If devas are real, than why don't they show us themself?

They are as real as Adam and Eve ie a metaphor. From what I gather through various readings and podcasts the Buddhist story of Mara is also not meant to be taken literally. These are fables. If a demon did appear it would have been in Siddartha's mind. Its unwise to take religious teachings literally in my opinion. You only have to look to these Christians who do so with the Old Testament to see the negative effects it has.

There is no reason to assume that the gods follow dharma. Some may. Others may not. It is my understanding that it is best to be human since humans have the combination of opportunity to practice and the suffering that that can motivate to practice. Gods with less suffering are not as motivated. But back to the original question, people make their own choices with or without gods, miracles, evidence, and so forth. This is what I love about buddhism. It is based on logic and evidence. You do not have to take anything on blind faith. Experimentation with positive practices produces positive results. Succumbing to negative states (anger, grasping, etc.) produces negative results.

You need to develop the divine eye faculty to see Devas and ghosts. Read the Visuddhimagga if you are genuinely interested in it.

When you walk in a park and find some ants walking in a row, bend down and look at the ants and observe what they are doing. Then wave your hands at them and say, "ants, how are you today?". They don't respond back. If you place your finger somewhere near their path, they would ignore it and continue onwards.

You would find that the ants are completely oblivious of your presence.

Similarly, the devas or brahmas who are said to be superior to humans, may be watching us and attempting to interact with us, but we may be completely oblivious of them.

We don't need to trust that the teachings of the Buddha are true by proving that devas and brahmas exist. All we need to be convinced of, is that the Buddha was truly enlightened in the nature of reality, just as we trust what Einstein taught in physics, because we are convinced that Einstein was enlightened in his area of physics. And just like physics, the Buddhist teachings are very empirical, in the sense that it is verifiable by practical experience.

In this answer, I stated that it's quite possible to have "retrograde realization" (to quote Andrei Volkov) i.e. to realize upon reading some teachings of the Buddha, that it really fits your own observation of the workings of your mind. However, if the Buddha did not point it out, you would not have noticed. This kind of "aha" moments can convince you also, of the truth of the Buddha's enlightenment and skill in teaching.

You can read the story of the world's happiest man, Tibetan Buddhist monk Matthieu Ricard, through whom neuroscientists empirically verified the efficacy of the Buddha's teachings, using 256 sensor nodes. Ricard also encouraged us to similarly verify the Buddha's teachings in his statement: “Try sincerely to check, to investigate. That’s what Buddhism has been trying to unravel — the mechanism of happiness and suffering. It is a science of the mind.”

To quantify just how happy Ricard is, neuroscientists at the University of Wisconsin attached 256 sensors to the monk’s skull. When he meditated on compassion, the researchers were shocked to see that Ricard’s brian produces a level of gamma waves off the charts. He also demonstrated excessive activity in his brain’s left prefrontal cortex compared to its right counterpart, meaning he has an abnormally large capacity for happiness and a reduced propensity towards negativity, the researchers say.

During the same study, the neuroscientists also peeked into the minds of other monks. They found that long-term practitioners—those who have engaged in more than 50,000 rounds of meditation—showed significant changes in their brain function, although that those with only three weeks of 20-minute meditation per day also demonstrated some change.

First, we have to distinguish between mundane devas and supramandane deities. The mundane devas can either follow Dharma or not, but usually they do not, because of their illusion of everlasting happiness. This means they are not compassionate and so they don't have a cause to deign to humans, nor human beings have an ability to see them, just like ants don't have ability to see humans and/or communicate with them, or just like humans usually don't treat ants as their peers.

Second, those mundane devas who follow Dharma might be compassionate, yet they can hardly be noticed by those humans who haven't achieve an ability to see devas and/or supramandane deities.

Last but not least, the supramandane deities require a practitioner to have special abilities and/or to be determined by some special causes to see them. E. g. all the - if I am not mistaken - Kashmiri women put together are the manifestation of the Shri Devi's speech, yet which mortal can perceive all the Kashmiri women at once?

Good people have no doubt in Devas, having no doubt in devas, they watch out their deeds, knowing that they are next and here. Watching out their deeds, they are no more ugly and bad smelling for Devas and those established in good ways are not deprived to come even in a human life in reunion with them.

Devas, like good people, avoid uglines and bad smell. Those who watch over their qualities are not in lack of their company.

Would you, for example, join a community of pigs and act in their ways so that you get recognised and be followed by them? What else as a pig keeper, those who gain benefit of them, would a common pig follow aside of it's kind?

Likewise Devas do not appear to common men, will be not found in their reunion. Even if they appear from time to time, it's not for those incapable to see and hear the meaning of their voice.

Maybe an inspiring story for those open to it:

“Devas possess divine sight and divine hearing, enabling them to see and hear over great distances. They know about the good and bad of human affairs better than do humans themselves. Couldn't you find a way to make humans more aware of right and wrong? I feel that you are more capable of it than we human teachers are. Is there any way you could do this?” ...An Impeccable Human Being

[Note: This is a gift of Dhamma and not meant for use of commercial purposes and other wordily gains but intended and bound to awakening and liberation, and so good shared.]

They are around, just that you don't see them. Likewise bacterias are everywhere, you don't see them.

Not seeing/hearing is not existing obviously is scientifically proven false, but people tend to dwell in this fallacy without remorse.

The way to learn is to improve the capacity. Bacterias can be seen by inventing microscope, but the Buddha seen them 2500 years ago. Maybe one day someone can invent devascope to see them; yet again you can learn what Buddha was capable and see them ?year ahead the inventor ~ :D

^{- The OP asks for elaboration, I extend my answer -}

Dialogue for those who's minds are not contaminated by the neo-Buddhist. (Neo-Buddhists - those who believed in their "scientifically-authenticated-Buddha".)

