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I like Mathematics but I hate the language of Mathematics. Mathematicians chose to sacrifice readability in favor of terseness; they invented a large number of

I like Mathematics but I hate the language of Mathematics. Mathematicians chose to sacrifice readability in favor of terseness; they invented a large number of abstractions, often with only tiny differences between them. Also, descriptions of concepts tend to focus on the wrong characteristics... Maths would be far more accessible if mathematicians described everything in plain English and reused abstractions to describe similar concepts instead of inventing entirely new words. It's possible, they just don't want to do this because it wouldn't make them sound as clever. As a developer, I can explain a blockchain as: 1. A decentralized ledger which relies on an asymmetric signature scheme such as EdDSA, zero-knowledge proofs or other mechanism to authenticate on-chain messages. A blockchain network forms either a structured (deterministic) or unstructured (stochastic) P2P mesh, ideally with each node having a partial view and propagating messages through the network via a gossip protocol. Blockchain nodes adhere to a consensus mechanism such as PoW or PoS (or variants) to provide byzantine fault tolerance and resilience to forks given certain finality conditions. Or: 2. A ledger which is replicated across multiple nodes/computers which are connected together. The blockchain is usually a ledger of accounts involving financial transactions. The authenticity of each transaction can be independently verified by anyone by checking that a digital signature on any transaction corresponds to the account which claims to have sent the transaction - This is possible because each account is associated with a 'public key' which anyone can see and which can be used to verify that a signature was generated by the sender since only the sender could have known the 'private key' (secret) which was used to generate this specific signature given this specific transaction and this specific public key.

tel 5y ago
Mathematical papers are essentially mathematicians shipping pseudo code back and forth. There are good reasons for it, but it’s not meant for most audiences. Mathematicians absolutely do write accessibly from time to time, but when they do so you have to be fortunate enough to be in the audience. Often these are aimed at only the most general of audiences and thus are pretty sparse in detail.
Jtsummers 5y ago
> Maths would be far more accessible if mathematicians described everything in plain English Are you sure about that? Take Kepler's Laws of Planetary Motion as an explanation of orbital mechanics and try and do anything with just these plaintext definitions (courtesy of Wikipedia): The three laws state that: 1. The orbit of a planet is an ellipse with the Sun at one of the two foci. 2. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. 3. The square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit. Now try and apply this without ever falling into mathematical notations. And translate this into every language under the Sun unless you really want it to only be comprehensible to English readers. Or take this formula, converted into plain English: The distance of a planet from the sun is proportional to the semi-latus rectum and one more than the product of the eccentricity of the orbit and the cosine of the angle between the planet's current position and its nearest approach. To help out since at least one term in there may be unfamiliar to most readers (courtesy of Wikipedia): The latus rectum is the chord parallel to the directrix and passing through a focus; its half-length is the semi-latus rectum (ℓ). Now, take that and suppose we have the distance from the sun and all the other values, but not the angle, rephrase that abomination so that we can solve for the angle. Without using mathematical notation. The only good thing about dropping mathematical notation is that we'd be able to slow down technological process substantially as we wouldn't even be able to get to orbit anymore. That idea of "solve for θ" is "just" a basic application of algebra. An act that would become impossible to do with any kind of reasonable efficiency and confidence about correctness without something like our current mathematical notation, and plain English (very anglocentric, guess we don't want anyone outside the anglosphere to participate) would be a poor alternate.
Koshkin 5y ago
Indeed, mathematical notation is often used (and abused) where plain language would suffice. This is so widespread, in fact, that one might think that there is a conspiracy, or a contest, to come up with as unreadable a text as possible. On the other hand, the (original) purpose of mathematical notation, in its condensed form, is facilitating and, in many cases, automating reasoning and calculations on a piece of paper. (You wouldn't want do perform long division using words, believe me.) Also, the plain language may bring the possibility of an uncertainty in meaning and/or misinterpretation, so a definition or a theorem stated using notation instead often serves to minimize that possibility.

tel 5y ago

Mathematical papers are essentially mathematicians shipping pseudo code back and forth. There are good reasons for it, but it’s not meant for most audiences. Mathematicians absolutely do write accessibly from time to time, but when they do so you have to be fortunate enough to be in the audience. Often these are aimed at only the most general of audiences and thus are pretty sparse in detail.

Jtsummers 5y ago

> Maths would be far more accessible if mathematicians described everything in plain English Are you sure about that? Take Kepler's Laws of Planetary Motion as an explanation of orbital mechanics and try and do anything with just these plaintext definitions (courtesy of Wikipedia): The three laws state that: 1. The orbit of a planet is an ellipse with the Sun at one of the two foci. 2. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. 3. The square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit. Now try and apply this without ever falling into mathematical notations. And translate this into every language under the Sun unless you really want it to only be comprehensible to English readers. Or take this formula, converted into plain English: The distance of a planet from the sun is proportional to the semi-latus rectum and one more than the product of the eccentricity of the orbit and the cosine of the angle between the planet's current position and its nearest approach. To help out since at least one term in there may be unfamiliar to most readers (courtesy of Wikipedia): The latus rectum is the chord parallel to the directrix and passing through a focus; its half-length is the semi-latus rectum (ℓ). Now, take that and suppose we have the distance from the sun and all the other values, but not the angle, rephrase that abomination so that we can solve for the angle. Without using mathematical notation. The only good thing about dropping mathematical notation is that we'd be able to slow down technological process substantially as we wouldn't even be able to get to orbit anymore. That idea of "solve for θ" is "just" a basic application of algebra. An act that would become impossible to do with any kind of reasonable efficiency and confidence about correctness without something like our current mathematical notation, and plain English (very anglocentric, guess we don't want anyone outside the anglosphere to participate) would be a poor alternate.

Koshkin 5y ago

Indeed, mathematical notation is often used (and abused) where plain language would suffice. This is so widespread, in fact, that one might think that there is a conspiracy, or a contest, to come up with as unreadable a text as possible. On the other hand, the (original) purpose of mathematical notation, in its condensed form, is facilitating and, in many cases, automating reasoning and calculations on a piece of paper. (You wouldn't want do perform long division using words, believe me.) Also, the plain language may bring the possibility of an uncertainty in meaning and/or misinterpretation, so a definition or a theorem stated using notation instead often serves to minimize that possibility.