This equation transformed how we fight COVID. Here's how.

Joseph Fourier developed this mathematical technique in the early 1800s while studying heat flow. Mathematicians, physicists, and engineers apply Fourier transforms across signal processing, quantum mechanics, and structural biology. The transform earned Fourier lasting recognition as one of history’s most influential mathematical innovations.

Max von Laue discovered X-ray diffraction by crystals in 1912. William Henry Bragg and William Lawrence Bragg (father and son) developed practical crystallography, winning the 1915 Nobel Prize. Dorothy Hodgkin determined vitamin B12 and insulin structures. Modern structural biologists solve tens of thousands of protein structures annually using this technique.

Dorothy Hodgkin pioneered electron density map interpretation, solving complex structures like penicillin, vitamin B12, and insulin. Modern crystallographers computationally generate electron density maps revealing atomic positions. Automated model-building software assists structure determination but human expertise remains essential for map interpretation.

William Lawrence Bragg formulated Bragg’s law at age 22 in 1912. He and his father William Henry Bragg won the 1915 Nobel Prize in Physics—Lawrence remains the youngest Nobel laureate in science. Crystallographers apply Bragg’s law daily to interpret diffraction patterns and calculate crystal structures.

Max Perutz and John Kendrew developed heavy atom isomorphous replacement methods solving the phase problem for myoglobin and hemoglobin in the 1950s-1960s. Jerome Karle and Herbert Hauptman created direct methods earning the 1985 Nobel Prize. Modern crystallographers employ molecular replacement when homologous structures exist.

Jacques Dubochet, Joachim Frank, and Richard Henderson developed cryo-EM techniques earning the 2017 Nobel Prize in Chemistry. The “resolution revolution” beginning around 2013 transformed cryo-EM from low-resolution tool to atomic-resolution technique. Structural biologists now solve thousands of structures annually using cryo-EM.

Kurt Wüthrich developed NMR methods for protein structure determination, earning the 2002 Nobel Prize in Chemistry. Richard Ernst pioneered multidimensional NMR and Fourier transform techniques. Chemists and structural biologists apply NMR to determine structures, study dynamics, and analyze molecular interactions in solution.

Jason McLellan’s research group determined SARS-CoV-2 spike protein structures within weeks of genome release in early 2020. Multiple structural biology teams worldwide rapidly solved spike structures using cryo-EM. These structures guided vaccine development by Moderna, Pfizer-BioNTech, and other manufacturers.

Katalin Karikó and Drew Weissman developed nucleoside modifications enabling stable therapeutic mRNA. Jason McLellan and Barney Graham identified spike-stabilizing mutations based on previous coronavirus structural studies. Vaccine developers at Moderna and BioNTech incorporated these structural insights into COVID-19 vaccines.

Gilead Sciences originally developed remdesivir for Ebola treatment. Structural biologists determined how remdesivir inhibits SARS-CoV-2 RNA polymerase using cryo-EM. Multiple research groups crystallized and imaged remdesivir-polymerase complexes revealing atomic-detail mechanism during COVID-19 pandemic.