You need tools to prove something and mathematics is widely accepted as a tool to prove all kinds of things...

6 apples = 2 x 3 apples

Mathematical operations like addition, multiplications etc usually are dealing with numbers or variables representing the quantification of units.
The type of units can be all kind of things like hours in time, feet or meter in space, lbs or kg in weights etc.
Notice, the process of quantification involves taking measurements in finite. One minute = 60 seconds like a stop watch we chop it off the starting time to the end of time measurements. The distance between LA to NY is x miles. In other words, the measurements in finite = the end point - starting point.
All kinds of things in reality can be measured in finite way and has to be measured this way.

What is reality? It's just an event that exists in the space-time dimension. Bill Clinton as a president (time ref.point= between period of 1992-2000; space ref. point= in US) was a reality. Bush is a son of a ....(well, that's arguable)...But, It's not realistic to say Blair is a president of United States (since time and space ref.points= nada). In other words, Blair as the president of United States is an imaginary event.

'Things' in reality by its very nature is limited. The unlimited thing or infinite only exists in mathematical mind or mindscape or whatever you want to call it.
Since human part of 'Things in reality' the way our mind works is limited or finite hence our logic does not build well to deal with infinity.

The problem arises when our finite mind try to deal with infinity. In early 1600s Galileo nicely asserted: "When we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this I think is wrong, for we cannot speak of infinite quantities as being the one greater or less than or equal to another"

This assertion is supported by an example called Galileo's paradox:
1->1; 2->4; 3->9; 4->16; 5->25; 6->36...

The paradoxical situation arises because, on the one hand, it seems evident that most natural numbers are not perfect squares (2,4,9 etc); so that the set of perfect squares is smaller than the set of all natural numbers; but, on the other hand, since every natural number is the square root of exactly one perfect square, it would seem that there are just as many perfect squares as natural numbers.

Galileo said:"We can only infer that the totality of all numbers is infinite, and that the number of squares is infinite...;neither is the number of squares less than the totality of all numbers, nor the latter greater than the former; and finally, the attributes 'equal', 'greater', and 'less' are not applicable to infinite, but only to finite quantities."

Note, Galileo himself did not really know how to deal with this situation; this was to be the task of Georg Cantor, some 250 years later. In other words, infinite has a different set of rules, a different arithmetics from finite numbers.

Everyone who has ever survived a first year calculus course knows, the formula:
(f(x+dt) - f(x)/dt)

The quantity dt is called an infinitesimal, and obeys many strange rules. if dt is added to a regular number, then it can be ignored, treated like zero. But, on the other hand, dt is rearded as being different enough from zero to be usable as the denominator of a fraction. So is dt zero or not? Adding finitely many infinitesimals together just gives another infinitesimal. But adding infinitely many of them togehter can give either an ordinary number, or an infinitely large quantity.

Why mentions mathematical mumbo-jumbo?

If atheist believes there is no God unless it's proven otherwise then atheist still leaves the possibility of the existency of God remains open... atheist asks for proof.

If the proof of God is something related to 'human senses' or 'Things' atheist can see, touch, smell, and hear...The thing is, the process of human senses by its nature is limited or finite process, hence the problem arises since God by characteristics definition CAN NOT be FINITE! God is characterized by the absence of limit or INFINITE!

Says who?

Plotinus was the first thinker after Plato to adopt the belief that God or the Absolutely One, it has never known measure and stands outside of number, and so is under no limit either in regard to anything external or internal; for any such determination would bring something of the dual into it.

St. Augustine who believed not only that God was infinite but also that God could think infinite thoughts.

and many others, but one of the best is:
Georg Cantor who created a theory of the actual infinite which by its apparent consistency said:
"The actual infinite arises in three context: first when it is realized in the most complete form, in a fully independent other-worldly being, in Deo, where I call it the Absolute Infinite or simply Abo****e; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type. I wish to make a sharp contrast between the Absolute and what I call the Transfinite, that is, the actual infinites of the last two sorts, which are clearly limited subject to further increase, and thus related to the finite"

Note: Cantor is one of the best infinite-mathematicians and he acknowledges the Absolute Infinite, if atheist knows better, try to have a theory that beats his...

To ask proof God existence based on direct empirical data (which is itself a result of finite measurement) is demanding to put infinite into rules of finite which only leads you nowhere just like Galileo's paradox.

Based on direct empirical data, no human can prove God Existence but applying the same rule atheist also can not prove the inexistency of God either. Why not? because The Absolute Infinite is free from all kinds of influence, like Cantor said fully independent other-worldly being. Since the process to prove or disprove the existency of God is finite hence coercing infinite to finite would be an impossible task. Notice Cantor said only the Transfinite the last two sorts of the actual infinites related to the finite NOT the Absolute Infinite.

Is God only imagination or not realistic since it there is no space and time ref.points exist? Unless of course, if you believe in christian doctrines God in human form visited Earth 2000 years ago in Bethlehem.

A Big If, If atheist for some reasons finally believe in God, would you believe in God who goes to the bathroom?

Back to the question, Is God only imagination or not realistic since it there is no space and time ref.points exist? Or if The unlimited thing or infinite only exists in mathematical mind or mindscape or whatever you want to call it, does it mean God exists only in our mind?

Again, this type of questioning or processing information of finite won't be applicable to the Absolute Infinite. Why not? Again, see Galileo's Paradox and Cantor's first context of actual infinite.

There is a limitation of human mind among others to answer specially this kind of questions. Where's the proof? Read Godel's Incompleteness Theorem.

