My teacher told that boron exhibits only a $+3$ oxidation state, but he also wrote the unbalanced reaction
$$\ce{B + C -> B4C}.$$ Carbon has greater electronegativity than boron leaving us with $\ce{\overset{+1}{B}_4\overset{-4}{C}},$ which contradicts what he taught.
We may not have all boron atoms equivalently bonded to carbon in $\ce{B4C}$, so we might not be able to assign all boron atoms an equal oxidation state of +1. For that matter, assuming a carbon oxidation state of -4 might also be a reach.
A better candidate for boron(I) is boron monofluoride, $\ce{BF}$, which is unstable but isolable:
Boron monofluoride can be prepared by passing boron trifluoride gas at 2000 °C over a boron rod. It can be condensed at liquid nitrogen temperatures (−196 °C).1
Given the inherent instability of the $\ce{BF}$ molecule as such, the condensate would likely be a polymer.
Boron monofluoride is formally isoelectronic with molecular nitrogen and carbon monoxide, but the great polarity of the boron-fluorine bond and the different orbital sizes and energies of the two atoms prevents good pi overlap; therefore boron monofluoride is not triple-bonded:
Despite being isoelectronic to the triple-bonded species CO and N2, computational studies generally agree that the true bond order is much lower than 3. One reported computed bond order for the molecule is 1.4, compared with 2.6 for CO and 3.0 for N2.[2]
Thus boron monofluoride is much less stable than would be expected if the triple bond could have formed. For that matter, even carbon monoxide with its less decremented bond order thermodynamically favors dispropotionation (and sooting of industrial equipment with the resulting elemental carbon) upon cooling from high temperature.
Boron monofluoride is better known as a ligand in transition metal complexes, where it can indeed be considered a boron(I) species in a stable compound if it is considered a two-electron donor to a metal less electronegative than boron. For instance, the WP article mentions $\ce{(PF3)4Fe(BF)}$, citing [3]; counting the boron monofluoride (and the trifluorophosphine) as two-electron donors would be consistent with the 18-electron rule. A fully charactetized organometallic complex, with $\ce{BF}$ as a two-electron sigma donor and pi acceptor (again meeting the 18-electton ruke with two electrons from the boron), is given by Drance et al.[4], illustrated below from the abstract.
Cited References
Timms, P. L. (1972). "Low Temperature Condensation". Advances in Inorganic Chemistry and Radiochemistry. p. 143. ISBN 0-12-023614-1.
Martinie, R. J.; Bultema, J. J.; van der Wal, M. N.; Burkhart, B. J.; van der Griend, D. A. & de Kock, R. L. (2011). "Bond Order and Chemical Properties of BF, CO, and N2". Journal of Chemical Education. 88 (8): 1094–1097. Bibcode:2011JChEd..88.1094M. doi:10.1021/ed100758t.
Vidovic, Dragoslav; Aldridge, Simon (2011). "Coordination chemistry of group 13 monohalides". Chemical Science. 2 (4): 601. doi:10.1039/C0SC00508H
Drance, M. J.; Sears, J. D.; Mrse, A. M.; Moore, C. E.; Rheingold, A. L.; Neidig, M. L.; Figueroa, J. S. (2019). "Terminal Coordination of Diatomic Boron Monofluoride to Iron". Science. 363 (6432): 1203–1205. Bibcode:2019Sci...363.1203D. doi:10.1126/science.aaw6102. PMID 30872521. S2CID 78094683.
Boron mostly favours the +3 oxidation state. However, boron does form some compounds in +1 O.S. but they are unstable and rearranges to stable molecule (such as boron monofluoride in @Oscar's answer which polymerizes by itself to compounds containing 10-12 boron atoms).
Apart from the monofluoride, I found one example of boron(I) complex which is a radical intermediate.
The one-electron reduction of a cyclic (alkyl)(amino)carbene (CAAC)-stabilized arylborylene carbonyl complex yields a dimeric borylketyl radical anion, resulting from an intramolecular aryl migration to the CO carbon atom. Computational analyses support the existence of a $\ce{[(CAAC)B(CO)Ar]^{.-}}$ radical anion intermediate. Further reduction leads to a highly nucleophilic dianionic (boraneylidene)methanolate.
Ref.: Rang M, Fantuzzi F, Arrowsmith M, Krummenacher I, Beck E, Witte R, Matler A, Rempel A, Bischof T, Radacki K, Engels B, Braunschweig H. Reduction and Rearrangement of a Boron(I) Carbonyl Complex. Angew Chem Int Ed Engl. 2021 Feb 8;60(6):2963-2968. doi: 10.1002/anie.202014167. Epub 2020 Dec 11. PMID: 33191596; PMCID: PMC7898892. (link)
