a One-Dimensional Potential
- Sobolev extension by linear operators
- Strictly pseudoconvex domains in $C^n$
- Stability of Ultraviolet-Cutoff¶Quantum Electrodynamics with Non-Relativistic Matter
- On the absence of splash singularities in the case of two-fluid interfaces
- A Radon-Nikodym theorem for finitely additive set functions
- Topologically protected states in one-dimensional continuous systems and Dirac points
- The Eigenvalue Sum of a One-Dimensional Potential
- Fitting a Cm-Smooth Function to Data
- Two nonequivalent conditions for weight functions
- The N-body problem in quantum mechanics
- Topologically Protected States in One-Dimensional Systems
- Extension of C-Smooth Functions by Linear Operators
- Juhl's formulae for GJMS operators and Q-curvatures
- The Atomic and Molecular Nature of Matter.
- Scalars convected by a two‐dimensional incompressible flow
- Almost sharp fronts for the surface quasi-geostrophic equation.
- Splash singularity for water waves
- Finiteness Principles for Smooth Selection
- A spherical surface measure inequality for convex sets
- Behavior of several two-dimensional fluid equations in singular scenarios
- Scaling exponents in fluid turbulence: some analytic results
- Stability of Coulomb systems in a magnetic field.
- Splash Singularities for the One-Phase Muskat Problem in Stable Regimes
- The canonical seminorm on Weak L
- Maximal seminorms on Weak $L^{1}$
- Finite time singularities for water waves with surface tension
- Extension of $C^{m, \omega}$-Smooth Functions by Linear Operators
- Interpolation of data by smooth non-negative functions
- An upper bound for the number of electrons in a large ion.
- Reconstructing a neural net from its output
- The Density in a Three-Dimensional Radial Potential
- Interval Arithmetic in Quantum Mechanics
- Estimates for double Hilbert transform
- ESTIMATES FOR THE BERGMAN AND SZEGÖ PROJECTIONS FOR PSEUDOCONVEX DOMAINS OF FINITE TYPE WITH LOCALLY DIAGONALIZABLE LEVI FORM
- Turning waves and breakdown for incompressible flows
- Nodal domains and growth of harmonic functions on noncompact manifolds
- Simultaneous approximation in Lebesgue and Sobolev norms via eigenspaces
- A Lieb-Thirring Bound for a Magnetic Pauli Hamiltonian
- On electrons and nuclei in a magnetic field
- Waves in Honeycomb Structures
- Analytic Sharp Fronts for the Surface Quasi-Geostrophic Equation
- The Eigenvalue Sum for a Three-Dimensional Radial Potential
- Bifurcations of edge states -- topologically protected and non-protected -- in continuous 2D honeycomb structures
- An Easy Proof of the Fundamental Theorem of Algebra
- Almost Sharp Fronts for SQG: The Limit Equations
- Estimates of Kernels on Three-Dimensional CR Manifolds.
- Defect Modes for Dislocated Periodic Media
- On hypoellipticity of second order operators
- Recovering a Feed-Forward Net From Its Output
- The Structure of Linear Extension Operators for $C^m$
- Reconstruction and Interpolation of Manifolds. I: The Geometric Whitney Problem
- An example related to Whitney extension with almost minimal $C^m$ norm
- Continuous Solutions of Linear Equations
- Lower bounds for Schrödinger equations
- Fitting a Putative Manifold to Noisy Data
- Essays on Fourier analysis in honor of Elias M. Stein
- A local Bernstein inequality on real algebraic varieties
- The $C^m$ Norm of a Function with Prescribed Jets II
- Splash Singularities for the Free Boundary Navier-Stokes Equations
- The Ambient Metric (AM-178)
- Bernstein's inequality on algebraic curves
- The Cm Norm of a Function with Prescribed Jets I
- Photonic realization of topologically protected bound states in domain-wall waveguide arrays
- Potato Chip Singularities of 3D Flows
- The spine of an SQG almost-sharp front
- Bernstein’s inequality and the resolution of spaces of analytic functions
- On the asymptotic eigenvalue distribution of a pseudo-differential operator.
