“Believing in infinity is like believing in God” — an article about a professor at a prestigious university asserting the mathematical philosophy of “ultrafinitism,” which denies the very existence of infinity, even at the risk of backlash from the math community, became a hot topic on 5ch’s Science News+ board.
In the thread, posters didn’t just question infinity — they raised philosophical counter-questions about whether zero, straight lines, and pi really “exist” at all, and the discussion spread all the way to physics topics like vacuum fluctuations, the heat death of the universe, and the finiteness of time. Opinions split between those who see infinity as an unnecessary concept for everyday life and compulsory education, and those who countered that infinity is indispensable to the practical side of modern mathematics, such as analysis.
“Believing in Infinity Is Like Believing in God” — The “Inconvenient Truth” an Elite University Professor Declares Even at the Cost of Making Enemies in the Math World
The philosophy of “ultrafinitism,” which denies infinity, has long been dismissed as heretical in the mathematical world.
But this philosophy is said to offer new insight not just into equations, but into our very worldview.
Source: news.yahoo.co.jp / Read the original article here
2AnonymousAug 30, 2026 20:57
Well yeah, if you try to count all the way to infinity, the resources needed to do the counting run out eventually.
If you treat information and energy as equivalent, infinity can't exist in this world — at least not this one.
3AnonymousAug 30, 2026 21:06
It'd be religious groups making enemies here, not academia ("gakkai").
74AnonymousAug 31, 2026 14:31
Re: #3
"Academia" (gakkai) is also slang for a religious group, you know (a pun — 学会 is short for Soka Gakkai too).
4AnonymousAug 30, 2026 21:07
Unfortunately, the concept of infinity was born from a religion that has no single god.
5AnonymousAug 30, 2026 21:09
Well then, guess I'll migrate to this thread together with Laura (Masaru) (apparent meme/character reference, origin unclear).
6AnonymousAug 30, 2026 21:09
That's ridiculous.
By that logic, straight lines wouldn't exist either, and neither would zero.
11AnonymousAug 30, 2026 21:24
Re: #6
In non-Euclidean geometry or whatever, straight lines can't exist as such, right?
And of course, "nothingness" is a religious concept too — there's no such thing as nothing in this world.
Nobody can prove otherwise.
27AnonymousAug 30, 2026 22:05
Re: #6
Straight lines do exist.
All you need is a size-0 point, another size-0 point, and the relationship connecting them.
Zero exists as information. So do 1 and 2 — they don't exist in physical spacetime, but they exist as information.
12AnonymousAug 30, 2026 21:24
If nothingness = 0, then the universe is filled entirely with 0.
The reason 0 stays fixed at 0 forever is also nothingness = 0 → occasionally it becomes something other than 0 = a fluctuation = the birth of our current universe.
13AnonymousAug 30, 2026 21:26
Re: #12
Empty space and "nothingness" are different things.
Vacuum seems to carry vacuum energy and the like.
14AnonymousAug 30, 2026 21:28
Re: #13
What I'm getting at is that vacuum energy might just be a fluctuation between 0 and 1.
15AnonymousAug 30, 2026 21:30
Re: #14
Sure, that's true.
But that's still different from nothingness.
Vacuum is an observed phenomenon, but "nothing" is a product of imagination.
Not a single person has ever confirmed nothing exists.
18AnonymousAug 30, 2026 21:35
There are things like the vastness of the universe that could be called practically infinite, so I think the concept of infinity is fine to keep around·······
29AnonymousAug 30, 2026 22:06
Re: #18
In reality, the universe doesn't allow for infinity.
It's limits on top of limits, everywhere.
The idea that space alone is infinite is pure speculation — nobody's actually confirmed it.
20AnonymousAug 30, 2026 21:40
A concept is a fantasy.
So then, what exactly is a fantasy?
33AnonymousAug 30, 2026 22:18
Re: #20
Fantasy = requires a person.
Concept = shareable across time and space.
26AnonymousAug 30, 2026 22:01
I'd honestly like to see how you'd define e or π
without using the concept of infinity.
34AnonymousAug 30, 2026 22:19
Re: #26
Isn't π just circumference divided by diameter?
35AnonymousAug 30, 2026 22:23
Re: #1
Once you exceed the limit of numbers a human can count, I think it's fine to just treat it as infinity.
Once something exceeds human cognition, it's basically the same as God.
36AnonymousAug 30, 2026 22:25
Re: #35
Kind of like how ancient people supposedly counted "1, 2, many"?
No idea if that's actually true though.
44AnonymousAug 30, 2026 23:20
The conclusion changes depending on whether you place the observer as a human or not.
What matters here is that the subjectivity in this question is placed on humans.
48AnonymousAug 30, 2026 23:35
Re: #44
You're misunderstanding what "observer" means — go have a chat with a few different AIs.
46AnonymousAug 30, 2026 23:25
Isn't time infinite too?
Does it ever come to an end?
55AnonymousAug 31, 2026 00:17
Re: #46
There's a theory that time doesn't exist at all.
Apparently every moment in time exists simultaneously, like a stack of overlapping photos.
