The difference is it misses a key factor. Demonstration of effectiveness. We have good reasons to accept math and the axioms because we can demonstrate their effectiveness. Anyone can do this at any time. — Tom Storm

Look at the size of the mathematical corpus:

https://writings.stephenwolfram.com/2014/08/computational-knowledge-and-the-future-of-pure-mathematics/

So how big is the historical corpus of mathematics? There’ve probably been about 3 million mathematical papers published altogether—or about 100 million pages, growing at a rate of about 2 million pages per year. And in all of these papers, perhaps 5 million distinct theorems have been formally stated.

The overwhelmingly vast majority of these 5 million theorems are useless and irrelevant. In what way would they be effective?

We can't even agree on which gods or why gods or how gods. — Tom Storm

There are alternative religions, just like there are alternative foundations for math. Two billion people agree on Christianity. Two billion on Islam. A similarly large number on Buddhism. There are obscure religions with a small number of followers, just like there are obscure math theories.

Furthermore, religion can be very effective. It can successfully prevent governments from overruling the laws of nature. It can also be effective at motivating individuals and stimulate their survival instinct. It can motivate individuals to maintain faith in life and in the future and keep reproducing from generation to generation. The birth rate for atheists may be crashing and burning, but religious communities keep going strong.

You ignoring context and equivocate "exist", "faith", "proof" .... no wonder you're talking nonsense. — 180 Proof

As soon as you switch to personal attacks, it means that you feel that you are losing the debate.

In mathematics, "faith" in axioms is more about agreement on foundational principles rather than belief without evidence. — Tom Storm

Faith in axioms still requires belief without evidence. Religious people also agree on the foundational principles of their faith. What's the difference?

No one has asked for a "mathematical proof" — 180 Proof

There is no other "proof" than mathematical proof. The OP asks "Can anyone prove a god?"
Well, Gödel gave mathematical proof. And now suddenly, no one asked for it!

only you have offered one that amounts to nothing more than a "higher-order modal" tautology. — 180 Proof

Gödel's proof is no more tautological than any other mathematical proof.

Is this an example of faith? — Tom Storm

Accepting a truth without evidence is faith. Therefore, an axiom represents faith. If you are not willing to do that, then why do it in mathematics?

So, confirming you do not even know what yoi are talking about, Gödel only proves a mathematical expression and not, as you've claimed, "that god exists". — 180 Proof

Every proof does only that. In that case, why ask for "proof", if proof can never be satisfactory?

By "faith" I mean worship of supernatural mysteries e.g. "a god" (re: OP), not mere (un/warranted) trust in a usage or practice. Context matters. — 180 Proof

Yes, so what's the difference?

"Godlike" (e.g. Spinoza's metaphysical Deus, sive natura) is not equivalent to any supernatural god (e.g. "God of Abraham") so this "proof" is theologically irrelevant. — 180 Proof

You did not prove this.

More specifically, his argument consists of some undecidable (i.e. disputable) formal axioms — 180 Proof

Axioms are not undecidable.

https://en.wikipedia.org/wiki/Undecidable_problem

In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer.

The standard truth status of axioms is not characterized as undecidable.

even if valid, it is not sound — 180 Proof

This argument can be made about every mathematical theorem, simply by rejecting the axioms on which the theorem rests.

nothing nonformal, or concrete, is "proven". — 180 Proof

Proof only exists in mathematics, which is never about the physical universe. Therefore, it is impossible to prove anything "concrete". That is not how proof works.

This might shed more light on where you think Wittgenstein went wrong. — Joshs

In fact, Gödel's first incompleteness theorem trivially follows from Carnap's diagonal lemma. If you want to attack Gödel's theorem, you can pretty much only do that by pointing out a gap in the proof for the diagonal lemma or by pointing out that the lemma does not apply because isProvable(n) is not a legitimate predicate in PA. Wittgenstein did not do that. Instead, Wittgenstein struggled somewhat with his own flawed interpretation of Gödel's theorem without pointing out a legitimate flaw in the proof.