- Construction of Almost-Sharp Fronts for the Surface Quasi-Geostrophic Equation
- Fitting a Sobolev function to data I
- Stability of nonrelativistic quantum mechanical matter coupled to the (ultraviolet cutoff) radiation field.
- Sharp Finiteness Principles For Lipschitz Selections
- Lp spaces over finitely additive measures
- Edge States of continuum Schroedinger operators for sharply terminated honeycomb structures
- A Lieb-Thirring bound for a magnetic Pauli Hamiltonian, II
- Classes of spatially inhomogeneous pseudodifferential operators.
- The Jet of an Interpolant on a Finite Set
- Smooth Interpolation of Data by Efficient Algorithms
- Structural stability for the splash singularities of the water waves problem
- A number-theoretic estimate for the thomas-fermi density
- The Brenner-Hochster-Koll\'ar and Whitney Problems for Vector-valued Functions and Jets
- ON KOHN’S MICROLOCALIZATION OF ∂̅ PROBLEMS
- Convergence on almost every line for functions with gradient in $L^p({\bf R}^n)$
- Symplectic geometry and positivity of pseudo-differential operators.
- A geometrical constraint for capillary jet breakup
- A trigonometric sum relevant to the nonrelativistic theory of atoms.
- Continuum Schroedinger operators for sharply terminated graphene-like structures.
- The Structure of Sobolev Extension Operators
- FIXED POINT FORMULA FOR THE BERGMAN KERNEL
- A planar face on the unit sphere of the multiplier space _{}, 1<<∞
- Stability of matter with magnetic fields
- The Energy Asymptotics of Large Coulomb Systems
- Interpolation by linear programming I
- Singular integral operators with complex homogeneity
- The Euler and Navier-Stokes equations
- On the lowest eigenvalue of a pseudo-differential operator.
- Drops: The collapse of capillary jets
- Extensions, interpolation and matching in $R^D$
- Erratum: Pointwise convergence of Fourier series
- A BMO theorem for -distorted diffeomorphisms on ℝD and an application to comparing manifolds of speech and sound
- Nearly optimal interpolation of data in C2(R2). Part I
- Fitting Smooth Functions to Data
- Selected theorems by Eli Stein
- Scalars convected by a 2D incompressible flow
- A Planar Face on the Unit Sphere of the Multiplier Space M p , 1 < p < ∞
- Pseudo-differential operators with positive symbols
- No-splash theorems for fluid interfaces
- A note on joint analyticity
- Generators for the $C^m$-closures of Ideals
- Advances in Analysis: The Legacy of Elias M. Stein
- Continuous linear combinations of polynomials
- Reconstruction of a Riemannian Manifold from Noisy Intrinsic Distances
- On L p Estimates of the Cauchy-Riemann Equation
- Efficient Algorithms for Approximate Smooth Selection
- Fitting a manifold of large reach to noisy data
- The spin of the ground state of an atom
- Some examples of C infty extension by linear operators.