Because you CAN NOT know what is God, the totality of truth that is the ultimate reality is inevitable some information (like this kind of questions) we simply can not know the answer. this is the fundamental result of modern logic established seventy years ago called godel's proof where godel pointed out that human mind reasons by starting with axioms and from axioms he builds theorems.

Kurt Godel pointed out in any system of axioms you must in order the system to be consistent is must have missing some axioms. You can not capture in any system of logic all of the truth without building a self-destructing mechanism. It's like a sound system that capables to produce any kind of sounds. It can produce a very sound that vibrates so hard that shakes and destroys itself to pieces. In other words, in every axiom-system eventually run into problems that it cannot solve at all hence called Incompleteness Theorem.

This is a mathematical result proven mathematically not some guess work!
If atheist still insists on asking this type of questions, try to disprove the Godel's theorem prior to ask.

To help us escaping from confusions, God sent His prophets to mankind.
christian believes God reveals Himself while muslim believes God reveals His Wills. God reveals what God wants us to know. Through oberservations of His creations relatively we confirm the existency of God. 'Relatively' implies some have confirmed and some still at lost and decided to become atheist.

Nobody was born as an atheist. Atheist is the by product of one's own logical thinking. At least atheist got some portion right...."There is no God", what atheist needs is the remaining, to complete the sentence "There is no God, but He, most Gracious, most Merciful"

In contrast to christianity, the islamic position is in agreement with what it is known to be the facts of modern logic (in, some videos of mathematician professors revert to Islam). Also, Muslim has the amazing Al-Qur'an.

Al-Qur'an, 004.082 (An-Nisa [Women])

004.082 أَفَلا يَتَدَبَّرُونَ الْقُرْآنَ وَلَوْ كَانَ مِنْ عِنْدِ غَيْرِ اللَّهِ لَوَجَدُوا فِيهِ اخْتِلافًا كَثِيرًا
004.082 Do they not consider the Qur'an (with care)? Had it been from other Than Allah, they would surely have found therein Much discrepancy.

It is not natural for human being to claim a book free of error. Al-Qur'an can not be made by human but rather must be revealed from Allah to our beloved prophet Muhammad S.A.W

For 1400 years, the unbelievers try to find mistakes in it to no avail. Sure you may find people who claim they found lots of errors in it (********************). But either they are too ignorance to hear the explanations of so-called errors by muslim experts or they only interested to shout errors and close the door.

Go ahead find one mistake, if you do, the vatican may love to hear from you and may even pay you millions of dollars. But the chances are, whatever you might find, the so-called mistake won't be new rather an old song being recycled again and again for 1400 years.

You won't find any contradictions in Al-Qur'an rather contra-distinctions.

Al-Qur'an, 002.023-024 (Al-Baqara [The Cow])

002.023 وَإِنْ كُنْتُمْ فِي رَيْبٍ مِمَّا نَزَّلْنَا عَلَى عَبْدِنَا فَأْتُوا بِسُورَةٍ مِنْ مِثْلِهِ وَادْعُوا شُهَدَاءَكُمْ مِنْ دُونِ اللَّهِ إِنْ كُنْتُمْ صَادِقِينَ
002.023 And if ye are in doubt as to what We have revealed from time to time to Our servant, then produce a Sura like thereunto; and call your witnesses or helpers (If there are any) besides Allah, if your (doubts) are true.

002.024 فَإِنْ لَمْ تَفْعَلُوا وَلَنْ تَفْعَلُوا فَاتَّقُوا النَّارَ الَّتِي وَقُودُهَا النَّاسُ وَالْحِجَارَةُ أُعِدَّتْ لِلْكَافِرِينَ
002.024 But if ye cannot- and of a surety ye cannot- then fear the Fire whose fuel is men and stones,- which is prepared for those who reject Faith.

Millions of non-muslims speak/write and some are experts in Arabic language. For 1400 years, none has satisfy this the ayah/verse said... of a surety ye cannot!

Of course, many unbelievers (their free will decision) will never turn to Islam,
Al-Qur'an, 007.179 (Al-Araf [The Heights])

007.179 وَلَقَدْ ذَرَأْنَا لِجَهَنَّمَ كَثِيرًا مِنَ الْجِنِّ وَالإنْسِ لَهُمْ قُلُوبٌ لا يَفْقَهُونَ بِهَا وَلَهُمْ أَعْيُنٌ لا يُبْصِرُونَ بِهَا وَلَهُمْ آذَانٌ لا يَسْمَعُونَ بِهَا أُولَئِكَ كَالأنْعَامِ بَلْ هُمْ أَضَلُّ أُولَئِكَ هُمُ الْغَافِلُونَ
007.179 Many are the Jinns and men we have made for Hell: They have hearts wherewith they understand not, eyes wherewith they see not, and ears wherewith they hear not. They are like cattle,- nay more misguided: for they are heedless (of warning).

When you are at dinning table do you take those meals which you would not so much as look at? No, assuredly. So, you shall not receive that which you will not desire. If you desire to know God ask for guidance in your heart.

Human logic can err; most of the time they almost always err; It is certain that without Iman (Faith based on confirmation of logic) it is impossible to know God.

If you ask once and get no guidance. Well, Have you seen people who practice shooting at a mark? Assuredly they shoot many times in vain. they never wish to shoot in vain, but are always in hope to hit the mark. You who ever desire to know God, keep asking, if God wills, surely you will receive guidance.

The carnal eyes can only see things gross and external: But believers have spiritual eyesight which is the Iman/faith of God, wherefore we can see our God in every place (metaphorically speaking).