Pretty sure I read that in Newton (the Japanese science magazine).
95AnonymousAug 31, 2026 20:41
Re: #46
There are various concepts of "time," but
generally speaking, time is just change of state measured against some particular yardstick.
Now, in this universe, entropy keeps rising, and eventually everything becomes so diluted that no state changes happen anymore.
But right around that point, black holes will kick Hawking radiation into full gear, and the universe will see state changes again — in other words, time starts back up.
The scale here is absurd:
it takes 10^106 years for Hawking radiation to finish.
That's roughly 700 billion times the universe's entire history so far, times a trillion, times a trillion, times a trillion, times a trillion, times a trillion… and it keeps going at that scale.
It looks infinite at a glance, but compared to true infinity it's an extremely small number — and in the end it's still just state change measured by a particular yardstick.
What's more, during all that time, light experiences zero proper time — not even one second passes for it — yet it still keeps flying through the universe (or through black holes?) regardless.
In other words, whatever is actually driving this universe's state is the essential thing, and whether *that* is infinite or not, we still don't know.
66AnonymousAug 31, 2026 07:39
I skimmed a few articles introducing this guy's ideas, and honestly his whole argument boiled down to a "housewife's common sense" take of "you don't really need infinity in everyday life, right?"
68AnonymousAug 31, 2026 07:50
Re: #66
In that case it just becomes "elementary and middle school arithmetic, math, and science don't need infinity."
And that part is certainly true.
70AnonymousAug 31, 2026 10:23
There will always exist integers that have never once appeared in any text throughout human history.
Almost all real numbers will never, for all eternity, have their exact value pinned down.
In other words, their existence is basically that of a ghost.
72AnonymousAug 31, 2026 14:04
Re: #70
Flip it around, though, and you could say any information that ever appears in history is necessarily contained somewhere within infinity.
For example, treat π as a sequence of digits.
Run it through some kind of encoding to convert it into characters.
Do that, and eventually every piece of information will show up (be written) in there somewhere.
For example, Shakespeare's plays.
For example, the entire history of Earth.
For example, the position of every particle of matter.
All of it is recorded somewhere in the digit sequence of π.
78AnonymousAug 31, 2026 15:34
Doesn't make sense to me.
Does this guy think pi's digits are finite too?
94AnonymousAug 31, 2026 20:32
Re: #78
Actually, things that look infinite sometimes aren't infinite at all.
For example, take an equation where time drops out when you manipulate it — that's not because time is infinite, it's because the concept of time just doesn't apply there.
Pi doesn't "go on forever" —
pi is simply a state that exists.
Humans just perceive it as going on infinitely,
but pi is just π.
Same with the speed of light — measure it in miles or whatever and it looks like it goes on forever, but it collapses down to c.
And when you combine formulas that express these basic states,
you get things like Δx·Δp = h/4π describing the state of the universe.
So basically, sure, humans can imagine anything as infinite if they try hard enough, but in reality some of those things turn out to be one specific, simple state — the exact opposite of infinite.
82AnonymousAug 31, 2026 16:14
Are you seriously saying pi has a finite number of digits?
84AnonymousAug 31, 2026 16:19
Re: #82
Isn't that just because a "perfect circle" doesn't actually exist in this world?
87AnonymousAug 31, 2026 17:02
Re: #82
Is there actually a way to treat pi as having an infinite number of digits?
96AnonymousAug 31, 2026 20:54
Same as imaginary numbers —
it's just a concept.
99AnonymousAug 31, 2026 21:03
Re: #96
Right.
Imaginary numbers are just a concept too, but they're so practically indispensable to modern life
that this isn't even at the level of an "inconvenient truth" you believe or don't believe.
113AnonymousSep 1, 2026 00:39
Outside of analysis, everything's finite.
Infinity is actually the minority case — but when you look at where math is actually applied in the real world, in chemistry, physics, architecture, and so on, most of it comes down to analysis, which runs on infinity.
Even measuring your weight or height involves infinity, doesn't it?
120AnonymousSep 1, 2026 06:21
Re: #113
Number theory and geometry are infinite too, you know.
Background and Key Points of This Debate
Ultrafinitism is a philosophy of mathematics that doubts the existence not just of infinity, but even of very large finite numbers — a minority position long dismissed as heretical by the vast majority of mathematicians. Mainstream modern mathematics, namely analysis and calculus, relies heavily on infinity through concepts like limits and the real numbers, so taking this stance seriously would mean rethinking everything from education to applications in physics and engineering. Many posts in the thread treated “infinity,” “nothingness (zero),” and “whether concepts exist” as one and the same issue, but these are mathematically distinct discussions — and the thread never really untangled the distinction between “actual infinity” and “potential infinity” that the article and the professor’s argument were originally pointing at. The tangents into pi, entropy, and the finiteness of time all trace back to that same root cause: disagreement over what “infinity” is even supposed to mean.
※This article excerpts and summarizes the 5ch (Science News+) thread “[Math] “Believing in Infinity Is Like Believing in God” — The “Inconvenient Truth” an Elite University Professor Declares Even at the Cost of Making Enemies in the Math World.”
