Listed below are the few major point of differences between the Vedic mathematics and modern mathematics. Let us have a look:

Vedic Mathematics 
Modern Mathematics 
Origin 
It is the ancient Indian system which was rediscovered in 1911 to 1918 by Swami Bharti Krishna Tirathji Maharaj 
The advent of Modern Math came from Vedic Math, i.e. Vedic Math is considered to be the ancestor of modern mathematics

Formulas 
There are 16 sutras and 13 sub sutras in the complete system 
There are myriad formulas which are used invariably for different branches

Coherence 
All the formulas and approaches are interrelated and maintains uniformity to derive the answers 
There is no consistency and relation between the formulas as there are different formulas for different topics which cannot be used elsewhere

Approaches or Methods 
The approaches are simple and fast. To derive one answer, more than one approach can be chosen as per convenience 
The approaches are detailed (time consuming) and only one approach has been defined to derive a solution for a particular set of questions

Efficiency 
It involves only 2 or 3 steps to solve a question. 
To derive a correct inference, step by step procedure has to be followed.

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