Could you provide your own critique of Platonic explanations of the mathematics, lie that of Goedel, or the correspondence theory of truth? This might shed more light on where you think Wittgenstein went wrong. — Joshs

Wittgenstein wrote the following "notorious paragraph" on Gödel's first incompleteness theorem in his "Remarks on the Foundations of Mathematics":

https://en.wikipedia.org/wiki/Remarks_on_the_Foundations_of_Mathematics

Wittgenstein wrote

I imagine someone asking my advice; he says: "I have constructed a proposition (I will use 'P' to designate it) in Russell's symbolism, and by means of certain definitions and transformations it can be so interpreted that it says: 'P is not provable in Russell's system'. Must I not say that this proposition on the one hand is true, and on the other hand unprovable? For suppose it were false; then it is true that it is provable. And that surely cannot be! And if it is proved, then it is proved that it is not provable. Thus it can only be true, but unprovable." Just as we can ask, " 'Provable' in what system?," so we must also ask, "'True' in what system?" "True in Russell's system" means, as was said, proved in Russell's system, and "false" in Russell's system means the opposite has been proved in Russell's system.—Now, what does your "suppose it is false" mean? In the Russell sense it means, "suppose the opposite is proved in Russell's system"; if that is your assumption you will now presumably give up the interpretation that it is unprovable. And by "this interpretation" I understand the translation into this English sentence.—If you assume that the proposition is provable in Russell's system, that means it is true in the Russell sense, and the interpretation "P is not provable" again has to be given up. If you assume that the proposition is true in the Russell sense, the same thing follows. Further: if the proposition is supposed to be false in some other than the Russell sense, then it does not contradict this for it to be proved in Russell's system. (What is called "losing" in chess may constitute winning in another game.)

Wittgenstein mishandled Gödel's witness:

P <-> not provable([P])

By the way, first of all, P could be also be undecidable. We should not simply assume that the problem would necessarily be decidable (true or false). Otherwise, our approach could possibly constitute abuse of the law of the excluded middle.

Next, if P is true then P is not provable.
If P is false then P is provable.

Hence, P is [1] undecidable, or [2] true and not provable, or [3] false and provable.

In fact, we don't know what the actual truth status is of P. That is also not necessary.

Gödel's incompleteness theorem states that there exist in Peano arithmetic (PA) logic sentences that are undecidable, or, true and not provable, or, false and provable. Hence, in constructivist terms, P is indeed a legitimate witness for Gödel's theorem, making his theorem intuitionistically unobjectionable.

Hence, there is nothing wrong with Gödel's witness.

When Wittgenstein wrote:

Just as we can ask, " 'Provable' in what system?," so we must also ask, "'True' in what system?"

Gödel's work is about "provable from PA" and therefore "true in the natural numbers" (as well as all other nonstandard models of arithmetic).

When Wittgenstein wrote:

If you assume that the proposition is provable in Russell's system, that means it is true in the Russell sense, and the interpretation "P is not provable" again has to be given up.

Wittgenstein assumes the soundness of PA ("Russell's system"), i.e. provable implies true.

Gödel's theorem does not assume neither the consistency nor the soundness of PA. The theorem states that "There possibly exist false statements that are provable", i.e. are inconsistent, and also "There possibly exist true statements that are not provable", i.e. are incomplete. So, PA is possibly inconsistent and/or possibly incomplete. The theorem does not say which one it is. It could even be both.

While it is perfectly fine to assume PA's consistency in (ordinary) mathematics, it is not good practice to assume it in metamathematics, where it is often part of the question at hand, such as in Gödel's theorem.

In fact, Gödel proves in his second incompleteness theorem that if PA can prove its own consistency, then PA is necessarily inconsistent. Wittgenstein was clearly also not aware of Gödel's second incompleteness theorem. Consistency was even more the question and not a valid assumption in Gödel's second incompleteness theorem.

In my opinion, Wittgenstein's remarks on Gödel's theorem are confused. He did not point out a problem with Gödel's theorem. What problem in that case? Wittgenstein rather pointed out a problem with his understanding.

For Wittgenstein, the mathematician is an inventor not a discoverer, and mathematical proposition are normative. — Richard B

Wittgenstein considered his contribution to the philosophy of mathematics to be his chief contribution:

https://en.wikipedia.org/wiki/Ludwig_Wittgenstein%27s_philosophy_of_mathematics

Ludwig Wittgenstein considered his chief contribution to be in the philosophy of mathematics, a topic to which he devoted much of his work between 1929 and 1944.

Wittgenstein has, however, gone into history as someone who does not understand mathematics particularly well:

https://philpapers.org/archive/FLOOSW.pdf

Wittgenstein's remarks on the first incompleteness theorem 1 have often been denounced, and mostly dismissed. Despite indirect historical evidence to the contrary," it is a commonplace that Wittgenstein rejected Godel's proof because he did not, or even could not, understand it.

