Summary judgment was entered for Morris Communications Company on Christopher Miller’s Americans with Disabilities Act claim on July 22, 2005. Miller, in response, filed motions with the district court for immediate entry of a *882default judgment and under Rule 60(b) for relief from judgment. The district court denied both motions, stating as to the latter one that it “ha[d] no jurisdiction to hear further motions in this case or rule on their merits.” (R13:275:4.)
During the district court’s consideration of those motions, Miller sent e-mails and facsimiles directly to the court. The district court on three occasions ordered Miller to stop. In the first order, dated July 25, 2005, the court wrote that “[i]t is improper for a litigant to correspond directly with a Judge presiding over his or her case via telephone, letter or email,” and instructed Miller that any communication about an action he wanted the court to take should be filed directly with the clerk’s office.
In the second order, dated October 14, 2005, the district court noted that Miller had continued to send e-mail messages directly to the court requesting that it file attachments for him electronically. The district court warned Miller that if he did not stop communicating directly with the court he would be held in contempt of court and subjected to sanctions.
In the third order, dated November 28, 2005, the district court explained that, after its preceding order, Miller had emailed several more messages to the court, to the courtroom deputy, to various employees of the clerk’s office and to every judge in the Middle District of Florida. In addition to those e-mails, Miller had also faxed copies of the communications to some of the judges in the Jacksonville, Florida courthouse. The district court ordered Miller to stop sending e-mails and faxes to the judges and employees of the Middle District of Florida. It warned him that any further improper communications would result in a $10,000 civil contempt fine for each recipient of each document.
Despite that warning, Miller did not stop. He continued to send e-mail messages. As a result, the district court ordered Miller to show cause why he should not be held in contempt of court and sanctioned $70,000 for violating the no-email- or-fax order. When Miller did not show cause or even show up at the show cause hearing, the district court ordered that he be held in contempt and that judgment be entered against him for $70,000. That order was issued on November 30, 2005.
Even after that order Miller continued to send the district court more e-mails. In response, the court amended the judgment that was based on its November 30, 2005 order so that Miller would have to pay $180,000 within thirty days or be arrested.
Miller then filed two motions for relief from judgment: one for relief from the summary judgment on his ADA claim, and the other for relief from the $180,000 sanctions judgment. Almost unbelievably, he also sent more e-mails to the district court’s chambers. As a result, the district court ordered that judgment be entered against Miller for an additional $20,000, bringing the total amount of the sanctions against him to $200,000. After a hearing, the district court in a single order, dated February 3, 2006, denied both of Miller’s motions for relief from judgment. Miller appeals that order.1
*883I.
Miller contends that the district court abused its discretion in its February 3, 2006 order denying his motion for relief from summary judgment because: (1) the court refused to consider evidence that Morris committed fraud by destroying relevant evidence and concealing the destruction from the court; and (2) the court refused to hear arguments in support of his motion at the hearing. Miller is wrong on both accounts.
“[T]he law is clear that Rule 60(b) may not be used to challenge mistakes of law which could have been raised on direct appeal.” Am. Bankers Ins. Co. of Fla. v. N.W. Nat’l Ins. Co., 198 F.3d 1332, 1338 (11th Cir.1999). That is, a motion for relief may not be used by the losing party in the district court to circumvent the jurisdictional requirement that he appeal the merits of the underlying judgment within thirty days. See Burnside v. E. Airlines, Inc., 519 F.2d 1127, 1128 (5th Cir.1975) (per curiam) (“The well-recognized rule, however, and that which comports with the time limit imposed by [Federal] Rules [of Appellate Procedure] 4(a) and 3(a), precludes the use of a Rule 60(b) motion as a substitute for a proper and timely appeal.”).
Here, the discovery issues were raised by Miller numerous times both before and during the district court’s consideration of the summary judgment motion. Miller could have filed a Federal Rule of Civil Procedure 56(f) motion to extend the time for discovery, or moved for discovery sanctions against Morris (including a default judgment), and then appealed the district court’s decision as to these motions. But he chose not to. He cannot now, five months later, use a Rule 60 motion to make an end run around the jurisdictional requirement that he appeal the merits of the judgment within thirty days of its entry.
Accordingly, the district court did not abuse its discretion in finding that Miller failed to demonstrate any ground under Rule 60(b) entitling him to relief from the summary judgment entered in favor of Morris. And because Miller failed to suggest any arguably valid ground for relief, the district court did not abuse its discretion in denying him a hearing on the motion. See Cano v. Baker, 435 F.3d 1337, 1342-43 (11th Cir.2006) (per curiam) (“The district court did not abuse its discretion by denying Cano’s request for an evidentiary hearing and to make specific factual findings of fact on the evidence she submitted in support of her Rule 60(b) motion.... Because the district court’s underlying decision was based on its lack of authority to grant the relief requested by Cano as a matter of law, there would have been no reason to hold an evidentiary hearing.”).
II.
As to Miller’s appeal from the denial of his motion for relief from the contempt judgments sanctioning him $200,000, he contends that: (1) the judgments are void because the district court did not have jurisdiction to enter them; (2) they are improper because the court knew that he could not pay that much; and (3) it was necessary for him to send the e-mails and faxes because the court’s rules prevented him from filing his papers electronically without first obtaining authorization.2
*884Miller’s first argument is based on the following statement in the district court’s order denying his first Rule 60(b) motion: “As Plaintiff has exhausted all avenues for relief, the Court has no jurisdiction to hear further motions in this case or rule on their merits.” (R13:275:4.) Miller argues that since the district court said it did not have jurisdiction to hear any further motions, it follows that the court did not have jurisdiction to issue contempt orders and sanctions.
Miller reads too much into the district court’s statement. The district court was simply stating its opinion about jurisdiction to enter further orders directly relating to the merits of the case. The court did still have jurisdiction to entertain Rule 60(b) motions relating to the judgments it had entered. See Fed.R.Civ.P. 60(b). And, more importantly, the court still had jurisdiction to protect itself and other judicial officers and personnel from improper communications from a disgruntled litigant. See Martin v. Automobili Lamborghini Exclusive, Inc., 307 F.3d 1332, 1335 (11th Cir.2002) (“Courts have the inherent authority to control the proceedings before them, which includes the authority to impose ‘reasonable and appropriate’ sanctions.”).
Miller’s arguments that the court should not have held him in contempt for continuing to send the communications and that it knew he could not pay the amount it ordered are contentions that go to the merits of the sanctions judgments. They could have been raised in a timely appeal from those judgments, but none was filed. A Rule 60(b) motion cannot be used to skirt the strict thirty-day jurisdictional requirement for filing a notice of appeal. See Am. Bankers Ins. Co. of Fla., 198 F.3d at 1338; Burnside, 519 F.2d at 1128. Accordingly, the district court’s order denying Miller’s Rule 60(b) motion for relief of the sanctions judgments is due to be affirmed.
AFFIRMED.