In case the title is confusing, this is the older meaning of "Apology." Not, "I'm sorry," but "defense." This is a defense and justification for the field of mathematics.
Yeah, interesting that the meanings shifted over time. EG, look at Google Translate (E>L) where apology (E) becomes excusatione (L) with a back translation (L>E) of 'excuse'. Today an apology may or may not come with an excuse but back then an apology must have been a rationalization for some action.
> No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems unlikely that anyone will do so for many years.
Poor guy, if he had just heard about gps and about modern cryptography!
This is a favorite of mine and got me through some tough days in undergrad. I'm no longer a young man and I don't really pursue mathematics anymore, but it was a good reminder of a good days.
I also loved reading this book (and the prologue by C.P. Snow on the two cultures). Yet, it is amazing to see that this is not the only possible world view among mathematicians. For example, Vladimir Arnold has essentially the opposite view [1]: "Mathematics is the part of physics where experiments are cheap".
There is a bit of irony that for all the "maths for maths' sake" argument of this apology, one of Hardy's most lasting achievements was a basic principle of genetics -- the Hardy-Weinberg equilibrium https://en.wikipedia.org/wiki/Hardy%E2%80%93Weinberg_princip...
Hardy's idea that math is a young man's game is wrong & discriminatory against those that lack opportunities to education early in their life. Or for whatever reason pursued math at a later age.
just to clarify, it would be an observation to say "Most Mathematicians produce their best work when they're young" or "Most gymnasts who make it to the olympics are young"
But to say that X is a young mans game is inherently discriminatory.
Isn't that a bit strict? It seems that "x is a young man's game" can be read either in an empirical ("historically, only young men do x") or normative ("only young men should do x") sense, the former of which might be slightly inaccurate because there are exceptions, but otherwise seems fine.
A view held by some seems to be that since even the empirical observation may "perpetuate" the situation, stating it is "problematic" in itself, but I don't suppose this is what you mean here.
I take it he was referring to having the time and energy when you're young, as opposed to becoming a professional and being swamped with obligations such as work and family. Holding the Sadleirian chair likely means constant social and academic obligations.
The current version (in print) includes a sizeable forward by Snow, which is at least as interesting.
And the irony of this entire writeup is that number theory is now beyond "useful", as the underpinning for cryptography and security in our modern systems.
I have heard of this "apology", but never got around to reading it. On p. 12 right now. The author makes certain statements about age of people in math which are basically statistics arguments from a few famous examples and his "limited experience".
Also, a lot is different since the days of Hardy.
At least, now I see where some mathematicians get their pretentiousness :)
idk why people are getting so hung up on this point. it is obviously true that more great mathematics has been produced by young people. obviously there are exceptions, but they add credence to the general case
I've heard similar arguments about age and physics. I've always theorized that as time progresses the body of work one must be familiar with in order to make new contributions grows as well. We should therefore expect that in modern times, major contributions should come from more experienced individuals.
> I've always theorized that as time progresses the body of work one must be familiar with in order to make new contributions grows as well.
As I see it, this is not too big a problem. Usually people get on a very narrow path and specialize in a tiny part of a larger discipline. There's a lot of new research being done in algebra, analysis, geometry, statistics, whatever; but as a researcher you are expected to choose a very narrow sub-sub -...-sub-discipline and ignore everything else. That's very much doable. An analyst who can't read number theory papers is not a rarity. Likely a rule.
In case the title is confusing, this is the older meaning of "Apology." Not, "I'm sorry," but "defense." This is a defense and justification for the field of mathematics.
As in Newman's Apologia Pro Vita Sua (L: A defence of one's own life)
so that's where Christian "Apologetics" comes from
Yeah, interesting that the meanings shifted over time. EG, look at Google Translate (E>L) where apology (E) becomes excusatione (L) with a back translation (L>E) of 'excuse'. Today an apology may or may not come with an excuse but back then an apology must have been a rationalization for some action.
> No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems unlikely that anyone will do so for many years.
Poor guy, if he had just heard about gps and about modern cryptography!
>or relativity
Which was used for the atomic bomb.
How come? I never heard about that.
Relativity is essential for nuclear physics, because of the high energy densities.
Special relativity, not general, just to be clear.
You'd need general if you wanted to divert asteroids and crash them with pinpoint accuracy on your enemy's cities.
This is a favorite of mine and got me through some tough days in undergrad. I'm no longer a young man and I don't really pursue mathematics anymore, but it was a good reminder of a good days.
Thanks for posting :)
I also loved reading this book (and the prologue by C.P. Snow on the two cultures). Yet, it is amazing to see that this is not the only possible world view among mathematicians. For example, Vladimir Arnold has essentially the opposite view [1]: "Mathematics is the part of physics where experiments are cheap".
[1] https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html
There is a bit of irony that for all the "maths for maths' sake" argument of this apology, one of Hardy's most lasting achievements was a basic principle of genetics -- the Hardy-Weinberg equilibrium https://en.wikipedia.org/wiki/Hardy%E2%80%93Weinberg_princip...
Hardy's idea that math is a young man's game is wrong & discriminatory against those that lack opportunities to education early in their life. Or for whatever reason pursued math at a later age.
See people like: https://en.wikipedia.org/wiki/Yitang_Zhang that produced good math at a later stage.
It’s an observation, not a prescription. Is it “discriminatory” to suggest that gymnastics is a young person’s game?
Yes
edit:
just to clarify, it would be an observation to say "Most Mathematicians produce their best work when they're young" or "Most gymnasts who make it to the olympics are young"
But to say that X is a young mans game is inherently discriminatory.
Isn't that a bit strict? It seems that "x is a young man's game" can be read either in an empirical ("historically, only young men do x") or normative ("only young men should do x") sense, the former of which might be slightly inaccurate because there are exceptions, but otherwise seems fine.
A view held by some seems to be that since even the empirical observation may "perpetuate" the situation, stating it is "problematic" in itself, but I don't suppose this is what you mean here.
I take it he was referring to having the time and energy when you're young, as opposed to becoming a professional and being swamped with obligations such as work and family. Holding the Sadleirian chair likely means constant social and academic obligations.
The current version (in print) includes a sizeable forward by Snow, which is at least as interesting.
And the irony of this entire writeup is that number theory is now beyond "useful", as the underpinning for cryptography and security in our modern systems.
I have heard of this "apology", but never got around to reading it. On p. 12 right now. The author makes certain statements about age of people in math which are basically statistics arguments from a few famous examples and his "limited experience".
Also, a lot is different since the days of Hardy.
At least, now I see where some mathematicians get their pretentiousness :)
idk why people are getting so hung up on this point. it is obviously true that more great mathematics has been produced by young people. obviously there are exceptions, but they add credence to the general case
I've heard similar arguments about age and physics. I've always theorized that as time progresses the body of work one must be familiar with in order to make new contributions grows as well. We should therefore expect that in modern times, major contributions should come from more experienced individuals.
> I've always theorized that as time progresses the body of work one must be familiar with in order to make new contributions grows as well.
As I see it, this is not too big a problem. Usually people get on a very narrow path and specialize in a tiny part of a larger discipline. There's a lot of new research being done in algebra, analysis, geometry, statistics, whatever; but as a researcher you are expected to choose a very narrow sub-sub -...-sub-discipline and ignore everything else. That's very much doable. An analyst who can't read number theory papers is not a rarity. Likely a rule.