The first half of Marijo's answer was excellent, but it's fine to use "achieving" here. In all of Marijo's examples, "to" is showing the idea of "direction". It isn't being used to make a verb infinitive. The "-ing" is turning the verb into a gerund, and gerunds act like nouns. ****SO, if you can put a noun after the "to", you can put a gerund there, too.*** I am getting used to *the weather* (noun)--> I am getting used to *exercising* frequently. (gerund) I am partial to *cake* (noun) [I am partial to X= I like X]--> I am partial to *swimming*. (gerund) Bob is a disgrace to *his family* (noun)-->Bob is a disgrace to *teaching*. (gerund) And, in your example: We are getting closer to *New York* (noun)--> We are getting closer to *winning* the war. (gerund)

The -ing in 'achieving' indicates that something is happening at the present time. So, "the world is getting closer to achieving one of the most important public health goals of out time" means that the world is getting closer to this goal at this very moment. 'Achieve' as a word on it's own normally indicates something which will occur in the future, for example, "The world will soon achieve one of the most important public health goals." Additionally, 'achieved' indicates something has occurred in the past, so, "the world has finally achieved one of the most important public health goals." A simple template to follow is: -ed = Past -ing = Present no suffix = Future Though this won't apply in all cases, it should hopefully give you an idea of why certain verbs are used in certain instances. I hope this helps!

Yes, there's a pretty easy way. Well, sort of easy. Try to put the word "it" after the "to". If it "works," this is because the "to" is actually a preposition and part of the verbal phrase. For example: I'm looking forward to ... (something OR doing something) I'm looking forward to it. GOOD I want to it. NOT GOOD. I want to go. GOOD ("to" here is part of the infinitive) I am accustomed to it. GOOD I am accustomed to getting up at eight every morning. (GOOD) I hope I've explained it well!

Hi there, Kelvinho! The structure "to+verb-ing" is possible because the verb is actually working as a gerund, so it takes place when: (1) the prepostion "to" is part of a phrasal verb: I am looking forward to attending the party (2) the to is part of an adjective + preposition combination: A lot of women aren’t accustomed to being treated so well! (3) the to is part of a noun + preposition combination: His addiction to gambling has caused a lot of stress for his family. However, in your example, "achieving" is not well used. It does belong to any of the cases described above. It would be better to say: ...closer to the achievement of one of the most important... References: https://english.stackexchange.com/questions/38964/how-to-use-to-v-ing