The Math we learnt in High school is pre-19th Century up to Newtonian Calculus of 17CE.

The birth of Modern Math since 19CE till WW2 is the “Abstract Algebra” from French Revolution Galois “Group Theory” 群论.

After WW2 till now, Mathematics faces the crisis of “Truth”: whether its Foundation is correct.

**3 schools of fight on the Fondation of Mathematics**:

**1. Russell** (Logic with Types to fix the “Russell Paradox” in Set Theory Crisis)

**2. Hilbert** (Axiomatization of all Mathematics)

**3. ****Brouwer** (Intuitionism) against ＂排中律＂ (Law of the Excluded Middle)

**Winner**: **Godel **“The Incomplete Theorem” (不完备定律)

However, the by-product of these 3 school fights give rise to new Math discovery in Machine Proofing (2010s):

**Homotopy Type Theory (HoTT)** = **Logic** (Proof) + **Type** (Intuitionist) + **Topology** (Homotopy).

ie.

Math Proof = Computer Program