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Q: Geometric brownian motion in stochastic differential equations?
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Did Albert Einstein discovered math?

No he is known for General relativity, Special relativity, Photoelectric effect, Brownian motion, Mass-energy equivalence , Einstein field equations,Unified Field Theory, Bose-Einstein statistics


What is the name of a mathematical model describing a particles haphazard movement?

Brownian motion see http://en.wikipedia.org/wiki/Brownian_motion


What problems did Einstein try to solve?

1. When Maxwell's Equations predict an electro-magnetic wave travelling at a certain speed, what frame is that speed measured from? 2. How to explain the photo-electric effect. 3. How to explain Brownian Motion. 4. Can gravity be added to special relativity? If he had solved any one of the above issues, Einstein would have been regarded as one of the great minds of the 1900s. He solved all of them! However, he was unable to solve either of these: 1) Can the electric field be added to general relativity? 2) Is there a general paradigm for our Universe in which quantum mechanics is only a useful subset of reality? They both remain unsolved today.


How does one express the probability of an event and how does probability relate to science?

The probability of an event is usually expressed as a fraction between 0 and 1 or the corresponding percentage. There are many processes in science that have some random element: from the Brownian motion of molecules in a fluid to genetics. The outcomes cannot be determined in advance: only the probabilities of the possible outcomes.


Is this sequence correct 1-2-5-10-13-26-29-61?

Any ordered set of numbers (and other things) is a sequence. There need not be any discernible pattern to the sequence (Brownian motion, for example), or a pattern which is understood only by the person who defined the sequence. With the last category in mind, every ordered set of numbers is a correct sequence.