When the part – ourselves – encounters the Whole, it discovers its origin and destiny; time becomes eternity and space becomes infinity.
Is it possible to draw a parallel between mathematics and spirituality? Is there a common denominator that allows such a comparison?
Mathematics is a science based on a rational method; spirituality is founded on faith and intuition. Mathematics is objective, while spirituality is subjective.
The scientific method requires experimentation that allows precise data collection, enabling reproducibility of experiments by different researchers [1]. In spirituality, experiences are internal and cannot be guaranteed to be repeatable or even comparable to others.
The language of the exact science is clear, rigorous, and precise; in spirituality, the inner experience cannot be fully expressed in words.
Scientific knowledge is contingent; truth or falsity can be determined through experiments. In spirituality, the only and universal Truth is inherent to Divinity, and the boundary between true and false in the transient reality in which humans live is imprecise.
Science is predictive: it establishes laws, theories, and models that allow predictions. Spirituality is surprising, disconcerting, and unpredictable.
In short: scientific knowledge is verifiable, and anything that cannot be proven is nothing but a hypothesis – which automatically excludes the possibility of any comparison with spirituality.
However, Gödel’s first incompleteness theorem tells us, in summary, that in arithmetic there are absolute truths that cannot be proven [2]:
“Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent and effectively generated formal theory that proves certain truths of basic arithmetic, there exists an arithmetic statement that is true but not provable within the theory.”
On the other hand, a geometric explanation of the concept of Divinity is attributed to Hermes Trismegistus [3]:
“God is an infinite sphere whose center is everywhere and whose circumference is nowhere.”
Infinity is a concept that interests both mathematics and spirituality, and we propose some unpretentious reflections on it, given its incredible complexity.
The concept of infinity interested Georg Ferdinand Ludwig Philipp Cantor, a 19th-century German mathematician who worked to facilitate its understanding. Cantor claimed that there is not just one “infinity”, but several “infinities”, including the absolute understood as God (this theory was opposed by the church, which considered it a challenge to the unique infinitude of God):
“Infinity always arises in three contexts: first, when it presents itself in its most complete form, in a supernatural entity completely independent, in Deo, which I call Absolute Infinity or simply the Absolute; second, when it occurs in the eventual, in the created world; third, when the mind understands it abstractly as a mathematical magnitude, number, or type of ordering.” [4]
Cantor became famous for developing the set theory [5]. A set is a well-defined collection of objects, called elements, that share a common characteristic. Thus, the letters of the alphabet form a set, but so does the collection of cups in your kitchen or socks in your drawer – all are sets with clearly defined characteristics.
Among his various works, we want to mention the comparison the famous mathematician made between two sets: the set of natural whole numbers and the set of real numbers.
Natural whole numbers are 1, 2, 3, 4, and so on, meaning their set contains an unlimited quantity of characters.
Real numbers include rational and irrational numbers, encompassing positive and negative numbers, integers, fractions, decimals, and repeating and non-repeating decimals [5]. To study the infinitude of this set, Cantor used the numbers between 0 and 1 – all starting with zero point something – but with a special characteristic: they all have an endless quantity of digits after the decimal point. For example, dividing 1 by 3 gives a repeating decimal with infinite digits: 0.3333… However, dividing 1 by 2 gives 0.5, a finite number of digits after the decimal; in this case, to participate in Cantor’s study, an infinite number of zeros is added after the last digit, resulting in: 0.5000….
These two sets are certainly infinite, but are they the same size?
Cantor proposed a simple criterion for comparing sets: they are equivalent if they have the same number of elements. He also developed the so-called “diagonal argument,” available for further study in various sources [5, 6].
Thus, he demonstrated that there are more numbers in the set of real numbers than in the set of natural whole numbers, namely, an uncountable infinity and a countable infinity, respectively..
Isn’t it curious to know that there are more numbers between 0 and 1 (uncountable infinity) than the sum of all whole numbers (countable infinity)?
What do these numbers represent in esoteric language?
In Benita Kleiberg’s article [7] on the number of God, we read the following statements:
“Therefore, in Jewish mysticism, the divine is described as the unfathomable Ain Sof, literally meaning ‘without end.’ This spiritual non-existence of Ain Sof is the source from which all life emerged. In Jewish mysticism, this life is schematically represented by the ten Sephiroth of the Tree of Life, which form the plan of creation. In other words, we can understand the divine Ain Sof as the number 0, a nothing from which everything originated.”
…
“Therefore, the monad, the unique plan of the spherical form, the number 1, is the quintessential symbol of Divinity expressed in our world, as the first emanation.”