Wittgenstein's take on the matter was rejected unanimously:

https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

On their release, Bernays, Dummett, and Kreisel wrote separate reviews on Wittgenstein's remarks, all of which were extremely negative.[38] The unanimity of this criticism caused Wittgenstein's remarks on the incompleteness theorems to have little impact on the logic community.In 1972, Gödel stated: "Has Wittgenstein lost his mind? Does he mean it seriously? He intentionally utters trivially nonsensical statements", and wrote to Karl Menger that Wittgenstein's comments demonstrate a misunderstanding of the incompleteness theorems writing:

It is clear from the passages you cite that Wittgenstein did not understand [the first incompleteness theorem] (or pretended not to understand it). He interpreted it as a kind of logical paradox, while in fact is just the opposite, namely a mathematical theorem within an absolutely uncontroversial part of mathematics (finitary number theory or combinatorics).[39]

In my opinion and based on what he wrote in his "Remarks on the Foundations of Mathematics", Wittgenstein was just confused. In my opinion, Wittgenstein did not understand model theory either:

https://plato.stanford.edu/entries/wittgenstein-mathematics/

From this it follows that all other apparent propositions are pseudo-propositions of various types and that all other uses of ‘true’ and ‘truth’ deviate markedly from the truth-by-correspondence (or agreement) that contingent propositions have in relation to reality. Thus, from the Tractatus to at least 1944, Wittgenstein maintains that “mathematical propositions” are not real propositions and that “mathematical truth” is essentially non-referential and purely syntactical in nature.

For example, the notion of truth in Peano arithmetic theory is defined as correspondence with the set-theoretical structure of the natural numbers. This is an abstract, Platonic reality and not the physical reality, but regardless, truth is still based on correspondence. Hence, arithmetical truth is not syntactical in nature.

Every time I have read something that Wittgenstein has written about mathematics in which he commits himself to a verifiable claim, it turns out to be simply wrong. Hence, Wittgenstein's contribution to the philosophy of mathematics is mostly ... confusion.

Sour Grapes — Vera Mont

What exactly would I envy? Dealings with the HR department of a university? I have never had to go through any HR department. I find the practice insulting. It says everything about your station in life. I am semi-retired now. If I was ever going to work again, I'd rather swear fealty as a serf to the lord of the manor than to deal with an HR department.

Perhaps you have learned a lot but still don't know everything there is to know, and perhaps you have made some wrong assumptions. — fishfry

Stephen Wolfram writes on this subject:

https://writings.stephenwolfram.com/2014/08/computational-knowledge-and-the-future-of-pure-mathematics

Curating the math corpus. So how big is the historical corpus of mathematics? There’ve probably been about 3 million mathematical papers published altogether—or about 100 million pages, growing at a rate of about 2 million pages per year. And in all of these papers, perhaps 5 million distinct theorems have been formally stated.

So, in order to know everything there is to know about mathematics, you need to read 3 million papers. Did I read them? Did I ever said that I read them? Did I even read 0.1% of them?

Knowledge is a gigantic database of (claim,justification) two-tuples that is for 99.999% stale and irrelevant. The only meaningful way of finding out what is relevant, is to work your way back from solutions that solve problems all the way into the math that directly or indirectly facilitates the solution.

So, is knowledge a good thing? Possibly, but it is first and foremost, utterly useless.

The idea of feeding students with some arbitrary excerpt from such knowledge database, assuming that it will ever be useful to them, is misguided and nonsensical.

That is the reason why the education system fails. Its knowledge-acquisition strategy simply does not make sense.

The only way to pick the right things to learn, is by going in exactly the opposite direction. You start by trying to solve a practical problem, for which there exists someone willing to pay for the solution, and only then you learn knowledge as required for producing the solution.

Whatever is real does not require faith — 180 Proof

Numbers are not "real". They are abstractions. Their use ultimately requires faith in Peano's axioms. So, you can't do math without faith. In all practical terms, you can't do science or technology without at least some math.

Hence, you can't live as a human without faith. Can you live as an animal without faith? No, because animals also use if only very basic arithmetic for their survival.

only a god can "prove a god". — 180 Proof

Gödel has proved the existence of a Godlike entity from higher-order modal logic.

https://en.wikipedia.org/wiki/G%C3%B6del%27s_ontological_proof

Gödel wasn't a god.

In fact, proving the existence of something is much easier than proving the impossibility that it would exist. In the first case, you only need to locate a suitable entity, just like Gödel did. In the second case, you need to inspect all possible candidates and demonstrate that they are unsuitable. Hence, you need to be an omniscient being in order to prove that an omniscient entity does not exist. Hence, only God can prove atheism.

So, the correct statement is:

Only a god can disprove the existence of God.

