This is more for fun and something of a thought experiment. If I was to devise a religion, what would it look like?

First, you need statements of faith:

P ≠ NP.
The axiom of choice is essentially useless, and so should therefore be discarded. Set theory should be reduced to Zermelo–Fraenkel set theory and not ZFC. The only use of the axiom of choice is to quickly find a result, and then to see if that result can be proved without the axiom.
All phenomena, apart from the creation of this universe, are natural and can be investigated scientifically through observation.

These are statements that cannot be proven true or false, and the truth of which can be chosen by the individual. The belief that there is an omnipresent, omnipotent and omniscient being is no different than belief that P ≠ NP or that the axiom of choice is not applicable to reality.

One can consider the axiom of choice to be mathematics version of art. The results are beautiful, but absolutely useless in any application to the real world. Any theorem that requires the axiom of choice cannot have any impact on real-world applications. For example, the axiom of choice guarantees that:

the well-ordering of the real numbers (we've never found one),
the existence of subsets of the real line that cannot be measured (non-measurable sets) when all subsets that can be described can have their total length measured (for example, the length of the set (1, 2) and [3, 4] is two, even if the first interval does not contain the end points), and
we can divide a sphere into pieces in such a way the sphere can be divided into pieces such that the sphere can be disassembled into those pieces just like a wooden sphere puzzle, except the pieces are non-measurable and these pieces can be rearranged, just like our wooden sphere, into two spheres, each of the exact volume as the original sphere.

The last is called the Banach–Tarski paradox, and was supposed to demonstrate the non-applicability of the axiom of choice; however, the axiom of choice makes it so easy to generate results, and therefore papers, however, the consequences of any of these papers is equally non-applicable.

The axiom of choice was described by Ernst Zermelo. and thus, each religion needs an arch-heretic, and thus, Zermelo, who first correctly described the axioms of set theory prior to the introduction of the axiom of choice, became a heretic when introducing this absurd idea just so that he could "prove" his well-ordering theorem.

As most mathematicians and computer scientists today make no absolute claims on the final question of if P = NP, we have no such heretics with respect to this question.

And if you haven't observed all of this as being tongue-in-cheek, you need a life, or a descent education in mathematics...

Sacred sites

Next, every religion needs sacred areas:

Any waterfall taller than greater than 144 cubits (c₂).
Any cascading waterfall where the vertical drop is greater than 288 cubits (two c₂) over a distance of less than 1728 cubits (half a mile).
Any hill 100% taller than any hill within 144 times its height from the surrounding minimum.
Any escarpment or cliff greater than 144 cubits (c₂).
Any spring.
Any geyser.
Older trees.
Canyons.

This is better than specific cities, as such natural landscapes are ubiquitous, but many are certainly unique, such as the Externsteine and Niagara Falls. The more unique and grand, the more sacred.

Prophets

No prophets. Prophets are annoying, as each claims to be the last, and each wants to impose on humanity their particular version of morality for all time.

Calendar

Every religion requires their own calendar, so one Solar Year will be 365.2421875 days with the following formula: Year 0 is not a Leap year, but each 4th Solar Year going forward and back is a Leap Year, unless that Solar Year is also a multiple of 128 years going forward or back in time, in which case, it is a Common Year. The start of a year is approximately around the Winter Solstice. Thus, the celebration of the New Year and the Winter Solstice may occasionally coincide, but not always.

Weeks

A week has six days, and there are 61 weeks in a Leap Year. A Common Year has 60 weeks of six days, and a week of five days. The days of the week are Mersaday, Venuday, Mariday, Yupiday, Saturday and Sunday.

Solar months

There are twelve Solar Months of 30 days each, and thus each month has five weeks. This leaves a 1st week of either five or six days depending on whether it is a Common or a Leap Year, respectively, and this creates a Holiweek between the sixth and seventh months. The names of the Solar Months are January, February, March, April, May, June, July, August, September, October, November, December. The Summer Solstice generally falls on the Holiweek.

Seasons

The first three months are Winter, the next three are Spring, the next week is the Solstine holiweek, which does not fall into any season, the next three are Summer and the last three are Autumn.

