Imagine you are on vacations with no laptop or internet connectivity and suddenly there is a need for drafting a horoscope as some one falls ill or some mishap has occured. How would you do the complex calculations to find the rising sign at your place, longitudes of all planets etc? It would be a big task but Ancient Mathematics enables us to do the same in a few minutes without any computers and that too accurately! Thats the beauty of the Ancient Mathematics.
Prediction of eclipses( there's an extensive use of 3D Geometry and intensive calculations are involved) may make any modern Mathematician sweat doing it without computers and also the ideas 3D Geometry could well be extended from the first principle of Einstein's Geometry( Riemann Geometry, 4D Geometry)
Now let me ask you a question - do you use Google search or facebook or linked in? I am sure, you do, and the good news is that Ancient Mathematics could be applied to improve upon the speed of responses further from all these & more. Ancient Mathematics enables a lot of work to be done at a level which makes things much faster.
Also if we look at the world around us all that has come up like air-conditioner or fan in your office, buildings, cars, internet etc, have a usage of mathematics in their inventions. The base of all this as you know is Engineering Mathematics. If Mathematics were not there - these gadgets would not have been invented!
Now Electrical Engineers use Laplace transform or differential equations to solve problems to do with circuits or control systems, all this can be tackled much faster by the use of Ancient Mathematics.
The music you hear or the movie you watch - before it reaches you, it may have a lot of Mathematics from Fourier analysis applied on to it. Once again Ancient Mathematics provides powerful alternate insights to do things faster and also understand and master the relevant mathematics, more easily.
While Flying in an aircraft don't forget the complex analysis used to design wings - all this is also better tackled by Ancient Mathematics (better tackled means = faster to do computations and easier to understand by the Mathematician/ Engineer).
The credit goes to untiring work done by Mr. Tan (his great and inspiring books), which have provided the bridge of Ancient Indian Mathematics from swami ji to the present state of the art. It enables us to be able to effectively look at most of the Engineering problems from Ancient Mathematics perspective as well apart from the Modern Maths. This indeed is a great leap for Ancient Mathematics!! Now the roads are open for more exploration.
A food for thought for all of us(courtesy Mr.Tan) - we have Trigonometry,3D Geometry, Complex Analysis, Vectors, Coordinate Geometry - all targeted to look at the properties of 3D space! Why so much of cluttering? No one has asked this question.
Ancient Mathematics' approach sort of integrates our views to look at these different areas in a unified manner. It is the unification (synthesis) as Mr.Tan suggested to me that makes the difference between Ancient Mathematics and Modern Mathematics.
Also one could apply a lot of ideas of limits, Pythagoras Theorem within Ancient Mathematics and extend them for n number of dimensions (ekadhika rule) and see how beautifully Ancient Mathematics helps us look at things from a different perspective.
Ancient Mathematics helps the mind to go to the roots of problem and it also solves it - thus helping us in other areas as well, like Management, Physics etc. It helps in building alternative solutions to a given problem.
Last but not the least -It's all hands on, the proof of the pudding is in eating! The speed of execution/computation by Ancient Mathematics and the ease to learn it can be demonstrated experimentally for any specific area in Engineering along with two groups of people one looking at the use of Modern Mathematics and the other doing it by Ancient Mathematics. I am sort of convinced that all this can be empirically established. All real and doable!!!
Best wishes and a happy journey through Ancient Mathematics!
It has been a matter of great pleasure and pride for me to be a student of Ancient Indian Mathematics which is also used to predict eclipses accurately! And at the same time being a humble student of Mr. Tan who has been guiding me through my journey of Ancient Mathematics.