That would obviously lead to an interesting contradiction.

There obviously many features of h.sapiens that are biological in origin - practically everything about human physiology and anatomy can be understood through the lens of evolutionary biology. — Wayfarer

I consider evolutionary biology to be largely conjectural. If you truly understand something, then you can build it by yourself from scratch. So, as far as I am concerned, evolutionary biology does not truly understand what they are talking about.

But what about the religious experience, in particular, can be understood through that perspective? — Wayfarer

Religion is much more modest than evolutionary biology. It even starts by saying that even though we may ourselves be unable to create biological devices/beings from scratch, there is someone else who actually can. This take on the matter sounds much more plausible to me.

So let’s get clear on what you mean by ‘designed’. Where do you think your idea fits into that overall set of ideas, or does it not? — Wayfarer

I look at biology as a technology that we mostly fail to reverse engineer, if only, because we do not have access to its design documents. In a sense, it is superior to our own technology, because it seems to embed the factory that produces the device inside the device. We can't do that.

Biology as a technology is analogous to Von Neumann universal constructors:

John von Neumann's universal constructor is a self-replicating machine in a cellular automaton (CA) environment. It was designed in the 1940s, without the use of a computer. The fundamental details of the machine were published in von Neumann's book Theory of Self-Reproducing Automata, completed in 1966 by Arthur W. Burks after von Neumann's death.[2] It is regarded as foundational for automata theory, complex systems, and artificial life.[3][4] Indeed, Nobel Laureate Sydney Brenner considered Von Neumann's work on self-reproducing automata (together with Turing's work on computing machines) central to biological theory as well, allowing us to "discipline our thoughts about machines, both natural and artificial."

The reality is that in all practical terms we can't do self-replication with our technology. So, biology is simply a superior technology.

Therefore, my analogy that tries to map something that we do understand, the technology of computing devices, to some fragment of biology, is necessarily limited. We simply cannot reverse engineer it. If we could, we obviously would.

The very notion of "design" is tied to our technology. The term may be too simplistic when discussing non-human technology. What exactly does it correspond to in that case? I think we must accept the limitations of what we truly understand, reflected by the technology that we master and the problems that we can solve. If we truly understood biology, we would be able to build biological devices from scratch, which we can't.

Therefore, the term "design" merely reflects the limitations of what we understand. If we truly understood the technology of biology, we would probably dedicate a better term to reflect a particular important document that describes how it truly works.

Can anyone prove a god, I enjoy debates and wish to see the arguments posed in favour of the existence of a god. — CallMeDirac

To prove from what?

There is no context-free proof. A thing like that does not exist. You always need system-wide premises, i.e. an axiomatic theory that you first accept without proof.

If the next question is going to be, Yes, but how do you prove your system-wide premises? then we have landed in the middle of a pointless exercise in infinite regress.

In "Posterior Analytics", Aristotle already pointed out why you will eventually always have to accept unproven system-wide premises. After the 2500 years since Aristotle, this will obviously not stop infinite regressionists from engaging in their favorite exercise, i.e. infinite regression.

Kurt Gödel has proven the existence of a godlike entity from five axioms in higher-order modal logic:

https://en.wikipedia.org/wiki/G%C3%B6del%27s_ontological_proof

It means that the belief in a godlike entity is equiconsistent with the belief in five axiomatic modal expressions.

The standard criticism on Gödel's proof is obvious and should be expected:

Most criticism of Gödel's proof is aimed at its axioms: as with any proof in any logical system, if the axioms the proof depends on are doubted, then the conclusions can be doubted. It is particularly applicable to Gödel's proof – because it rests on five axioms, some of which are considered questionable. A proof does not necessitate that the conclusion be correct, but rather that by accepting the axioms, the conclusion follows logically.

Every proof implies at best equiconsistency with the system-wide premises explicitly relied on in the proof. A proof can never mean more than that. There simply does not exist a proof that embodies more truth than that. That is simply not possible.

Still, Gödel's proof has the merit of raising the bar.

Instead of attacking the notion of Godlike entity, one must now first learn higher-order modal logic and attack the five axiomatic expressions in his proof. Atheist often seem to believe that they are smarter than religious people. Fine, in that case, show us your mettle and try to meaningfully attack Gödel's subtleties in higher-order modal logic.