Year 0

Year 0 is that year with the brightest recorded supernova, which was visible from April 17, 1006 to May 1, 1006 according to the Julian Calendar. The year from Winter Solstice to Winter Solstice that contained this supernova will have the designation of being the year of lucis luporum, or the year of the light of the wolves, or LL or Year 0. The previous Winter Solstice was on December 15, 1005 according to the Julian Calendar, so that will be the first day of Year 0; that is, January 1st, 0 or January 1st, LL. Years before this are labeled ALL for ante lucem luporum and years after this are labeled PLL (poll) for post lucem luporum. You can, of course, also use the more colloquial BW, YW or AW for before the wolves, year of the wolves, and after the wolves, respectively. Year 0, LL or YW had Danish Viking raiders led by Sweyn Forkbeard raid south-eastern England from the Isle of Wight to Reading in the Thames Valley where they overwinter at the Wallingford river crossing. Thus, this river crossing will be a place of pilgrimage on the Winter Solstice, as that was the settlement of the Danes at the end of Year 0.

Thus, 2022 is the year 1016 PLL, so in general, just subtract 1006 for any year CE, and any negative number is ALL. Thus, 1 CE is 1005 ALL. Any year BCE is converted to this system by adding 1005 and the year, too will be ALL. Thus, Caesar marched on Rome in 45 BCE or 1050 ALL.

Lunar months

In addition to Solar months, there are also Lunar Months. A Lunar Month extends from new moon to new moon, a period of approximately 29.5 days. Month 0 is that Lunar Month that spans the same supernova, and this happens to start close to April 1st, 1006 of the Julian Calendar (technically, the actual New Moon was at 23:57 on the previous day, but the fact that this particular New Moon is so close to midnight is never-the-less quite remarkable). With Month 0 being 29 days, each Lunar Month going forward or backward in time will alternate between 30 and 29 days, unless that Lunar Month is a non-zero multiple of 32, in which case that month will also have 30 days, unless the Lunar Month is also a non-zero multiple of 1536, in which case, it will have only 29 days, unless the Lunar Month is also a non-zero multiple of 958 464, in which case it will be 30 days. Thus, Month 0 will actually have 30 days. Thus, each Lunar Month is either 29 or 30 days, with slightly more than half being 30 days. The last cycle occurs only once every 77 493 years, the second last cycle (1536 Lunar Months) occurs approximately every 124 years and two months, the second cycle (32 Lunar Months) occurs every two years and seven months, and of course, the first cycle is every second month. The cycles are thus 1-2-32-1536-958 464. The second cycle is sixteen times that of the first, the third cycle is 48 times that of the second, and the fourth cycle is 624 times the third: 2-16-48-624. These themselves have the second being 8 times the first, the third being three times the second, and the fourth being thirteen times the third: 8-3-13.

The period of time consisting of the two last days of a Lunar Month together with the first two days of the next Lunar month is described as the New Moon Interlude, where the Moon is either new or a faint crescent at most. A New Moon will occur during one of these four days.

To demonstrate, this formula places the New Moon Interlude in January 2000 as being the 5th to the 8th, and the New Moon did occur on the sixth at 18:14. The Lunar Month starting January 7th is the 12291th Lunar Month.

Similarly, the New Moon Interlude in January 2001 is the 23rd to the 26th, and the New Moon was on January 24th at 13:07. The Lunar Month starting January 25th is the 12304th Lunar Month. As can be observed, this technique does indeed, even after 1000 years, track the Lunar Months reasonably well.

These numbers have the additional beauty that they are 2, 2^5, 2^9 × 3 and 2^13 × 3^2 × 13. Thus, the prime factors of these numbers, 2, 3 and 13, are sacred with respect to the Moon.

There are either twelve or thirteen New Moon Interludes per Solar Year, and thus, thirteen or fourteen different Lunar Months in any given Solar Year. The name of these months is based on the order, so the first Lunar Month of a Solar Year, be it one day or 30 days, will be called Thora, and the next 29 or 30 days will be Friga, and so on. Not every year will have a Hela. If a Lunar Month crosses the New Year, the days before the New Year are in the month of Hermoda or Hela, and the days after the New Year in the month of Thora.