We can understand that the set between 0 and 1 would represent the unfathomable and unknowable God and His hidden manifestation, which will become the number 1, the first emanation.
Divine creation, represented by the set of natural numbers, is infinite and countable, encompassing the universe and celestial bodies, our planet and all living and non-living beings, continents and oceans, plants, animals, and human beings.
The hidden God is Ain Sof, literally “without end”, an uncountable infinity from which everything originated.
Reading the eighth book of the Corpus Hermeticum [8], we can reflect that the things not created and kept in silence would be an uncountable infinity. And the things that were made and manifested are a countable infinity.
“Who could praise You enough according to Your worth? Where shall I direct my eyes to praise You? Upward, downward, inward, or outward?
…
“And why should I sing Your praises? For what You created or for what You did not create? For what You manifested or for what You keep hidden? … Even what does not exist, You are. You are all that came to be and all that has not yet been manifested.”
In his work on set theory, Cantor reached surprising conclusions that frightened part of the 19th-century mathematical community and earned him criticism from colleagues and former professors.
For example, when verifying the properties of infinite sets (compared to finite sets), Cantor and his friend Richard Dedekind found that: in an infinite set, the whole can be equal to one of its parts [5]. In spirituality, we could understand this statement as the mathematical expression of divine Omnipresence, of the point at the center of the infinite sphere – which is God – that is everywhere. This point is also at the center of the human being, as the manifestation of Divinity, in the form of an atom of the Spirit’s spark; finding this atom within oneself is the same as seeing the Unknowable and its grandeur. At that moment, the part, which is us, encounters the Whole, discovers its origin and destiny; time becomes eternity and space becomes infinity.
Studying the numbers he called transfinite, Cantor concluded that the number of points in a line segment just 1 millimeter long is the same as the number of points in the entire volume of the universe! This leads us to reflect that the true inner path of spiritual liberation — leading us from the transient reality in which we live to the infinite fields of pure Universal Truth—may be less than one millimetre long, and that, mathematically, we could traverse it in the blink of an eye.
Although we feel limited in space and time, spirituality tells us – and mathematics suggests – that we are part of a countable infinity. Still, we carry the immeasurable within our hearts.
But only when our analytical mind steps aside and gives away to a deeper understanding — one that shines at the inner core of our being — can our awareness recognize that the finite and the infinite, the countable and the uncountable, mirror and weave into one another in a reality of breathtaking and unspeakable beauty. Only then do we understand that we belong to this reality and, with profound gratitude, allow our hearts to echo Hermes’ hymn of praise in the following words
“And how would I sing Your praise? As if something belonged to me, as if I possessed something of my own or were anything other than You! For You are all that I can be; You are all that I can do; all that I can say. For You are everything, and there is nothing beyond You!”
References:
[1] LAKATOS, Eva Maria; MARCONI, Marina de Andrade. Metodologia científica. 2. ed. São Paulo: Atlas, 1985.
[2] Mathematics. Avaible at: logic – Explanation of proof of Gödel’s Second Incompleteness Theorem – Mathematics Stack Exchange Accessed at: 2 August 2025.
[3] REEGEN, Jan G. Ter. LIBER VIGINTI QUATTUOR PHILOSOPHORUM – O LIVRO DOS VINTE E QUATRO FILÓSOFOS. Veritas (Porto Alegre), [S.L.], v. 47, n. 3, p. 441-452, 30 dez. 2002. EDIPUCRS. LIBER VIGINTI QUATTUOR PHILOSOPHORUM – O LIVRO DOS VINTE E QUATRO FILÓSOFOS | Veritas (Porto Alegre)
[4] Infinito absoluto. Avaible at: Infinito absoluto – Wikipédia, a enciclopédia livre. Accessed at: 2 August 2025.
[5] UNIVERSIDADE FEDERAL DO CEARÁ (Brasil). George Cantor e os transfinitos. Seara da Ciência. Avaible at: George Cantor e os transfinitos – Seara da Ciência Accessed at: 2 August 2025.
[6] BOUYER, Florian. O conceito de infinito e seu uso na matemática. 2022. UNESP para Jovens. Avaible at: Unesp Para Jovens | O conceito de infinito e seu uso na matemática. Accessed at: 2 August 2025.
[7] KLEIBERG, Benita. God as number. LOGON, 28 fev. 2024. Category Science. Available at: God as Number – LOGON Accessed at: 2 August 2025.
[8] VAN RIJCKENBORGH, Jan. The Egyptian Arch-Gnosis and its call in the eternal present – Part 2. Rozenkruis pers, Haarlem 2020