But they’re not designed - not unless you’re defending an intelligent designer. Are you? — Wayfarer

I personally believe that it is a non-human technology that embodies particular design principles. The analogy I see it through are technology devices with embedded software, i.e. firmware. There are lots of parallels. It is obviously not exactly the same. However, there are still surprisingly many similarities. An acceptable way to analyze something for which you do not have design documents, is to compare it to things for which you do have them. That is why I view biological devices through the lens of modern computing devices with embedded firmware. For example our own eyes are quite similar to embedded cameras with embedded firmware. It is not a perfect analogy but it is still better than nothing.

Biology operates through mechanisms and principles that are not designed or created by humans, whereas technology is inherently a product of human creativity and engineering. — Wayfarer

Biological systems are designed according to principles that appear similar to us to a technology, but clearly not of human origin. I use the term biological technology to point out that to an important extent we are similar to technological devices.

Assuming you don't mean "firmware" literally; sticking to the metaphor, what is the soul? Does it not also code the hardware so that it operated effectively? Is the soul, software? The operating system for the software? — ENOAH

The soul is what is gone when we die. Its role while we are alive is not clearly determined.

Is it necessarily instilled in us biologically? Or is that a favored interpretation because your's is currently a physicalist view?

Could it have been instilled in each human soul; this innate desire for religion? — ENOAH

In my opinion, impossible to say. The notion of soul is also part of religion. I personally believe that we have both some form of firmware as well as a soul.

What technology are you referring to? I thought we were discussing biology. — Wayfarer

Biology is a natural technology. We did not design it. We only very partially understand it. Still, it works surprisingly well.

Designed by whom or what? — Wayfarer

Not by humans, because that would lead to infinite regress. So, the technology is clearly of non-human origin. The rest is foundationalist belief. In religion, the belief is that the universe and humanity were created by the same creator.

Humans are biologically the same everywhere, but culturally and intellectually they’re vastly different. — Wayfarer

Every human is even individually unique. By design so.

If that’s so, you should be able to provide a citation. — Wayfarer

Quran 30:30 (Ar-Rum): So be steadfast in faith in all uprightness ˹O Prophet˺—the natural Way of Allah which He has instilled in ˹all˺ people. Let there be no change in this creation of Allah. That is the Straight Way, but most people do not know.

So why bring Islam into it? why not just stick to biology? — Wayfarer

Because the idea that religion is biologically innate comes from there. It is standard Islamic doctrine.

Do Muslims believe that it’s biological firmware? Or doesn’t it matter whether they believe it? — Wayfarer

I use the term "firmware" metaphorically here. It's a bit like the software embedded in specialized devices, such as your phone's camera, but obviously implemented in a completely different technology.

We do not control or even properly understand this technology because we did not design it.

The Quran does not contain its implementation details. If it did, we would probably not understand it anyway.

Do you think Muslims would agree that ‘fitrah’ is a biological drive? — Wayfarer

The term "fitrah" in Islam refers to all behavior that is innate. So, where else does it come from, if not from our biological firmware?

We are not a completely blank slate:

https://en.m.wikipedia.org/wiki/Instinct

Instinct is the inherent inclination of a living organism towards a particular complex behaviour, containing innate (inborn) elements.

Humans are, however, incredibly flexible. We are able to override a lot of innate behaviors while animals cannot.

For example, people may be able to modify a stimulated fixed action pattern by consciously recognizing the point of its activation and simply stop doing it, whereas animals without a sufficiently strong volitional capacity may not be able to disengage from their fixed action patterns, once activated.

This flexibility is both an advantage and a disadvantage. Humans are beyond any doubt the species that is the most prone to corruption, depravity, and degeneracy.

It doesn’t need to be invalidated. It’s simply irrelevant, even if it is the case. — Wayfarer

It is irrelevant until it isn't anymore.

Spolsky's law: All non-trivial abstractions, to some degree, are leaky.

The organic-chemistry composition of the stomach is mostly irrelevant but not completely.

The innate inclinations of humanity, its biological firmware, is actually even less irrelevant. A lot of human behavior is determined at the biological level.

But I don’t know if on that basis you could say that language is biological feature — Wayfarer

Yes, I believe that language is a biological feature that is part of the biologically preprogrammed firmware of humans. Otherwise, there would be humans in history or throughout the world that do not use language.

studying it through the perspective biology would be more suitable than through, say, linguistics or anthropology. — Wayfarer

That would be in my opinion unsuitable. For example, every stomach is ultimately built from atoms. That does not mean that you should address a stomach ache by means of theories in nuclear physics. But then again, this does not invalidate the observation that every stomach consists of atoms at some deeper level of observation detail.

But why do you think that maps against biology? — Wayfarer

Whenever a behavior is universal throughout history and throughout the world, it can only be biological. Otherwise, there would be or have been numerous societies in the past and/or throughout the world that did not have it. Every society that has ever existed, had a religion.