Thus, the 13th day of Hela may be followed by the 14th day of Thora. The months are:

Thora, Friga, Tyra, Heimdallra, Lokia, Vidara, Valia, Bragia, Ithunna, Njorda, Ullra, Forsetia, Hermoda and Hela.

Solar holidays

Next, you need holidays:

The New Year according to the Solar Calendar.
The Holiweek surrounding the Summer Solstice and the Winter Solstice, unless the New Year's Day and the Winter Solstice coincide, in which case, January 2nd will also be a holiday.
The spring and autumnal equinoxes.

Note, you need on average one holiday per Solar month. These can be planned...

Lunar holidays

Minor holidays include:

Once every 6585 days, 7 hours, 42 minutes and 23 seconds is a eclipse cycle, and on that day when the Sun, Moon and Earth perfectly align, that will be a holiday. This holiday occurs only once every eighteen years.

Counting and digits

Next, you need a counting system: base 12, not base 10:

The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, x, ε, so x represents "10" things and ε represents "11" things. 10 represents a dozen, and 100 a gross (144).
We start by dividing the day into 6₁₂ periods, each period is divided into 100₁₂ minutes and each minute into 100₁₂ seconds. Thus, there are 1.44 of these seconds per each of our seconds.
Define the distance that light travels in one of these seconds to be 100000000₁₂ c, so that 1 c is one cubit (well closer to 1'7 ¹/₁₆" or 484 mm).

In this week, one week is 6 days, two is 10, and one Solar Month is 26 days. A Solar Year is either 265 or 266 days. A Lunar Month is 25 or 26 days.

The unit c may also be written as c₀, but the zero is usually dropped. c₁ is 10 cubits (5.808 m), c₂ is 100 cubits (69.696 m), c₃ is 1000 cubits (≈ 836 m) so two c₃ is approximately one mile. Six c₃ is approximately the distance a human can walk in one hour, so one league or three miles.

For volume, a cubic cubit is the default measure of volume, and is approximately 30 gallons. A cubic c₋₁ is approximately 2.2 ounces.

This is more for fun, so enjoy.

A sacred text...

Everyone needs a sacred text, so here's one, and it can be described as "sacred", as it relies on belief that the axiom of choice is not applicable to reality. After all, if the axiom of choice did apply to reality, it would be simple to convert one gram of gold into two. Perhaps the alchemists of old were true-believers of the axiom of choice before the arch-heretic Ernst Zermelo articulated it. This sacred text cannot, however, be a textbook: it needs to be written in the same spirit (pun intended) as all other religious texts.

Nature, you have been our dwelling place for all generations.
Before the mountains were brought forth or ever you had formed this Sun and this Earth,

from the beginning of time to everlasting you are our universe.

You turn us back to dust and say, “Turn back, you mortals.”
For ten hundred thousand years in your sight are but an aeon, a blink of the eye, like yesterday when it is past or like a watch in the night.

Verily and primally, 13 789 aeons have passed since the beginning of time.

For all time, aeon is ten hundred thousand years. In the beginning, there was nothing, and then ten of a thousand of aeons and three out of eight times as much again the universe appeared and began to expand. The heat was such that nothing substantive could exist. For a third of one hundredth of one thousandth of this time, the universe burned with such heat, until finally it cooled and all was dark and the darkness was filled with gas.

Out of the dark, after twenty thousand years twenty thousand times, the gases formed into enormous balls and the weight was so great that the core began to burn, and burn they did. This happened millions of millions of millions of times over and these burning stars lit the darkness, not with the heat that there once was, points of light all around, and if one came close enough to one, there would be heat and light.

These stars spun and they clung to each other spun around each other forming a hundred thousand million spirals. Stars would be born and stars would die, some disappearing, while others exploding in a fire a million times a million times as bright and one hundred thousand times as hot. And out of their death would come new stars. And when the universe was twice a third of its age, a small star appeared nearer to the edge of its spiral, and in the next hundred aeons, around it many worlds grew, but while those too close were too hot and those further away were too cold, two worlds would be where it was warm enough for water to melt, but not so hot as for it to boil.

