Fourier Transformation in Data Science

Data Science =
Math (Fourier FFT) +
AI (Convoluted Neural Network) +
Big Data

丘城桐:基础数学和AI, Big Data

AI and Big Data are Twins, their Mother is Math.

“AI 3.0“ today, although impressive in “DeepLearning“, is still using “primitive” high school Math, namely:

AI has not taken advantage of the power of post-Modern Math invented since WW II, esp. IT related, ie :

That is the argument of the Harvard Math Dean Prof ST Yau 丘城桐 (First Chinese Fields Medalist), who predicts the future “AI 4.0“ can be smarter and more powerful.

… Current AI deals with Big Data:

  1. Purely Statistical approach and experience-oriented, not from Big Data’s inherent Mathematical structures (eg. Homology or Homotopy).
  2. The Data analytical result is environment specific, lacks portability to other environments.

3. Lack effective Algorithms, esp. Algebraic Topology computes Homology or Co-homology using Linear Algebra (Matrices).

4. Limited by Hardware Speed (eg. GPU), reduced to layered-structure problem solving approach. It is a simple math analysis, not the REAL Boltzmann Machine which finds the most Optimum solution.


AI 1.0 : 1950s by Alan Turing, MIT John McCarthy (coined the term “AI”, Lisp Language inventor).

AI 2.0 : 1970s/80s. “Rule-Based Expert Systems” using Fuzzy Logic.

[AI Winter : 1990s / 2000s. Failed ambitious Japanese “5th Generation Computer” based on Prolog-based “Predicate” Logic]

AI 3.0 : 2010s – now. “DeepLearning” by Prof Geoffry Hinton using primitive Math (Statistics, Probability, Calculus Gradient Descent)

AI 4.0 : Future. Using “Propositional Type” Logic, Topology (Homology, Homotopy) , Linear Algebra, Category.

Big Data, Brain Storage

Our brain can store up to 3 terabytes of information, equivalent to 3 sets of this 1-terabyte (TB) hard-disk below.


IBM estimates everyday the world generates 2.5 EXABYTES (EB) of BIG DATA, more than 90% of which was created in the last 2 years via mobile devices (smartphones, tablets).

The next decade will be the “Big Data” Age. Companies and countries which can take advantage of such BIG DATA will rule the market and the world, with accurate forecast of consumer purchasing behavior, investment trends, weather prediction, military espionage, terrorist detection, epidemic prevention, etc.

‘Data-mining’ tools in Analytics applying powerful mathematics will be the tomorrow’s ‘Google Search Engine’. share