Let me assure you, there are enough evidences of terrorists crossing the borders. With footage available in public domain, there is no point in questioning the fact that terrorists are trying to cross the border into India.
An estimated 60K plus terrorists have been killed by Indian security forces, till date, since insurgency started. Pakistan has been trying to win over that piece of land for about 7 decades with multiple wars and skirmishes fought over it.
That makes it comparable with Operation Overlord, or Allied invasion or France over through the English channel ?
That also makes the endeavour one of the biggest failures in the history of mankind ? Because, so far, India has only gained territory and not lost a single inch to Pakistan ?
The point most people to seem to miss is that all this terrorism and infiltration stopped being about "freedom of kashmir" long long back - 1965 was the last serious attempt. All subsequent actions serve another purpose - prime example is Kargil.
It has to do with politics, diplomacy and economics of containing India.
Think about it a bit my friend. What has insurgency of Kashmir costed India
1. Militarily - India has to maintain an very large army numerically as a preventive measure. It costs us dearly. Delays modernization. A relatively smaller army of 500k - 750k would be a lot leaner, meaner and responsive instead of sluggish and ill equipped one we have now.
2. Economically - No need to elaborate on how much Pakistan and Kashmir specific forces costs us. It diverts essential money from social sector and infrastructure reforms urgently needed to raise the standard of living.
3. Diplomatically - Kashmir and the human rights issues which are absolutely inevitable despite IA practicing utmost restraint and minimum force. They do have to kill terrorists afterall and co-lateral damage will be there. This gives a platform to adversaries to block India at every turn when it aspires to get what it deserves like UNSC seat. Also provides an issue for Islamic countries to not support India whole heartedly in many international forums.
4. Moral - Due to the combination of above issues which has stunted the growth of India our citizens lack the confidence and self- assertiveness necessary to rise from their current status. Many of us specially villages far far from Kashmir pay the price indirectly. Kashmir based terrorism has it's ramification from Mumbai to New Delhi. It drives Hindus against Muslims. Creates social disharmony and discontent.
Pakistan realistically speaking has no even an iota of chance of gaining a single inch of Kashmir so why persist with this folly?
1. Neighbor's Envy.- Doesn't want India to become de-facto power in the region - All such countries ultimately do coerce and impose their will on the smaller and weaker regions
2. External Influences
a. China and India are natural competitors and with billion plus population and limited re-sources sooner or later it is going to be a zero sum game between them. So they do what India would have done had it been in it's position.
b. USA - With USA it was Indian closeness with USSR and cold- war factors which is changing now. It would take another decade for State Dept to shed it's anti India baggage when the old Pakistan hands are either retired or dead.
c. Gulf - They love playing both sides. Although religious fanatics among them can't see any other faith prosper hence the passive support to Pakistan to meddle in India and Kashmir
Solution
1. Stabler Pakistan - It is Pakistan's internal issues and weaknesses vis-a-vis India which makes it insecure. Probably a more prosperous and stable Pakistan would be content with what it has got.
2. Leadership - We need courageous and strong leadership in central in both parties who can with stand the pressure from fanatics on their side and have courage to give up their stated postures of Atoot Ang and Fort of Islam (Thanks Icarus for terminology) and convert LOC to IB.
Regards