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98% Certainty that Trump has reduced crime in DC

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It’s been 24 days since Trump sent the national guard into DC, and the crime rate has dropped by a factor of six. The murder rate went from 101 murders per year in 2024, one murder every 3.6 days, to one murder in 24 days. I find that the odds of this being coincidence is less than 2%. Car theft and other crime has dropped as well. I consider murder rate the best metric for crime because no murders go unreported, and none get misclassified as altercations or misunderstandings.

Using the National Guard to maintain order is not that unusual. Eisenhower sent them to Arkansas in opposition to the governor to ensure desegregation. LBJ sent them to Chicago to protect the Democratic convention of 1968.

To figure the odds that this improvement is coincidence, consider that the odds of a murder on any one day is 101/365 = .277. Based on this, the odds of no murder on any of particular days is, 1-.277 = .723. On any given day in DC it’s more likely to have no murders than to have a murder, but the odds get much lower for going many days without a murder, or for 24 days with only one. The chance of of having 24 days without murder, for example beginning at some set-start, would be (.773)24 = .0021 = 0.21%. The odds of having only one murder in this time is calculated similarly, as 24(.277)(.773)23 = 1.8%. This is to say that there is a 98.2% chance that the drop in crime rate is not accidental.

The D.C. Mayor Muriel Bowser had originally objected to the guard, but now is happy, or so Trump claims. If she removed them now on, she would have to argue that high crime rates are good. Other mayors may not want to be in this position.

A federal judge, Charles Breyer, just declared the use of the national guard illegal, by the way, a violation of the Posse Comitatus act of 1878 see the complete statement here. The Posse Comitatus act bars the use of federal troops for police activities, except federally related ones. Judge Breyer, decides that there is no federal justification and demands that the national guard leave within 10 days. Trump claims that various riots in DC and LA (and Chicago) constitute an insurrection, and adds that attacks on federal ICE agents and federal buildings makes it federal. Judge Breyer recognizes that many other presidents have used the guard for law and order, even in opposition to the governor. Eisenhower for example, or LBJ to protect the Democratic National Convention 1968, but sees no justification, here or (it seems) for Eisenhower or LBJ either. Judge Breyer seems to believe they all acted illegally. I don’t know enough law to judge, but recognize that allowing Trump to reduce the crime rate makes mayors and governors look bad. Detroit crime is awful, as is LAs, Chicago’s…

Robert E. Buxbaum September 4, 2025.

The second shortest math paper explained, Fermat’s last theorem conjecture.

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Shown below is the second shortest published math paper; it’s the shortest published math paper, except for this one. This paper relates to an extension to Fermat’s last theorem. That’s well known math, though I think a few words of background would help the educated lay reader.

By way of background, Fermat’s last theorem states that there is no set of integers for which An + Bn = Qn, where n is an integer larger than 2. Thus, there is no set where A3 + B3 = Q3 or A5 + B5 = Q5, etc. This theorem was really a conjecture until recently though Fermat claimed to have proven it in 1695.

The Euler conjecture of the title here, is related to Fermat’s conjecture/theorum: Either conjectured that the smallest collections of A, B, C, D.., whose power to the n, summed, will equal some whole number to the power n, Qn , must have at least as many components (A,B,C,D,..) as the exponent value, n. Thus, while you might find a set of five numbers, A, B, C, D, E where A5 + B5 + C5 + D5 + E5 = Q5, you can’t find a set of four numbers where A5 + B5 + C5 + D5 = Q5. The paper above disproves this conjecture in a most clear way; it shows a counter-example where A5 + B5 + C5 + D5 = Q5.

This is, in a sense, the ideal math paper: clear, short, important, and true. For background to this conjecture, the authors merely reference a page of a math history book.

Robert E. Buxbaum, March 17, 2025. The shortest paper ever is this gem in the journal of psychology.