At first, however, these worlds did not begin as a paradise but instead grew from the rocks that spun around this star. These rocks gathered and formed these twin worlds, one larger and the other half its size, and together they spun around the star. Their surface was molten rock, yet over time, these worlds shed their heat and the surfaces became solid. These worlds, however, attracted each other, and coming too close, the two collided in the greatest cataclysm these worlds had ever seen. The smaller was absorbed into the greater, and the greater world grew, but a piece of the smaller world survived this calamity, now half its size, and now began to spin not around the star, but around its now larger twin. At first they spun freely around their poles, and a day was less than half as long as it is now, but soon the smaller slowed its spin until only one side faced the larger, turning once a Month just as it spins once around the larger in that time, twice in fifty nine days today, and over time, the larger world also slowed its spin, until today when a man can walk twenty four leagues from one sunrise to the next.

As the smaller world spun around the larger, and as the larger spun around the star, and today every two-hundred and twenty three Months of smaller, the three fall in a straight line: the star, the larger and the smaller. Today, forty eight times in those two-hundred and twenty three Months does the smaller world come between the star and the larger, casting a shadow on the larger, and and in this time that the smaller world may pass in front of the star may be once but on occasion also twice, one Month apart.

After they collided, both worlds became molten again, yet again both shed their heat and a solid skin of rock formed around both. Around the larger, lifeless and swamp airs collected above the solid rock and rain would fall but boil and return to the lifeless air. The smaller cooled quicker and its skin became thicker, but the molten rock of the larger continued to made enough heat so that even today, only the top twelve leagues were solid. From time to time, the molten rock would break through the skin sending geysers of rock into the air, but as the skin thickened, it would be much more seldom, and on the smaller, the skin is so thick that this no longer occurs today. The flowing molten rock below the skin would, however, push against the rock skin and cause it to move, and cause it to quake and rumble, often causing great damage, but this, too, would grow more seldom.

Other rocks spinning around the star pelted these worlds, bringing water, life substances, coal, iron and minerals and precious metals to the surface. Rocks of gold, and of silver, and of copper and of other minerals and precious metals would strike here and there, leaving their gifts on the surface and below the surface of these worlds.

Three quarters of a thousand aeons passed, and it was now cool enough so that water could begin to fall and gather in the lowest places, and from there, the water continued to gather forming vast oceans between the rocks on the surface. And the lifeless and swamp airs were absorbed into these oceans.

With waters gathered in the oceans on the surface of the larger world, most of the heat on the surface now came not from the molten rock, but from the life-giving Sun, and the larger world became a life-bearing Earth. The smaller world would move the waters on the Earth and the waters of the oceans would rise and fall in harmony with that Moon. While the Sun gave heat when it was in the sky, and the Earth cooled where the Sun had sunk below the horizon, the moon would reflect light, sometimes more and sometimes less, lighting up the night sky many times more that from the light of the stars, and this would cycle once a Month, twice every fifty-nine days. When both the Sun and Moon pulled together or were in opposition in the sky, the tides would be greatest.

The oceans contained a soup of life substances and minerals and precious metals. Then, after one hundred aeons of the oceans forming, or eleven out of fifteen times the age of the universe or two out of eleven times the age of the Earth, the light from the Sun and the tides from the Moon and the life substances and minerals from the falling rocks made it possible for the first life: that is, that which is able to replicate itself. Small bubbles of soap surrounding life substances and minerals were able to absorb further life substances and minerals so as to be able to split in two, the two being copies of what the bubble that was there. These organisms so small you could not see them used green light, breathed the swamp airs, and used the lifeless airs to make sweetness, and from this sweetness they made flours and fats as well as frames that gave these bubbles strength. These bubbles reflected the red and blue lights so that their colonies appear as purple masses. After this, some life changed so that they would no longer produce their own sweetness and life substances, but instead consumed other life, using the consumed life and sweetness for their own growth.

