- 1900 Hilbert’s 17th Conjecture: Non-negative Polynomial <=> sum of 2 squares (Proved by Emile Artin in 1927)
- Computing Math : approximate by optimisation with “Linear Programs” which are faster to compute.
- Princeton Mathematicians applied it to self-driving cars.
Sum of 2 Squares <=> always non-negative ( ≥0)
Self-driving Car: Trajectory = P (x)
P(x) < 0 where the car’s position in the trajectory;
Obstacles are positions where P (x) ≥ 0.
This is one of the many cases of Pure Math turned to be Applied Math in last few decades. Other examples:
- Encryption in Blockchain / Bitcoin using Modular Form / Elliptic Curve (with which Prof Andrew Wiles proved the 350-year-old Fermat’s Last Theorem in 1994);
- Linear Algebra (Matrix, eigenVector/eigenValue) used in Google PageRanking Search Algorithm.
Is Applied Math => Pure Math ?
- The ancient“Chinese Remainder Problem” (韩信点兵 ) since Han dynasty (200 BC) was re-discovered by 19 CE Gauss in Modulus Arithmetic (“Number Theory” in Pure Math).