**Key Points**:

**1900****Hilbert’s 17th Conjecture****: Non-negative Polynomial <=> sum of 2 squares (**Proved by Emile Artin in 1927)- Computing Math : approximate by optimisation with “
which are faster to compute.**Linear Programs”** - Princeton Mathematicians applied it to self-driving cars.

https://www.wired.com/story/a-classical-math-problem-gets-pulled-into-self-driving-cars/amp

**Explain****: **

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.
- etc.

**Is Applied Math => Pure Math ?**

Yes!

- 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).

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Reblogged this on Singapore Maths Tuition.