Question

Do great saints know everything?

Answer

Here is one perspective about 'knowing everything' based on some scriptural statements:

I don't think the saints, mystics or bhaktas would know everything in the sense you have described. Only the Supreme Lord knows everything. The sages can know as much as He allows them to know for their service to Him. We see in Bhagavatam/Mahabharata that Arjuna had so many powers but on an occasion, right after Krishna left the planet, Arjuna says this (copied from here):

I have the very same Gandiva bow, the same arrows, the same chariot drawn by the same horses, and I use them as the same Arjuna to whom all the kings offered their due respects. But in the absence of Lord Krsna, all of them, at a moment’s notice, have become null and void. It is exactly like offering clarified butter on ashes, accumulating money with a magic wand or sowing seeds on barren land.

Commenting on this vers Srila Prabhupda says:

As we have discussed more than once, one should not be puffed up by borrowed plumes. All energies and powers are derived from the supreme source, Lord Krsna, and they act as long as He desires and cease to function as soon as He withdraws.

So the powers the yogis, siddhas or any one else can work only when He permits. The fact that Lord Krishna knows everything is confirmed in the Gita 7.26:

O Arjuna, as the Supreme Personality of Godhead, I know everything that has happened in the past, all that is happening in the present, and all things that are yet to come. I also know all living entities; but Me no one knows.

However it is also said, Yasmin vijnate sarvam evam vijnatam bhavati: If we undertand Him we will understand everything. What He gives us depends on how much and with what intent one surrenders unto Him. That He says in the Gita 4.11:

ye yatha mam prapadyante

tams tathaiva bhajamy aham

As all surrender unto Me, I reward them accordingly.

So the conclusion is the Supreme Lord knows everything and we can know as much as we understand Him and as much as He allows us to know.

Regarding saints having answers to what scientists are trying to findout:

We hear about airplanes, inter planterory travel, traveling on sun-rays, brahmastra and many other mystical things in our Vedic literature. Science is about yantra (mechanical) but the yogic methods are more subtle and function with mantra (mental/verbal). While these existed and exist today the goal of scientists and the saints are generally the opposite. The scientists want to make this material world a comfortable place for sense enjoyment. It says in Gita 'duhkhalayam asasvatam' that material creation is temporary and a miserable place. The essence of Gita is to remind us this human life is meant for self realization and surrender unto the Supreme Lord. Eternal bliss is a by-product of that self realization. So it is natural that our saints emphasized more on spirituality while keeping the material needs to a minimum (needs verses wants). That is why we see that even though the saints were highly intelligent and possessed many powers they didn't care to exhibit them because their goal is non-material. Helping humans escape of millions of births of suffering is more important than giving some sense pleasure in this one lifetime.

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