It always contains two things:

(1) a way of praying to the divine
(2) a set of rules not to break

If it is biological, then it is preprogrammed in one way or another into our biological firmware ("fitrah").

But then again, humanity is very flexible and adaptable. We are often able to overrule our own biological inclinations. Therefore, I believe that people are fundamentally religious but can also easily be trained not to be.

I hold that religion actually has a foundation discoverable in the essential conditions of our existence. — Constance

According to Islamic doctrine, religion is built into our preprogrammed biological firmware, called "fitrah" in Islam: https://en.wikipedia.org/wiki/Fitra

Humanity is, however, overly flexible.

It is trivially easy to deprave and degenerate humans away from their innate biological firmware. There is a lot of power to be had in doing so.

Therefore, the need eventually arose for religious scripture to appear which contains a copy in human language of the biologically preprogrammed rules that humans should not break and that government should never overrule. That is why during his investiture ceremony the new king was always forced to kneel to religion in order to be crowned. He had to acknowledge the supremacy of God's law.

If there are no tensions or even conflict between the political overlord and religion, then it is not a true religion. The more the political overlord complains about a particular religion, the more it is doing its main job, which is to constrain the political overlord, and therefore the more truthful it is. If religion is never an impediment to the expansion of state power, then it is a false religion.

Well, this is a philosophy site, so people here do understand why in the university math is studied, even if the applications to engineering etc. are different. — ssu

My own personal interest is also pure math rather than applied math. However, it has to be somehow relevant. The subjects I end up investigating are ultimately still inspired by practical use. For example, zero-knowledge arguments. If you dig under the hood, you end up investigating the properties of Weil and Tate pairings:

https://en.wikipedia.org/wiki/Weil_pairing

In mathematics, the Weil pairing is a pairing (bilinear form, though with multiplicative notation) on the points of order dividing n of an elliptic curve E, taking values in nth roots of unity. More generally there is a similar Weil pairing between points of order n of an abelian variety and its dual. It was introduced by André Weil (1940) for Jacobians of curves, who gave an abstract algebraic definition; the corresponding results for elliptic functions were known, and can be expressed simply by use of the Weierstrass sigma function.

The most interesting materials in the field are actually written by people like Vitalik Buterin, the founder of the Ethereum cryptocurrency. In order to implement zero-knowledge proofs in the Ethereum blockchain, he also ended up figuring out pairings:

https://medium.com/@VitalikButerin/exploring-elliptic-curve-pairings-c73c1864e627

Exploring Elliptic Curve Pairings

Trigger warning: math.

One of the key cryptographic primitives behind various constructions, including deterministic threshold signatures, zk-SNARKs and other simpler forms of zero-knowledge proofs is the elliptic curve pairing.

Vitalik's articles on the subject are much better than what you could ever find at any university.

A bit like Bill Gates (Microsoft) or Steve Jobs (Apple), Vitalik had to stop wasting his time and drop out of his university undergraduate in order to do something more important:

https://en.wikipedia.org/wiki/Vitalik_Buterin

He dropped out of university in 2014 when he was awarded with a grant of US$100,000 (equivalent to $128,704 in 2023)[19] from the Thiel Fellowship, a scholarship created by venture capitalist Peter Thiel and went to work on Ethereum full-time.

Hence, Vitalik is not just some credentialist postdoc idiot. The Ethereum market cap is now well over $400 billion. It is exactly because he really uses elliptic curve pairings, which is pure math, that he is much better at explaining the subject than anybody in the academia.

Vitalik has absolutely no university degree whatsoever but he wipes the floor in terms of knowledge with anybody who does. Credentialists are simply born idiots. Have always been. Will always be.

The worst thing you can do for the personality and mentality of any individual, is to give him a piece of paper that says that he now knows everything better than everybody else. I spit, pee, and shit on these people.

The academia claim that they lack practical experience but that they would somehow still be good at teaching theoretical subjects such as pure math. In reality, they aren't good at that either. The truth is that they are actually good for nothing.

The concert pianist actually intends to solve a problem. So does the athlete.

What problem does the math graduate intend to solve except for teaching math?

Concerning my academic background in a branch of applied math, if it were still relevant after decades, it would mean that I wouldn't have done anything meaningful in the meanwhile.

If a degree matters after your first job, it simply means that your first job did not matter.

My stints in pure math came much later. Sometimes because I was looking under the hood of the software I was using. Sometimes just out of interest.

