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Math & Digital Technology
The invention of mathematical software can be called the fifth major change in mathematics. It brought 2 major changes – making manual computational skills redundant and enabling processing of huge amounts of data.
Till about 5 decades back, even the scientific & mathematical world outside school was focussing on calculations with paper & pencil and mechanical calculators.
The past 5 decades have seen the development of software which could perform almost any calculations and even solve differential equations. The outside world quickly saw the advantage. Today almost no adult in a developed economy performs calculations manually.
Locating patterns in real life events needs analysis of vast amounts of data. The advent of AI (Artificial Intelligence), ML (Machine Learning) & Data Mining have accelerated the applications of math to a large number of real-life problems belonging to disparate disciplines.
Knowledge of mathematical techniques is becoming a necessary part of research in any discipline.
Math Today
Digital technology removed the drudgery of computation from math and allowed mathematicians & professionals to focus on the core mathematical issues. It also gave them powerful tools for analysing data.
Doing mathematics today requires a new set of skills required to make effective use of powerful new (procedural) mathematical tools which can be accessed even from our smartphones.
These new skills are in fact much closer to those in the humanities or the creative arts than most people yet realize. Human mind can bring to problems something that computers cannot begin to do, and maybe never will; understanding & intuition.
As of today, there are no topics in mathematics; only artificial barriers that we have erected to help organise the curriculum. At school, we study topics in discrete chunks and come to understand them as separate islands of knowledge. Yet the most powerful and interesting mathematics arises when we cut through these barriers.
This cutting through barriers & connecting seemingly disparate disciplines needs a lot of creative thinking.
There is a lot of freedom in mathematics to ask questions. Because of this freedom, innumerable questions are being asked and many branches of mathematics are emerging. We are also realising that asking relevant questions is more difficult than trying to answer them.
Today there are so many new areas in math that it is difficult for even renowned mathematicians to keep track of all the developments in the field. The days when the field of math was dominated by a Newton or Leibnitz or Gauss, who worked simultaneously in many branches of math, seem to be over.
Mathematics is currently being applied in domains where we have never imagined that it could be, including biological sciences, where cell life, tumor growth, body fluid dynamics, neurophysiology and many other processes and phenomena are described and investigated through precise mathematical models.
It is also true to say that in the absence of mathematics, some theories, like General Relativity Theory, Quantum Mechanics, or Quantum Field Theory (to name just a few) would not even exist.
Today, a background in math has become a necessity to understand and analyse the humongous amounts of data which is being generated in all fields of human involvement.
AI & Math
In brief, while AI includes reasoning, problem-solving, perception, natural language understanding, and decision-making, ML is about pattern training and pattern recognition across a variety of domains.
One may thus even say that ML is a sub-set of AI.
Math is the study of patterns. Artificial Intelligence (AI) technology & algorithms enable analysis of humongous amounts of data. These have thrown up patterns which were missed by mathematicians. In some cases AI has suggested directions for some unproven results in math.
Hence Math & AI are powering each other and becoming a formidable tool for research.
In the near future, AI is expected to take over the task of coding from most human coders! All the efforts to teach coding in schools, therefore would not be fruitful, except to introduce students to the idea of coding and the embedded logic.
An AI called Ithaca, developed by DeepMind, a Google company, is able to predict missing text in ancient Greek inscriptions and estimate the time frame and geographical origin of ancient inscriptions. Ithaca is trained on thousands of existing inscriptions to suggest text to fill the gaps in fragmented writings. Its suggestions tend to match those previously made by academics.
If this strategy is used the interpret the Indus Valley inscriptions, it would be be an invaluable find which will settle many controversies about the Indus Valley Civilization.
But AI needs to become much smarter to interpret daily language. There have been instances of "beach" being transcribed as "bitch", "buster" as "bastard".
Here is a link to a “Map of Mathematics” which shows the huge number of branches of math.
https://www.youtube.com/watch?v=OmJ-4B-mS-Y
The rigid distinction between Applied Math & Pure Math is becoming fuzzy with each intruding into the other domain.
According to mathematicians Terrence Tao “what is required today is a sufficiently deep understanding of all those procedures, and the underlying concepts they are built on, in order to know when, and how, to use those digitally-implemented tools effectively, productively, and safely”.
https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/
The human mind is more powerful than any computer. Rigour should not destroy human intuition. Maybe now we have a better understanding of Ramanujan’s ways of doing math.
Math is Becoming an Universal Language
This is a totally different view of math, from what prevailed just a century earlier.
While trying to communicate with aliens (if any) in the Universe, scientists included some sketches and symbols which display our understanding of mathematics. The underlying assumption was that any "living being" in the universe would also have similar mathematical ideas!
Math is an universal language!
Our education system needs to urgently take note of these developments.
Langlands Project
In the recent years, the realisation that math topics have become far apart have led to a project called "Langlands Project".
While math topics have become numerous and far apart, there is a firm conviction among mathematicians that bridges between these isolated islands can be discovered.
The inspiration started from Ramanujan's work connecting number theory & modular equations.
Another inspiration was the proof of "Fermat's Last Theorem" which took over 250 years to prove and which also bridged seemingly disparate disciplines.
Mathematicians are convinced as collaboration across disciplines increases, these bridges can be discovered or built.
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