- On Extensions of e Diffeomorphisms
- Solutions to A System of Equations for $C^m$ Functions
- The volume near the zeroes of a smooth function
- Non-conservation of dimension in divergence-free solutions of passive and active scalar systems
- On Smooth Whitney Extensions of almost isometries with small distortion, Interpolation and Alignment in $\Bbb R^D$-Part 1
- Extensions in $\mathbb R^D$
- The mathematics of large atoms
- The work of
- Editor's note on papers by Harvey-Lawson and by Luk-Yau
- The Bergman Kernel in Quantum Mechanics
- Analysis and applications: The mathematical work of Elias Stein
- A local Bernstein inequality on real algebraic varieties
- Some examples of C ∞ extension by linear operators
- Examples concerning Whitney's Cm extension problem
- Lower Bound on Quantum Tunneling for Strong Magnetic Fields
- Sharp finiteness principles for Lipschitz selections: long version
- $C^2$ Interpolation with Range Restriction
- Chapter Four. Poincaré Metrics
- On the Whitney distortion extension problem for $C^m(\mathbb R^n)$ and $C^{\infty}(\mathbb R^n)$ and its applications to interpolation and alignment of data in $\mathbb R^n$
- $C^m$ Semialgebraic Sections Over the Plane
- One Selected Theorems by
- Finiteness Principle II
- Erratum: Fitting a Cm-smooth function to data II (Revista Matematica Iberoamericana (2009) 25:1 (49-273))
- Chapter Nine. Scalar Invariants
- On Euclidean Motions, Distorted Smooth Extensions, Alignment and Interpolation of Data in $\Bbb R^D$
- BERNSTEIN^S INEQUALITY ON ALGEBRAIC CURVES by Charles FEFFERMAN and Raghavan NARASIMHAN
- Lower bounds for pseudo-differential operators
- Pseudo-differential operators with symbols admitting negative values
- 3 0 Ja n 20 01 Scalars convected by a 2 D incompressible flow
- WEIGHTED BOUNDEDNESS OF THE FRACTIONAL MAXIMAL OPERATOR AND RIESZ POTENTIAL GENERATED BY GEGENBAUER DIFFERENTIAL OPERATOR
- L(2) Cohomology of the Bergman metric.
- A BMO theorem for $\epsilon$ distorted diffeomorphisms from $\mathbb R^D$ to $\mathbb R^D$ with applications to manifolds of speech and sound
- 2 Estimates for solutions of the heat equation in Sobolev spaces 2 . 1 Energy estimates
- Elias M. Stein (1931–2018)
- Louis Nirenberg (1925–2020)
- About the cover: Tribute to Elias Stein
- Carleson's theorem
- Chapter Eight. Jet Isomorphism
- Chapter Six. Conformal Curvature Tensors
- On Whitney Extensions of almost isometries with small distortion, Interpolation and Alignment in $\Bbb R^D$
- Whitney problems for Sobolev functions
- ON SQUIRT SINGULARITIES
- On Distorted Smooth Extensions, Euclidean Motions and Alignment and Interpolation of Data in $\mathbb R^D$ II
- THEoREM 1. Let f = (f,, f ) be a sequence of functions on Rn. Form the sequence f*, whose hc-th term is the maximal function of fk. Then
- Sharp and almost-sharp fronts for the SQG equation
- ABSTRACTS OF TALKS WHITNEY WORKSHOP, BANFF 2013, AS OF APRIL 24
- A BMO theorem for $\epsilon$ distorted diffeomorphisms on $\mathbb R^D$ and an application to comparing manifolds of speech and sound
- The work of terence tao
- Chapter Seven. Conformally Flat and Conformally Einstein Spaces
- Anupperboundforthenumberofelectrons inalarge ion
- Erratum: Fitting a $C^m$-smooth function to data II
- Formation of Singularities in Fluid Interfaces
- Chapter Five. Self-dual Poincaré Metrics
- C A ] 1 7 Ju l 2 02 1 C 2 Interpolation with Range Restriction
- Optimal control with learning on the fly: a toy problem
- Conformal invariants
- III.23 The Euler and Navier–Stokes Equations
- Chapter One. Selected Theorems by Eli Stein
- On some singular convolution operators
- On the Atomic Energy Asymptotics
- The final oral exam
- Chapter Three. Formal Theory
- Chapter Two. Ambient Metrics
- PRELIMINARY VERSION Fitting a C m-Smooth Function to Data
- Invariant Curves for Degenerate Hyperbolic Maps of the Plane
- Cardinally Maximal Sets of Non‐Equivalent Order Types
- On the Whitney Extension-Interpolation-Alignment problem for almost isometries with small distortion in $\Bbb R^D$
- Chapter Two. Eli’s Impact: A Case Study
- V.5 Carleson’s Theorem
- WKB and the Periodic Table
- Number Theory and Atomic Densities
- Princeton lectures in analysis by Ellias M. Stein and Rami Shakarchi- A book review
- Water Waves With or Without Surface Tension

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