For example, I did my first foray in abstract algebra by looking under the hood of elliptic-curve cryptography. In fact, you understand abstract algebra much better if you have first been exposed to subjects like ECDSA and Shnorr signatures. The other way around is not true.

You have a credentialist view on knowledge. That is typical for teaching associates at university. They think that credentialism matters. Well, they have to, because their hourly rate clearly does not matter. The academia are full of postdocs and other idiots who think they know but who in reality have nothing to show for. Furthermore, the relevant math is elsewhere. They really do not understand, not even to save themselves from drowning, which areas in pure math power technology. That is why they are stuck in areas that are irrelevant.

Oh, goodie! The six people who still understand some aspect of 'manual' programming can teach it to their children, set up dynasties and rule the world — Vera Mont

Again wrong!

All the relevant software is free and open source. There is nothing hidden. It's all there for everyone to look at.

The question is rather: Why would you even look at it?

Well, you would need a problem to solve. That is the only legitimate reason to pick up any knowledge. Otherwise, you are just wasting your time.

So, how do you find a problem to solve?

Simple. Find someone who is even willing to pay you real money for solving the problem. That problem must be somehow real. Why else are they even willing to part with real dollars?

You will quickly discover that other people have similar problems and that they are also willing to pay real money for you to do that. It is always an entire market.

So, instead of looking at the curriculum of a university degree, instead look at what problems are mentioned in job adverts. Pick one. Figure out how much time it would take to give a meaningful response to the job adverts. It rarely takes more than a few months.

If they require credentials that take years to acquire, skip that job. They are clearly full of bullshit, and their scammy job advert is just the tip of the iceberg. You would be entering an overregulated market in which ability to solve problems takes a back seat on regulatory credentials and other nonsense. It is not a real job. Instead, you will be spending your days filling out meaningless paperwork.

You see, you don't need nine years to learn how to be a family doctor and hand out medical prescriptions to elderly patients. You'll just become a pawn in the hands of the government-orchestrated pharmaceutical mafia. If it takes years to merely join at the lowest level, it is always a scam. Don't spend your life ripping off other people and getting ripped off yourself.

Sounds as if you are arguing for an intellectually impoverished populace, and I wonder why? — wonderer1

They already are intellectually impoverished. They just don't know it.

In fact, university graduates are being placed in the worst situation possible. The university makes them believe that they know, but in fact, they know absolutely nothing of value.

Why would you even learn if you think that you know it all already? You can even prove that you know it all. Isn't that what your academic credential is for?

So, now you need to face potential employers. They perfectly well know that you don't know. They also know that you are convinced that you know, even though you don't. So, you still feel entitled. You think that you deserve the world, essentially for being useless and ignorant.

Instead of spending years regurgitating irrelevant trivia, do a 3-month boot camp. Employers will be more interested in hiring you.

And how can you pick the correct toll, if you don't know the arithmetical and algebraic procedures themselves? By at least learning to do them yourself, you understand them. — ssu

That would be the same question as how do you choose an encryption algorithm if you can't encrypt/decrypt manually?

I don't know anybody who actually can.

I can pretty much guarantee that almost nobody who uses libsodium can manually carry out any operation in xchacha20:

https://doc.libsodium.org/secret-key_cryptography/encrypted-messages

In fact, it is never seen as a requirement.

There are, of course, people like Daniel Bernstein who specialize in the knowledge of the level below libsodium but they are outnumbered 1 to 10000 by the people who just use libsodium.

The problem is that there's simply too much math to study at a slow pace. — ssu

You have to make choices.

But then again, you can only make those choices when faced with real-life problems to solve. Hence, it is the problem at hand that chooses what you should learn.

All other math is irrelevant in your particular context. It's too much anyway. Seriously, why even waste your time on that? In order to achieve what exactly?

No school on earth teaches you how to use libsodium. No university teaches you how xchacha20 works. They would not even be able to. Universities don't even teach you anything that is even remotely relevant in that respect. In fact, I spent most of my career -- I am semi-retired now -- picking up knowledge and using it, that no school or university ever even remotely mentions.

So yes, I used a lot of underlying math, hidden in programs and software libraries, some of which I somewhat investigated under the hood. It is totally unrelated to what universities teach. Universities are clearly not even aware of the existence of this kind of math.

Hence, if you are interested in relevant mathematics, you are wasting your time studying it at university, because in my decades-long experience, pretty much everything they do at university, is irrelevant to modern technology. These people cannot choose what to study and what not, simply because they don't use it themselves. They somehow believe that what they do, is meaningful, but it simply isn't.

