A must have for your script file to ease spreading a small proof of concept with dependencies!

PaketDependencyManagementMadeEasy.fsx

open System
open System.IO
open System.Diagnostics

let downloadDependencies deps =
    Environment.CurrentDirectory <- __SOURCE_DIRECTORY__

    if not (File.Exists "paket.exe") then
        async {
            let url = "http://fsprojects.github.io/Paket/stable"
            use wc = new Net.WebClient()
            wc.DownloadProgressChanged.Add(fun a -> printfn "Progress downloading paket.exe: %d" a.ProgressPercentage)
            let tmp = Path.GetTempFileName()
            let stable = wc.DownloadString(url) 
            do! wc.AsyncDownloadFile(stable |> Uri, tmp)
            File.Move(tmp,Path.GetFileName stable)
        } |> Async.RunSynchronously
        printfn "Finished downloading paket.exe!"

    let invokePaket args =
        use process = 
            new Process(
                StartInfo = 
                    new ProcessStartInfo(
                        FileName = "./paket.exe",
                        Arguments = args,
                        UseShellExecute = false))
        process.Start() |> ignore
        process.WaitForExit()
    if not (File.Exists "paket.dependencies") && not (File.Exists "paket.lock") then
        invokePaket "init"
    for dep in deps do
        sprintf "add %s" dep
        |> invokePaket
downloadDependencies [ "MathNet.Numerics"; "MathNet.Numerics.FSharp"] // Append the package names to this list! 

Good idea. Although I'm getting this message:

System.Net.WebException: The request was aborted: Could not create SSL/TLS secure channel.
ERR :    at System.Net.HttpWebRequest.EndGetResponse(IAsyncResult asyncResult)
ERR :    at System.Net.WebClient.GetWebResponse(WebRequest request, IAsyncResult result)
ERR :    at System.Net.WebClient.DownloadBitsResponseCallback(IAsyncResult result)
ERR : --- End of stack trace from previous location where exception was thrown ---
ERR :    at System.Runtime.ExceptionServices.ExceptionDispatchInfo.Throw()
ERR :    at Microsoft.FSharp.Control.AsyncBuilderImpl.commit[a](AsyncImplResult`1 res)
ERR :    at Microsoft.FSharp.Control.CancellationTokenOps.RunSynchronouslyInAnotherThread[a](CancellationToken token, FSharpAsync`1 computation, FSharpOption`1 timeout)
ERR :    at Microsoft.FSharp.Control.CancellationTokenOps.RunSynchronously[a](CancellationToken token, FSharpAsync`1 computation, FSharpOption`1 timeout)
ERR :    at Microsoft.FSharp.Control.FSharpAsync.RunSynchronously[T](FSharpAsync`1 computation, FSharpOption`1 timeout, FSharpOption`1 cancellationToken)

@amieres What version of Paket are you using? I think I got that once because of some change that Github made, and it required updating my Paket version.

I think I've also "resolved" that error by simply trying it again (was a transient network issue).

@amieres @NatElkins @realvictorprm
Might want to add:
System.Net.ServicePointManager.SecurityProtocol <- System.Net.SecurityProtocolType.Tls12 // Github uses TLS 1.2
to the top of the file after open statements.

I get this when pasting downloadDependencies into fsi:

warning FS0046: The identifier 'process' is reserved for future use by F#

@amieres that's not about paket. GitHub has disabled TLS <= 1.2 How to enable TLS 1.2.

@Zagrophyte

Might want to add:
System.Net.ServicePointManager.SecurityProtocol <- System.Net.SecurityProtocolType.Tls12 // Github uses TLS 1.2
to the top of the file after open statements.

You are right! That did the trick.
Thank you!