Life continued as such bubbles for a thousand aeons, until twenty-four hundred aeons ago when the first such bubbles began to use not green light and swamp air, but rather used blue light and water together with the lifeless air to make sweetness, and from this they produced life-giving air. These reflected the green light they no longer used so that colonies appear as green masses. Over hundreds of millions of years, this life-giving air gathered and killed much of the life that used the swamp gases.

And so it came to pass that some bubbles began to trap others within them, and the larger bubble worked in harmony with those that were engulfed. Those inside were protected and did not concern themselves about seeking life substances and sweetness, and instead specialized their tasks. Bubbles also began to reproduce not by splitting, but by sharing details on their structure with another, and these bubbles split into two: one that gave details, and another that received such details and incorporated both their own with the received details for a new bubble.

Life continued as individual bubbles until fifteen-hundred aeons ago when some of the remaining swamp air breathing bubbles split into two, but stuck together and form a whole that was greater than the two. This was the start of purple plants made up of many bubbles and the individual bubbles were able to perform specific tasks, and not every bubble was obligated to perform every task required for life. This finally created life that were more than individual bubbles.

Life continued as both bubbles and larger organisms changed and improved, and then between the surface of the Earth froze, and not just once but many times. The surface of the life-giving water froze everywhere or almost everywhere on Earth, and life that exists in oceans cannot exist when that water is frozen, so life now only existed below the ice in the absence of sunlight or where the Sun was hottest where there was sufficient heat to at least occasionally melt the ubiquitous snow and ice. The first two epochs of freezing spanned four-score-and-five aeons, the first being two-score and fifteen aeons, and with a warming of 15 aeons, the first bubbles that consumed others also began to divide but remained together to form the first animals of motionless sponges. These sponges sat and consumed bubbles that came near them, and yet, as these first appeared, there came another fifteen aeons where the world was plunged into cold.

After the first great freeze, it came to pass that those bubbles that made their own energy from sunlight and water and the lifeless air began to replicate, but their bubbles stuck together, and together, these formed the first plants: bubbles working together to gather sunlight and store the energy of life.

After the last great freeze, those bubbles that consumed others also began to divide but remain together forming the first animals in the form of motionless sponges. The first animals in the oceans and consumed bubbles and plants, and the oceans were filled with various and wonderous animals to behold. Yet one such animal developed a soft spine: some animals grew shells around this spine, while others absorbed the spine and surrounded it with flesh. Those with shells would be fated to remain small, but those with flesh would grow to dominate the world, but this would take time.

To do... molluscs and arthropods, including trilobites, develop and then dominate in the Ordovician. First land plants and later first fish, and then fish with jaws. Rocks continue to pelt the Earth, bringing minerals and precious metals, and still a hundred-fold more than today. This period, however, ended with first a world-wide cooling with great glaciers both North and South, followed by a warming and the cracking of the earth and the consumption of life-giving air and the spreading of swamp air. Three out of every five related plants and animals died.

To do... Silurian, with vascular plants, the spread of fungus, and the growth of crawling insects, including those with hundreds of feet, those with eight, and those with six. Also, jawed fish and fish with the first skeletons.

To do... Devonian, free-sporing vascular plants and leaves and roots. The fish expand, too. Age of the fish.

To do... Carboniferous, the four-footed skeletons animals. The lands collide and the mountains grew, age of the amphibians.

At the end, some of the apes developed a much greater capability of thought and reason... These apes and their cousins crossed the Sinai over and over, until finally, the first humans crossed the Sinai, and all other apes that came before were made extinct. The humans

Stupid sayings

Every religion requires a set of statements that are completely pointless. These are called deepities, as they sound profound and significant, but are actually rather pointless:

The fool has said in that individual's heart that there are supernatural phenomenon.
All works of literature are inspired by the authors and the society in which that individual lives; and some may be useful teaching, for reproof, for correction, and for training so that the person may be proficient and equipped for every good work, but that, too may depend on time and circumstance. All literature, however, is good for investigating the mind of the author and the society in which that individual lived.
The wages of harming others is negative judgement by others, and the wages of helping others is positive judgement by others.