Question: When I consider my own existence with respect to time I can imagine three possibilities: 

(1) **Time extends infinitely into the past.** In this case, how can the present, with me in it, exist, since there would be an infinite period of time that existed before the present. That seems illogical. 

(2) **Time had a starting point from which everything in our universe evolved to the present (t=1).** That possibility would require something (God) to start the clock ticking (t=0). But in this case we're back to square 1 with the problem of an infinite past. So the only possibility that makes sense to me is a third possibility 

(3) **Where time is some sort of abstraction in human consciousness that we need in order to relate cause and effect.**

Answer: 
I will attempt to present the stance of physicist [Julian Barbour](https://en.wikipedia.org/wiki/Julian_Barbour), who presented a compelling answer to this question in a lecture I saw him give in Oxford ([this lecture](https://www.youtube.com/watch?v=I5rExaKLEoU)). 

He is firmly *not* in the camp of the latter viewpoint in your title, but I wouldn't necessarily put him in the former camp either. He puts his view of time in terms of the [primary/secondary quality distinction](https://en.wikipedia.org/wiki/Primary/secondary_quality_distinction) and refers to Galileo, who in 1623 classified attributes such as color and sound as secondary characteristics of matter that are perceiver-dependent. Rather than photons entering eyes or vibrations entering ears, in the case of time we have our perception of the *successiveness* of events streaming through the system we know as consciousness. These progressions correspond with an increase in system complexity, with all consciousnesses experiencing a flow of time along a line of increasing complexity.

All in all a fascinating viewpoint that I've hardly done justice here. After the lecture, he recommended that people watch [this video](https://www.youtube.com/watch?v=WKsNraFxPwk) for a more in-depth look (assuming they didn't want to read *[The End of Time](https://en.wikipedia.org/wiki/The_End_of_Time_%28book%29)* or any of his papers) so I will pass that along as well. 

Lastly, I'll add something because it made me laugh and because it is bound to come up if you consider the implications of this position: When someone asked him what all this means about free will, he said “I'm not sure it matters much. It *feels* free anyway, and I'm excited to find out what I'll do next.”
Summations in math are completely true irregardless of "time" so the question itself has no meaning. Yes there is "time" but like gravity "it exists but doesn't mean all that much" until you start talking vast distances (say between Planets.) Yes, "time mattered" when your average speed of travel was at best 4mph across rough terrain going from say Philadelphia to Boston.

But once you fly an SR-71 from LA to New York in 45 minutes time really doesn't matter all that much.

It mattered a lot in the Railroad business as you didn't want two trains travelling on the same tracks in opposite directions "at the same time." But "speed of travel" (time) has been solved by aircraft. Our "modern age" is very much defined by "being put in a hurry" though which perhaps can be explained by the difficult distances "travel" encountered in North America when going by land to anywhere. ("Time is money.") 

This was never really true in Great Britain or Germany though as the terrain, distances and History favored those "with all the time in the World."

Americans were in a hurry...there was gold in California and silver in Nevada. "To get it you had to get there...and fast" apparently...