Maybe true, but it could also be that most people aren’t interested in the jobs that education helps with attaining, and so for the majority it is not that helpful. What would you propose? — Igitur

"Child labor". Like it used to be.

Harold Lowe was one of the officers on the Titanic:

https://en.wikipedia.org/wiki/Harold_Lowe

Harold Lowe was born in Llanrhos, Caernarvonshire, Wales, on 21 November 1882, the fourth of eight children, born to George Edward Lowe and Emma Harriette Quick. His father had ambitions for him to be apprenticed to a successful Liverpool businessman, but Harold Lowe was determined to go to sea. At 14, he ran away from his home in Barmouth where he had attended school and joined the Merchant Navy, serving along the West African Coast. Lowe started as a ship's boy aboard the Welsh coastal schooners as he worked to attain his certifications. In 1906, he passed his certification and gained his second mate's certificate, then in 1908, he attained his first mate's certificate.

Teach your brats to cook, to grow food, to work wood and metal. And how to get along with the neighbours, which is by having all these useful skills that can help them stay alive. The machines are no longer your friends. — unenlightened

We used to be hunter-gatherers. So, don't grow food. Hunt it instead.

There is just one problem with this view. There was a reason why we started growing food instead of hunting it. This planet was able to support less than a million hunter-gatherers. We are 8 billion now.

Mutatis mutandis, our current head count of 8 billion does not allow us to get rid of the machines. If we do that, we need to get rid of billions of people too. Who volunteers to leave first? Not me.

S0. A nation of innumerate illiterates who can't find North on a compass just need to be trained in which buttons to push. Maybe a chimp can instruct them.
I'm just lucky not to have any future! — Vera Mont

Wrong again.

Software needs to be maintained. If nobody knows how it works anymore, the software is simply dead. These people need to know how to do it manually. If you don't know how to do it manually -- excruciatingly and step by step -- you can't touch one line in the software either.

You see, the specialized knowledge is massively important to some people. However, shoving it down the throat of everyone else, is not the solution. They first need to learn how to use the software.

But then again, after using the software for years, there are always people who want to know more, and who want to know how it works and why it works. That is how I spent years developing small toy compilers and interpreters, because I wanted to know what my compiler or script engine was doing under the hood. That allowed me to read the source code of the tools I was using. That brought me to learning the computer-science math with regards to compiler construction.

You see, it is absolutely wrong to start the journey there. Just learn to use the tool first. Only if it truly piques your interest, it makes sense to look under the hood. Computer science graduates may learn some of it, but they learn it at the wrong time in their lives. They learn it at a point at which it simply does not matter to them. That is why they suck at it.

Also, teaching someone how to make an app wouldn’t be the same as teaching them how apps work. — Igitur

Someone with a degree in swimmology has read a lot of books about swimming, but he does not necessarily swim himself. That does not matter, because he can teach swimmology!

The “starting point” would be higher education. — Igitur

It used to be high school. Now, they delay it to higher education. But then again, if higher education were such a fantastic starting point, then why do so many of its graduates end up slinging coffee at Starbucks? The proof is always in the pudding, isn't it?

I was mainly saying the baseline education
was necessary for students who wish to go into jobs that have to do with them. Kind of like a way of introducing a lot of jobs that need to be done, but otherwise might not. (Like math related ones.) — Igitur

In fact, there are no math-related jobs. There is only math-containing software. There simply is no job where you have to manually compute math results. These students do not learn how to build such software. They also do not learn how to use such software. Instead, they learn how to fail at being themselves the software.

talking mostly about experimental fields of science here — Igitur

That's just another scam. The government spends money on "scientific research". Next, when there is scientific progress somewhere, the government is quick to claim credit for it, and then wants some more money for "scientific research".

There is an interesting German woman, Sabine Hossenfelder, who spent decades in scientific research and who explains in excruciating detail how the scam works. One of her videos:

What's Going Wrong in Particle Physics? (This is why I lost faith in science.)

They may come up anyway, but this education system probably either helps them learn about such subjects or helps more students to explore possibilities that they might not have without education. — Igitur

You cannot make progress inside the system, because that will almost always be shut down. Every innovation is in one way or another a threat to existing interests. That is why all progress is made outside the system. Example: cryptocurrencies. They dangerously threaten the monopoly of the banking system and associated government power and control. That is why they could never have emerged out of the academia or even the corporate world. The powers that be would have immediately nipped it in the bud. Same for the medical industry. Don't cure a disease that currently makes the pharmaceutical mafia billions already by not curing it.