_Prelude:

Buddhists from tradition and Buddhists at heart are seeing the emerging of the trend of neo-Buddhism, a Buddhism invented by applying so-called scientific methods, surgical skills and dissecting analysis are callously utilized. Taking the convenient standpoint that Buddhism is a religion/(not a religion) appealed to reasoning, unlike Christianity or other faith-based. Therefore, anything that's not scientifically proven should be stripped, for it's either misunderstanding/mis-translating the words, primitive superstitions or later additions by fanatic religious... etc. In a nutshell, they want to reduce the Buddha to be a merely human, any feature of Buddha a Buddha is committing suicidal scientific fraud.

Traditional Buddhist and Buddhist at heart knows the Buddha is the Buddha, yet Buddha is also human therefore it completed the teaching that we humans can become the Buddha, or be liberated forever like the Arhat/Arahant by dwelling in Nirvana.

The blindness of the neo-Buddhist is that they equal reasoning with science. Science is only one of the many methods for searching the ultimate, science is not the ultimate. Reasoning includes scientific methods, but scientific methods not the totality of reasoning. Buddha's teaching is the teaching from the ultimate, he is not searching for the ultimate; reasoning is a method taught by the Buddha to realize the ultimate by oneself, reasoning itself is not the ultimate.

We are seeing science characterized by the ability to re-adjust itself, such as Newtonian physics disproved by Einstein's Relativity. The day will come when E=mc² being disproved (I said the c, speed of light, is false. How do I know? I learnt it from the Sutras - not directly the Sutra with explicitly this saying but one has to really get it). This is the goodie of science - being able to adjust; the very way science survived is by disproving itself. Applicable is this rebuttal logic used by the Epicurean refuter on "pursuing happiness is the very reason happiness will never be obtained by the pursuer", likewise science is refuted. We can never predict what science will come up next, but surely can predict whatever come up next will be refuted late; hence a sound mind can infer thus see clearly that "scientific methods" we called nowadays can never obtain the ultimate. Therefore, can we trust scientific authentication? You know better than me. Do you trust someone who come up day after another day, time after another time, telling you, "Sorry, what I said before was wrong, in fact it should be so and so...?"

_{The Dialogue:}

Why don't the Devas show us themselves? I don't think I can answer this question on behalf of the Devas, or as the envoy of the Devas ;). Ultimately one should get his own answer by knowing it directly himself. But I put in my two cents to enrich this investigation:

A) It's really as hinted above, they are around but we don't see them since we don't have the ability to see them, nor it's their duty to let themselves be seen by us.

Here is the incident I read in the Vinaya, that may illustrate this: A Bhiksu/Bhikkhu chopped down certain village sacred tree for building his little hut, the tree Deva's kid just playing around that tree accidentally being chopped off his finger. The tree Deva, devastated, went straight to complain to the Buddha... You see, here this Bhiksu is definitely unable to see, if, for example, he didn't get accomplishment in Dhyana/Jhana. Else he wouldn't chop off the Deva kid's finger, nor it's for the kid to make himself visible in normal circumstance; the Deva didn't file complaint to him directly since he wasn't able to see him.

B) Only with special cause that the Deva to the human can be seen.

A case to illustrate this is from a linked Sutta I read in this forum. In it talked about a Bhikkhu visited by a Deva requested to bring him to the Buddha for asking a question, for the Buddha was surrounded by many higher Devas he didn't have a chance to get near. The reason for this Deva to seek for his help was due to in eons lives before, they were relatives... or something like that.

Therefore, there must be cause (Karma) to fulfill the criteria. Likewise, Aishwarya Rai won't come to see everyone in Mumbai, but she may come to see her friend if she has one there.

C) It's not allowed for the Devas to take "mass-appearing" to induce people following Dharma/Dhamma, for it violated the rule:

(i) Another incident I read in Vinaya, about Maudgalyāyana/Moggallāna being accused faking Dhyana/Jhana for he told the rest that State A would win the battle against State B for he saw the Yaksas (city protecting Deva of State A) winning the other Yaksas in their battle. But it turned out the opposite for while M. reporting this the battle of the Devas made a significant turn...

(ii) Another case I read from the Sutra, said Śakra/Sakka paying tribute to the Buddha for Buddha's teaching turned more people to good hence it increased his citizens decreased the Asura's citizens.

Therefore it shows that the Deva worlds and human world are synchronizing, the battle of the Devas is playing out in the human world, so is the human world reflected back to the higher realm. Imagine, if the Devas made their mass-appearing to induce followers, then the Asuras will do the same, then the battlefield will be shifted to the human world... can the human world sustain such turmoil? (I think the Mahābhārata was such event happened eons ago when Planet Earth was the celestial realm, or semi-celestial realm, before it degraded to be only suitable for humans).

(iii) Last, the Parinirmita-vaśavartin (pleasure from other's pleasure), the highest of the celestial realm ruled by desire, the Lord of this realm is Mara, named Pāpman (Pali: Pāpiya or Pāpimant), his sustaining and joy is produced by the desirous activities carried out in the lower realms, particularly the human realm, he won't allow this mass-appearing, he would prefer humans staying in Samsara, being under his rule.

Ok, it's a bit too sophisticated for it related to ample studies in the Sutras, Vinayas and Sastras to understand, especially many of the sources are not available in English.

The above is very pictorial, vivid, narratively dramatic... for in the tangible it manifested as people, places, events... but in the intangible, it should be decipher differently.

... is it enough now to buy a Big Mac meal in McDonald's, huh?